You are an expert Python programmer. Write correct, efficient Python 3 code that solves the problem and passes all tests. Output the code in the following format: ```python
<code>
```

PROBLEM:
You are given two strings, str1 and str2, of lengths n and m, respectively.
A string word of length n + m - 1 is defined to be generated by str1 and str2 if it satisfies the following conditions for each index 0 <= i <= n - 1:

If str1[i] == 'T', the substring of word with size m starting at index i is equal to str2, i.e., word[i..(i + m - 1)] == str2.
If str1[i] == 'F', the substring of word with size m starting at index i is not equal to str2, i.e., word[i..(i + m - 1)] != str2.

Return the lexicographically smallest possible string that can be generated by str1 and str2. If no string can be generated, return an empty string "".

Example 1:

Input: str1 = "TFTF", str2 = "ab"
Output: "ababa"
Explanation:
The table below represents the string "ababa"

Index
T/F
Substring of length m

0
'T'
"ab"

1
'F'
"ba"

2
'T'
"ab"

3
'F'
"ba"

The strings "ababa" and "ababb" can be generated by str1 and str2.
Return "ababa" since it is the lexicographically smaller string.

Example 2:

Input: str1 = "TFTF", str2 = "abc"
Output: ""
Explanation:
No string that satisfies the conditions can be generated.

Example 3:

Input: str1 = "F", str2 = "d"
Output: "a"

Constraints:

1 <= n == str1.length <= 104
1 <= m == str2.length <= 500
str1 consists only of 'T' or 'F'.
str2 consists only of lowercase English characters.

Your solution to the problem should be a method of the class Solution called generateString and should pass all tests. Use the following starter code:
```python
class Solution:
    def generateString(self, str1: str, str2: str) -> str:
        # Add your code here
```

SOLUTION:

Question:
PROBLEM:
You are given two strings, str1 and str2, of lengths n and m, respectively.
A string word of length n + m - 1 is defined to be generated by str1 and str2 if it satisfies the following conditions for each index 0 <= i <= n - 1:

If str1[i] == 'T', the substring of word with size m starting at index i is equal to str2, i.e., word[i..(i + m - 1)] == str2.
If str1[i] == 'F', the substring of word with size m starting at index i is not equal to str2, i.e., word[i..(i + m - 1)] != str2.

Return the lexicographically smallest possible string that can be generated by str1 and str2. If no string can be generated, return an empty string "".

Example 1:

Input: str1 = "TFTF", str2 = "ab"
Output: "ababa"
Explanation:
The table below represents the string "ababa"

Index
T/F
Substring of length m

0
'T'
"ab"

1
'F'
"ba"

2
'T'
"ab"

3
'F'
"ba"

The strings "ababa" and "ababb" can be generated by str1 and str2.
Return "ababa" since it is the lexicographically smaller string.

Example 2:

Input: str1 = "TFTF", str2 = "abc"
Output: ""
Explanation:
No string that satisfies the conditions can be generated.

Example 3:

Input: str1 = "F", str2 = "d"
Output: "a"

Constraints:

1 <= n == str1.length <= 104
1 <= m == str2.length <= 500
str1 consists only of 'T' or 'F'.
str2 consists only of lowercase English characters.

Your solution to the problem should be a method of the class Solution called generateString and should pass all tests. Use the following starter code:
```python
class Solution:
    def generateString(self, str1: str, str2: str) -> str:
        # Add your code here
```

SOLUTION:

assert Solution().generateString(str1 = "FF", str2 = "z") == "aa"

assert Solution().generateString(str1 = "FT", str2 = "c") == "ac"

assert Solution().generateString(str1 = "FT", str2 = "yz") == "ayz"

assert Solution().generateString(str1 = "TTT", str2 = "aaa") == "aaaaa"

assert Solution().generateString(str1 = "TTT", str2 = "xyz") == ""

assert Solution().generateString(str1 = "TF", str2 = "ab") == "aba"

assert Solution().generateString(str1 = "FFF", str2 = "a") == "bbb"

assert Solution().generateString(str1 = "TFTF", str2 = "abc") == ""

assert Solution().generateString(str1 = "TT", str2 = "a") == "aa"

assert Solution().generateString(str1 = "F", str2 = "fgh") == "aaa"

assert Solution().generateString(str1 = "FFF", str2 = "xyz") == "aaaaa"

assert Solution().generateString(str1 = "TTFT", str2 = "ij") == ""

assert Solution().generateString(str1 = "F", str2 = "a") == "b"

assert Solution().generateString(str1 = "FT", str2 = "a") == "ba"

assert Solution().generateString(str1 = "TF", str2 = "a") == "ab"

assert Solution().generateString(str1 = "FTF", str2 = "aaa") == "baaab"

assert Solution().generateString(str1 = "FFT", str2 = "aaa") == "abaaa"

assert Solution().generateString(str1 = "FF", str2 = "aa") == "aba"

assert Solution().generateString(str1 = "TF", str2 = "xy") == "xya"

assert Solution().generateString(str1 = "T", str2 = "z") == "z"

assert Solution().generateString(str1 = "T", str2 = "a") == "a"

assert Solution().generateString(str1 = "TFT", str2 = "aaa") == ""

assert Solution().generateString(str1 = "FT", str2 = "ab") == "aab"

assert Solution().generateString(str1 = "TTT", str2 = "de") == ""

assert Solution().generateString(str1 = "FFF", str2 = "aaa") == "aabaa"

assert Solution().generateString(str1 = "TF", str2 = "b") == "ba"

assert Solution().generateString(str1 = "TT", str2 = "ab") == ""

assert Solution().generateString(str1 = "T", str2 = "de") == "de"

assert Solution().generateString(str1 = "TFTF", str2 = "ab") == "ababa"

assert Solution().generateString(str1 = "TF", str2 = "aa") == "aab"

assert Solution().generateString(str1 = "FT", str2 = "aa") == "baa"

assert Solution().generateString(str1 = "TFF", str2 = "aaa") == "aaaba"

assert Solution().generateString(str1 = "FF", str2 = "xy") == "aaa"

assert Solution().generateString(str1 = "F", str2 = "d") == "a"

assert Solution().generateString(str1 = "TT", str2 = "aa") == "aaa"

assert Solution().generateString(str1 = "F", str2 = "abc") == "aaa"

assert Solution().generateString(str1 = "TT", str2 = "mn") == ""

assert Solution().generateString(str1 = "T", str2 = "abc") == "abc"

assert Solution().generateString(str1 = "TFFFTTFT", str2 = "dddd") == ""

assert Solution().generateString(str1 = "TTT", str2 = "mnopqrstu") == ""

assert Solution().generateString(str1 = "F", str2 = "z") == "a"

assert Solution().generateString(str1 = "TTFFTFTFF", str2 = "generated") == ""

assert Solution().generateString(str1 = "TFTFTFTFT", str2 = "xyz") == ""

assert Solution().generateString(str1 = "TFTFTFT", str2 = "uv") == "uvuvuvuv"

assert Solution().generateString(str1 = "FTFTFTFT", str2 = "mnop") == ""

assert Solution().generateString(str1 = "FTFTFT", str2 = "qrstuvwx") == ""

assert Solution().generateString(str1 = "FFFFFFFFFT", str2 = "xyz") == "aaaaaaaaaxyz"

assert Solution().generateString(str1 = "TTTTTTTTTTTT", str2 = "qrstuvwx") == ""

assert Solution().generateString(str1 = "FTFTFTFTFTFTFTFTFTFTFT", str2 = "abcdef") == ""

assert Solution().generateString(str1 = "TFTFTF", str2 = "ijklmnop") == ""

assert Solution().generateString(str1 = "TFTFTFTFTFT", str2 = "stuvwx") == ""

assert Solution().generateString(str1 = "TFTFTFTFTFT", str2 = "xyz") == ""

assert Solution().generateString(str1 = "TTTFTFTFT", str2 = "test") == ""

assert Solution().generateString(str1 = "FFFFFFFFFFFFFFFF", str2 = "abc") == "aaaaaaaaaaaaaaaaaa"

assert Solution().generateString(str1 = "TFTFTFTFTFT", str2 = "yz") == "yzyzyzyzyzyz"

assert Solution().generateString(str1 = "FTTTFFTTTTFFFF", str2 = "sample") == ""

assert Solution().generateString(str1 = "FTFT", str2 = "mnopq") == ""

assert Solution().generateString(str1 = "TFTFTFTFTF", str2 = "test") == ""

assert Solution().generateString(str1 = "TTFTFT", str2 = "zzz") == ""

assert Solution().generateString(str1 = "TTTTFFF", str2 = "efgh") == ""

assert Solution().generateString(str1 = "TTTFTFFTFF", str2 = "ghijkl") == ""

assert Solution().generateString(str1 = "FTTFT", str2 = "xyzw") == ""

assert Solution().generateString(str1 = "FFFFTTT", str2 = "ijkl") == ""

assert Solution().generateString(str1 = "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", str2 = "uvw") == "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"

assert Solution().generateString(str1 = "FFTTFFTF", str2 = "eeee") == ""

assert Solution().generateString(str1 = "FFFF", str2 = "wxyz") == "aaaaaaa"

assert Solution().generateString(str1 = "TFTFTFTFT", str2 = "xy") == "xyxyxyxyxy"

assert Solution().generateString(str1 = "TFFFT", str2 = "abc") == "abcaabc"

assert Solution().generateString(str1 = "TFTFT", str2 = "abcdefghi") == ""

assert Solution().generateString(str1 = "TTFT", str2 = "abc") == ""

assert Solution().generateString(str1 = "FFTFTFFT", str2 = "hhhh") == ""

assert Solution().generateString(str1 = "TFTFTFTFTFTFTFTFTF", str2 = "complex") == ""

assert Solution().generateString(str1 = "FTFTTFTF", str2 = "cccc") == ""

assert Solution().generateString(str1 = "TFTFTFT", str2 = "mnop") == ""

assert Solution().generateString(str1 = "FTFTFT", str2 = "mnop") == ""

assert Solution().generateString(str1 = "TFTFTFTFTFT", str2 = "abcdefg") == ""

assert Solution().generateString(str1 = "TTTTTTTTTTTT", str2 = "z") == "zzzzzzzzzzzz"

assert Solution().generateString(str1 = "FFFFFFFFFFFF", str2 = "a") == "bbbbbbbbbbbb"

assert Solution().generateString(str1 = "TTTFTTTT", str2 = "qrst") == ""

assert Solution().generateString(str1 = "FFFFFFFFFT", str2 = "abcdef") == "aaaaaaaaaabcdef"

assert Solution().generateString(str1 = "FTFTFT", str2 = "aaa") == ""

assert Solution().generateString(str1 = "TTTTTTTTTT", str2 = "ghijkl") == ""

assert Solution().generateString(str1 = "TTTTTTTTTT", str2 = "opqrst") == ""

assert Solution().generateString(str1 = "FTFTFT", str2 = "xyz") == ""

assert Solution().generateString(str1 = "TTFF", str2 = "qrstuvwx") == ""

assert Solution().generateString(str1 = "TFTFT", str2 = "abc") == ""

assert Solution().generateString(str1 = "TFTFTFTFTFTFT", str2 = "mnopqr") == ""

assert Solution().generateString(str1 = "FF", str2 = "wx") == "aaa"

assert Solution().generateString(str1 = "TTFTTFFFTTTFTFT", str2 = "qrstuvw") == ""

assert Solution().generateString(str1 = "TTTFTTTFTTT", str2 = "mnopqrstuvw") == ""

assert Solution().generateString(str1 = "FTFTFTFTFT", str2 = "xyz") == ""

assert Solution().generateString(str1 = "FFFF", str2 = "ghijkl") == "aaaaaaaaa"

assert Solution().generateString(str1 = "FFTFTT", str2 = "world") == ""

assert Solution().generateString(str1 = "FTFTFTFTFT", str2 = "abc") == ""

assert Solution().generateString(str1 = "TTFT", str2 = "uvw") == ""

assert Solution().generateString(str1 = "TTFTFFTFTFFTFT", str2 = "example") == ""

assert Solution().generateString(str1 = "FFFFFFFF", str2 = "abc") == "aaaaaaaaaa"

assert Solution().generateString(str1 = "TFFT", str2 = "lmnopqrstu") == ""

assert Solution().generateString(str1 = "FTFTFT", str2 = "def") == ""

assert Solution().generateString(str1 = "FFFFFF", str2 = "abcd") == "aaaaaaaaa"

assert Solution().generateString(str1 = "TFTFTFTFTFTFT", str2 = "abcdef") == ""

assert Solution().generateString(str1 = "TFFT", str2 = "vwxyz") == ""

assert Solution().generateString(str1 = "TTFTFTFTT", str2 = "world") == ""

assert Solution().generateString(str1 = "TFFFFFFFF", str2 = "wxyz") == "wxyzaaaaaaaa"

assert Solution().generateString(str1 = "TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT", str2 = "mnop") == ""

assert Solution().generateString(str1 = "TFT", str2 = "abcdef") == ""

assert Solution().generateString(str1 = "FTTFTFFT", str2 = "gggg") == ""

assert Solution().generateString(str1 = "TFFTFT", str2 = "abcd") == ""

assert Solution().generateString(str1 = "TTFTFTFFT", str2 = "lexicographically") == ""

assert Solution().generateString(str1 = "FTFTFTFTT", str2 = "stuv") == ""

assert Solution().generateString(str1 = "FFTFFT", str2 = "abc") == "aaabcabc"

assert Solution().generateString(str1 = "TTTTTTT", str2 = "abcd") == ""

assert Solution().generateString(str1 = "TF", str2 = "yz") == "yza"

assert Solution().generateString(str1 = "TTFT", str2 = "jklmno") == ""

assert Solution().generateString(str1 = "TFTFTFTFTFT", str2 = "mnopqrstuvw") == ""

assert Solution().generateString(str1 = "TFTF", str2 = "mnop") == ""

assert Solution().generateString(str1 = "TTTTTTTT", str2 = "a") == "aaaaaaaa"

assert Solution().generateString(str1 = "TFTFTF", str2 = "mnopqr") == ""

assert Solution().generateString(str1 = "TTT", str2 = "k") == "kkk"

assert Solution().generateString(str1 = "TFFTFF", str2 = "bcb") == "bcbbcbaa"

assert Solution().generateString(str1 = "TFTFTFTFTFTFTFTFTFT", str2 = "a") == "abababababababababa"

assert Solution().generateString(str1 = "FTFTFTFTFT", str2 = "uvw") == ""

assert Solution().generateString(str1 = "FTFTFT", str2 = "stuvwx") == ""

assert Solution().generateString(str1 = "FFTT", str2 = "abcd") == ""

assert Solution().generateString(str1 = "TTTTTTTTTTTTTTTTTT", str2 = "solution") == ""

assert Solution().generateString(str1 = "FTFTFTFFT", str2 = "example") == ""

assert Solution().generateString(str1 = "TFTFT", str2 = "efghij") == ""

assert Solution().generateString(str1 = "TFTFTFT", str2 = "wxyz") == ""

assert Solution().generateString(str1 = "TTTTTTTTT", str2 = "abcdefghi") == ""

assert Solution().generateString(str1 = "FTF", str2 = "abcd") == "aabcda"

assert Solution().generateString(str1 = "TFTFTFTFTFTFTF", str2 = "abcd") == ""

assert Solution().generateString(str1 = "TFTFTFTFTF", str2 = "uvw") == ""

assert Solution().generateString(str1 = "FTF", str2 = "zz") == "azza"

assert Solution().generateString(str1 = "TFT", str2 = "efghijkl") == ""

assert Solution().generateString(str1 = "TTTTTTTTTT", str2 = "yzab") == ""

assert Solution().generateString(str1 = "TTTTTTTTF", str2 = "mnopqr") == ""

assert Solution().generateString(str1 = "TFT", str2 = "def") == ""

assert Solution().generateString(str1 = "TFTFTF", str2 = "xyz") == ""

assert Solution().generateString(str1 = "TTTTTT", str2 = "aaa") == "aaaaaaaa"

assert Solution().generateString(str1 = "FTFT", str2 = "pqrstu") == ""

assert Solution().generateString(str1 = "FTFTFTFTFT", str2 = "mnopqrstuvwx") == ""

assert Solution().generateString(str1 = "FFFFFFFF", str2 = "abcd") == "aaaaaaaaaaa"

assert Solution().generateString(str1 = "TTFFTTFFTT", str2 = "abcdefgh") == ""

assert Solution().generateString(str1 = "FTFTFTFTFTFTFTFTFTFTFTFTFTFTFTFT", str2 = "defghijklm") == ""

assert Solution().generateString(str1 = "TFTFTF", str2 = "abcdefgh") == ""

assert Solution().generateString(str1 = "TF", str2 = "zzz") == "zzza"

assert Solution().generateString(str1 = "FTTFFTFF", str2 = "uvw") == ""

assert Solution().generateString(str1 = "FFFFFFFFF", str2 = "aaaa") == "aaabaaabaaab"

assert Solution().generateString(str1 = "TFTFT", str2 = "pqrstuvwx") == ""

assert Solution().generateString(str1 = "TFTFTFTFTFTFTFTFTFT", str2 = "abcdefghijklmnopqrstuvwxyz") == ""

assert Solution().generateString(str1 = "FFTTTFFFFTTFF", str2 = "abcdefghi") == ""

assert Solution().generateString(str1 = "FTFTFTFT", str2 = "efghijkl") == ""

assert Solution().generateString(str1 = "TTFFFFTT", str2 = "xyz") == ""

assert Solution().generateString(str1 = "FT", str2 = "mnopqr") == "amnopqr"

assert Solution().generateString(str1 = "FF", str2 = "abcdef") == "aaaaaaa"

assert Solution().generateString(str1 = "TTT", str2 = "yz") == ""

assert Solution().generateString(str1 = "TTTT", str2 = "aaa") == "aaaaaa"

assert Solution().generateString(str1 = "FTFTFTFTFTFT", str2 = "yz") == "ayzyzyzyzyzyz"

assert Solution().generateString(str1 = "TFFT", str2 = "rstuv") == ""

assert Solution().generateString(str1 = "FFTFTFTFF", str2 = "mnop") == ""

assert Solution().generateString(str1 = "TFT", str2 = "abcd") == ""

assert Solution().generateString(str1 = "FFFFFFFFF", str2 = "abcde") == "aaaaaaaaaaaaa"

assert Solution().generateString(str1 = "FFTFFT", str2 = "xyz") == "aaxyzxyz"

assert Solution().generateString(str1 = "TFTFT", str2 = "abcde") == ""

assert Solution().generateString(str1 = "FFFFFFFF", str2 = "abcdefgh") == "aaaaaaaaaaaaaaa"

assert Solution().generateString(str1 = "TTTFFFF", str2 = "aaaa") == "aaaaaabaaa"

assert Solution().generateString(str1 = "TFTFTF", str2 = "abc") == ""

assert Solution().generateString(str1 = "FTFTFTFT", str2 = "a") == "babababa"

assert Solution().generateString(str1 = "TTTTTTTTTTTTTTTT", str2 = "xyz") == ""

assert Solution().generateString(str1 = "TFTFFT", str2 = "xyz") == ""

assert Solution().generateString(str1 = "FFFFFFFFFT", str2 = "qrstuv") == "aaaaaaaaaqrstuv"

assert Solution().generateString(str1 = "TTTTTTTT", str2 = "aaaa") == "aaaaaaaaaaa"

assert Solution().generateString(str1 = "FFFFFFFFFFFFFFFF", str2 = "hijklmnop") == "aaaaaaaaaaaaaaaaaaaaaaaa"

assert Solution().generateString(str1 = "TFTFFTFTFTFFT", str2 = "xyzxyz") == ""

assert Solution().generateString(str1 = "TTTTTTTTT", str2 = "mnopqrst") == ""

assert Solution().generateString(str1 = "FFFTTFFT", str2 = "qrstu") == ""

assert Solution().generateString(str1 = "TTTTT", str2 = "ab") == ""

assert Solution().generateString(str1 = "FFFF", str2 = "abcdefgh") == "aaaaaaaaaaa"

assert Solution().generateString(str1 = "TFTFTFTFTFTFTFT", str2 = "abcdefg") == ""

assert Solution().generateString(str1 = "FFFFFFFFFT", str2 = "cdefgh") == "aaaaaaaaacdefgh"

assert Solution().generateString(str1 = "FFFFFFFFFF", str2 = "zyxwvut") == "aaaaaaaaaaaaaaaa"

assert Solution().generateString(str1 = "TFFTFTF", str2 = "abcd") == ""

assert Solution().generateString(str1 = "TTTTF", str2 = "mnop") == ""

assert Solution().generateString(str1 = "FTFT", str2 = "abcdefghijk") == ""

assert Solution().generateString(str1 = "TFTFTFTFT", str2 = "abcde") == ""

assert Solution().generateString(str1 = "FFTT", str2 = "yz") == ""

assert Solution().generateString(str1 = "TFFTTF", str2 = "abc") == ""

assert Solution().generateString(str1 = "TTFFTTFFT", str2 = "solution") == ""

assert Solution().generateString(str1 = "FFTTFF", str2 = "xyz") == ""

assert Solution().generateString(str1 = "FTFTF", str2 = "qrst") == ""

assert Solution().generateString(str1 = "FFTFTFTFT", str2 = "yz") == "aayzyzyzyz"

assert Solution().generateString(str1 = "TTFFTT", str2 = "abc") == ""

assert Solution().generateString(str1 = "FFFFFFFFFFFFFFFFFFFFFFFF", str2 = "mnopqrstuvwxyz") == "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"

assert Solution().generateString(str1 = "TTTTF", str2 = "abcde") == ""

assert Solution().generateString(str1 = "FTFT", str2 = "zz") == ""

assert Solution().generateString(str1 = "TFTFTFTFTFT", str2 = "abcdabcd") == ""

assert Solution().generateString(str1 = "FTTFFTFTT", str2 = "possible") == ""

assert Solution().generateString(str1 = "TFFFTF", str2 = "mnop") == "mnopmnopa"

assert Solution().generateString(str1 = "FFTFFTTFT", str2 = "output") == ""

assert Solution().generateString(str1 = "TTT", str2 = "qrstuv") == ""

assert Solution().generateString(str1 = "TTF", str2 = "abcd") == ""

assert Solution().generateString(str1 = "FFFFFFFFFFFF", str2 = "abcde") == "aaaaaaaaaaaaaaaa"

assert Solution().generateString(str1 = "FFFFFFFFTT", str2 = "abcd") == ""

assert Solution().generateString(str1 = "TTFF", str2 = "yz") == ""

assert Solution().generateString(str1 = "FFFFFFFF", str2 = "zz") == "aaaaaaaaa"

assert Solution().generateString(str1 = "FFFF", str2 = "xyz") == "aaaaaa"

assert Solution().generateString(str1 = "TTFT", str2 = "yz") == ""

assert Solution().generateString(str1 = "FFFF", str2 = "zzz") == "aaaaaa"

assert Solution().generateString(str1 = "FFFFFF", str2 = "zzz") == "aaaaaaaa"

assert Solution().generateString(str1 = "FFTFTFTFT", str2 = "complex") == ""

assert Solution().generateString(str1 = "TT", str2 = "qrstuv") == ""

assert Solution().generateString(str1 = "FFFFFFFF", str2 = "z") == "aaaaaaaa"

assert Solution().generateString(str1 = "FTF", str2 = "mnop") == "amnopa"

assert Solution().generateString(str1 = "FFTFFT", str2 = "qrst") == ""

assert Solution().generateString(str1 = "TFT", str2 = "efghijklmno") == ""

assert Solution().generateString(str1 = "FTFTFTFT", str2 = "pqrstuvwx") == ""

assert Solution().generateString(str1 = "FFTFFTFFT", str2 = "string") == ""

assert Solution().generateString(str1 = "FTFTFTFT", str2 = "ab") == "aabababab"

assert Solution().generateString(str1 = "FFTFTF", str2 = "bcd") == ""

assert Solution().generateString(str1 = "FTFTFTFT", str2 = "qrst") == ""

assert Solution().generateString(str1 = "TFTFTF", str2 = "uvw") == ""

assert Solution().generateString(str1 = "FTT", str2 = "efghijkl") == ""

assert Solution().generateString(str1 = "TFTFTFTFTFTFTFTFT", str2 = "abc") == ""

assert Solution().generateString(str1 = "TFFFFT", str2 = "def") == "defaadef"

assert Solution().generateString(str1 = "TFTTFF", str2 = "hello") == ""

assert Solution().generateString(str1 = "FFFFFFFFFFFFFFFF", str2 = "challenge") == "aaaaaaaaaaaaaaaaaaaaaaaa"

assert Solution().generateString(str1 = "TFTFFTFF", str2 = "ffff") == ""

assert Solution().generateString(str1 = "FTFTFT", str2 = "zzz") == ""

assert Solution().generateString(str1 = "TTTTTTTT", str2 = "abcdefghijk") == ""

assert Solution().generateString(str1 = "FTFTFTFTFTFT", str2 = "abcd") == ""

assert Solution().generateString(str1 = "FFTFT", str2 = "wxyz") == ""

assert Solution().generateString(str1 = "FTFTFFTTT", str2 = "smaller") == ""

assert Solution().generateString(str1 = "FTFTFTFTFTFTFTFT", str2 = "mnopqr") == ""

assert Solution().generateString(str1 = "TTTTTTTTTT", str2 = "mnop") == ""

assert Solution().generateString(str1 = "TTTFTF", str2 = "abc") == ""

assert Solution().generateString(str1 = "FTFTFTFTFT", str2 = "ab") == "aababababab"

assert Solution().generateString(str1 = "TFTFTFTFTFT", str2 = "ijklmn") == ""

assert Solution().generateString(str1 = "FFTTFFTT", str2 = "stuv") == ""

assert Solution().generateString(str1 = "FTFTFTFTFT", str2 = "jklmnop") == ""

assert Solution().generateString(str1 = "FTFTFFTTT", str2 = "input") == ""

assert Solution().generateString(str1 = "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", str2 = "zzzzzzzzzz") == "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"

assert Solution().generateString(str1 = "FFFFFFFFFT", str2 = "mnopqr") == "aaaaaaaaamnopqr"

assert Solution().generateString(str1 = "FFFFFFT", str2 = "bbbb") == "aaaaaabbbb"

assert Solution().generateString(str1 = "FTTFFTFTF", str2 = "hello") == ""

assert Solution().generateString(str1 = "FFTFTFT", str2 = "qrst") == ""

assert Solution().generateString(str1 = "FFFFFFFF", str2 = "lmnop") == "aaaaaaaaaaaa"

assert Solution().generateString(str1 = "FFFFFFFFFFFFFFFF", str2 = "zzzzzzzzzzzzzzzzzzzzzzzzzzzz") == "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"

assert Solution().generateString(str1 = "TFTFTFTFT", str2 = "stuv") == ""

assert Solution().generateString(str1 = "FFTFFTFFT", str2 = "qrst") == ""

assert Solution().generateString(str1 = "FFFFFFFF", str2 = "mnopqr") == "aaaaaaaaaaaaa"

assert Solution().generateString(str1 = "TTFFFFTT", str2 = "uvwxy") == ""

assert Solution().generateString(str1 = "FFFF", str2 = "vwxyz") == "aaaaaaaa"

assert Solution().generateString(str1 = "TT", str2 = "abcdef") == ""

assert Solution().generateString(str1 = "TTFFTTF", str2 = "mnop") == ""

assert Solution().generateString(str1 = "FFFF", str2 = "abcdefghijklmno") == "aaaaaaaaaaaaaaaaaa"

assert Solution().generateString(str1 = "TTFFTT", str2 = "mnop") == ""

assert Solution().generateString(str1 = "TTT", str2 = "abc") == ""

assert Solution().generateString(str1 = "TTTTTTTFT", str2 = "stuvwx") == ""

assert Solution().generateString(str1 = "FFFFFFFFFT", str2 = "uvwxyz") == "aaaaaaaaauvwxyz"

assert Solution().generateString(str1 = "TFTFTFTFTFTFT", str2 = "abcdabcd") == ""

assert Solution().generateString(str1 = "FFTTF", str2 = "xyz") == ""

assert Solution().generateString(str1 = "FFFFFFFFF", str2 = "a") == "bbbbbbbbb"

assert Solution().generateString(str1 = "TFTFT", str2 = "ijkl") == ""

assert Solution().generateString(str1 = "TFFTFT", str2 = "bca") == ""

assert Solution().generateString(str1 = "FTFTFT", str2 = "ijklmnop") == ""

assert Solution().generateString(str1 = "FFFFFT", str2 = "zyxwvut") == "aaaaazyxwvut"

Answer: assert Solution().generateString(str1 = "FF", str2 = "z") == "aa"

Answer: assert Solution().generateString(str1 = "FT", str2 = "c") == "ac"

Answer: assert Solution().generateString(str1 = "FT", str2 = "yz") == "ayz"

Answer: assert Solution().generateString(str1 = "TTT", str2 = "aaa") == "aaaaa"

Answer: assert Solution().generateString(str1 = "TTT", str2 = "xyz") == ""

Answer: assert Solution().generateString(str1 = "TF", str2 = "ab") == "aba"

Answer: assert Solution().generateString(str1 = "FFF", str2 = "a") == "bbb"

Answer: assert Solution().generateString(str1 = "TFTF", str2 = "abc") == ""

Answer: assert Solution().generateString(str1 = "TT", str2 = "a") == "aa"

Answer: assert Solution().generateString(str1 = "F", str2 = "fgh") == "aaa"

Answer: assert Solution().generateString(str1 = "FFF", str2 = "xyz") == "aaaaa"

Answer: assert Solution().generateString(str1 = "TTFT", str2 = "ij") == ""

Answer: assert Solution().generateString(str1 = "F", str2 = "a") == "b"

Answer: assert Solution().generateString(str1 = "FT", str2 = "a") == "ba"

Answer: assert Solution().generateString(str1 = "TF", str2 = "a") == "ab"

Answer: assert Solution().generateString(str1 = "FTF", str2 = "aaa") == "baaab"

Answer: assert Solution().generateString(str1 = "FFT", str2 = "aaa") == "abaaa"

Answer: assert Solution().generateString(str1 = "FF", str2 = "aa") == "aba"

Answer: assert Solution().generateString(str1 = "TF", str2 = "xy") == "xya"

Answer: assert Solution().generateString(str1 = "T", str2 = "z") == "z"

Answer: assert Solution().generateString(str1 = "T", str2 = "a") == "a"

Answer: assert Solution().generateString(str1 = "TFT", str2 = "aaa") == ""

Answer: assert Solution().generateString(str1 = "FT", str2 = "ab") == "aab"

Answer: assert Solution().generateString(str1 = "TTT", str2 = "de") == ""

Answer: assert Solution().generateString(str1 = "FFF", str2 = "aaa") == "aabaa"

Answer: assert Solution().generateString(str1 = "TF", str2 = "b") == "ba"

Answer: assert Solution().generateString(str1 = "TT", str2 = "ab") == ""

Answer: assert Solution().generateString(str1 = "T", str2 = "de") == "de"

Answer: assert Solution().generateString(str1 = "TFTF", str2 = "ab") == "ababa"

Answer: assert Solution().generateString(str1 = "TF", str2 = "aa") == "aab"

Answer: assert Solution().generateString(str1 = "FT", str2 = "aa") == "baa"

Answer: assert Solution().generateString(str1 = "TFF", str2 = "aaa") == "aaaba"

Answer: assert Solution().generateString(str1 = "FF", str2 = "xy") == "aaa"

Answer: assert Solution().generateString(str1 = "F", str2 = "d") == "a"

Answer: assert Solution().generateString(str1 = "TT", str2 = "aa") == "aaa"

Answer: assert Solution().generateString(str1 = "F", str2 = "abc") == "aaa"

Answer: assert Solution().generateString(str1 = "TT", str2 = "mn") == ""

Answer: assert Solution().generateString(str1 = "T", str2 = "abc") == "abc"

Answer: assert Solution().generateString(str1 = "TFFFTTFT", str2 = "dddd") == ""

Answer: assert Solution().generateString(str1 = "TTT", str2 = "mnopqrstu") == ""

Answer: assert Solution().generateString(str1 = "F", str2 = "z") == "a"

Answer: assert Solution().generateString(str1 = "TTFFTFTFF", str2 = "generated") == ""

Answer: assert Solution().generateString(str1 = "TFTFTFTFT", str2 = "xyz") == ""

Answer: assert Solution().generateString(str1 = "TFTFTFT", str2 = "uv") == "uvuvuvuv"

Answer: assert Solution().generateString(str1 = "FTFTFTFT", str2 = "mnop") == ""

Answer: assert Solution().generateString(str1 = "FTFTFT", str2 = "qrstuvwx") == ""

Answer: assert Solution().generateString(str1 = "FFFFFFFFFT", str2 = "xyz") == "aaaaaaaaaxyz"

Answer: assert Solution().generateString(str1 = "TTTTTTTTTTTT", str2 = "qrstuvwx") == ""

Answer: assert Solution().generateString(str1 = "FTFTFTFTFTFTFTFTFTFTFT", str2 = "abcdef") == ""

Answer: assert Solution().generateString(str1 = "TFTFTF", str2 = "ijklmnop") == ""

Answer: assert Solution().generateString(str1 = "TFTFTFTFTFT", str2 = "stuvwx") == ""

Answer: assert Solution().generateString(str1 = "TFTFTFTFTFT", str2 = "xyz") == ""

Answer: assert Solution().generateString(str1 = "TTTFTFTFT", str2 = "test") == ""

Answer: assert Solution().generateString(str1 = "FFFFFFFFFFFFFFFF", str2 = "abc") == "aaaaaaaaaaaaaaaaaa"

Answer: assert Solution().generateString(str1 = "TFTFTFTFTFT", str2 = "yz") == "yzyzyzyzyzyz"

Answer: assert Solution().generateString(str1 = "FTTTFFTTTTFFFF", str2 = "sample") == ""

Answer: assert Solution().generateString(str1 = "FTFT", str2 = "mnopq") == ""

Answer: assert Solution().generateString(str1 = "TFTFTFTFTF", str2 = "test") == ""

Answer: assert Solution().generateString(str1 = "TTFTFT", str2 = "zzz") == ""

Answer: assert Solution().generateString(str1 = "TTTTFFF", str2 = "efgh") == ""

Answer: assert Solution().generateString(str1 = "TTTFTFFTFF", str2 = "ghijkl") == ""

Answer: assert Solution().generateString(str1 = "FTTFT", str2 = "xyzw") == ""

Answer: assert Solution().generateString(str1 = "FFFFTTT", str2 = "ijkl") == ""

Answer: assert Solution().generateString(str1 = "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", str2 = "uvw") == "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"

Answer: assert Solution().generateString(str1 = "FFTTFFTF", str2 = "eeee") == ""

Answer: assert Solution().generateString(str1 = "FFFF", str2 = "wxyz") == "aaaaaaa"

Answer: assert Solution().generateString(str1 = "TFTFTFTFT", str2 = "xy") == "xyxyxyxyxy"

Answer: assert Solution().generateString(str1 = "TFFFT", str2 = "abc") == "abcaabc"

Answer: assert Solution().generateString(str1 = "TFTFT", str2 = "abcdefghi") == ""

Answer: assert Solution().generateString(str1 = "TTFT", str2 = "abc") == ""

Answer: assert Solution().generateString(str1 = "FFTFTFFT", str2 = "hhhh") == ""

Answer: assert Solution().generateString(str1 = "TFTFTFTFTFTFTFTFTF", str2 = "complex") == ""

Answer: assert Solution().generateString(str1 = "FTFTTFTF", str2 = "cccc") == ""

Answer: assert Solution().generateString(str1 = "TFTFTFT", str2 = "mnop") == ""

Answer: assert Solution().generateString(str1 = "FTFTFT", str2 = "mnop") == ""

Answer: assert Solution().generateString(str1 = "TFTFTFTFTFT", str2 = "abcdefg") == ""

Answer: assert Solution().generateString(str1 = "TTTTTTTTTTTT", str2 = "z") == "zzzzzzzzzzzz"

Answer: assert Solution().generateString(str1 = "FFFFFFFFFFFF", str2 = "a") == "bbbbbbbbbbbb"

Answer: assert Solution().generateString(str1 = "TTTFTTTT", str2 = "qrst") == ""

Answer: assert Solution().generateString(str1 = "FFFFFFFFFT", str2 = "abcdef") == "aaaaaaaaaabcdef"

Answer: assert Solution().generateString(str1 = "FTFTFT", str2 = "aaa") == ""

Answer: assert Solution().generateString(str1 = "TTTTTTTTTT", str2 = "ghijkl") == ""

Answer: assert Solution().generateString(str1 = "TTTTTTTTTT", str2 = "opqrst") == ""

Answer: assert Solution().generateString(str1 = "FTFTFT", str2 = "xyz") == ""

Answer: assert Solution().generateString(str1 = "TTFF", str2 = "qrstuvwx") == ""

Answer: assert Solution().generateString(str1 = "TFTFT", str2 = "abc") == ""

Answer: assert Solution().generateString(str1 = "TFTFTFTFTFTFT", str2 = "mnopqr") == ""

Answer: assert Solution().generateString(str1 = "FF", str2 = "wx") == "aaa"

Answer: assert Solution().generateString(str1 = "TTFTTFFFTTTFTFT", str2 = "qrstuvw") == ""

Answer: assert Solution().generateString(str1 = "TTTFTTTFTTT", str2 = "mnopqrstuvw") == ""

Answer: assert Solution().generateString(str1 = "FTFTFTFTFT", str2 = "xyz") == ""

Answer: assert Solution().generateString(str1 = "FFFF", str2 = "ghijkl") == "aaaaaaaaa"

Answer: assert Solution().generateString(str1 = "FFTFTT", str2 = "world") == ""

Answer: assert Solution().generateString(str1 = "FTFTFTFTFT", str2 = "abc") == ""

Answer: assert Solution().generateString(str1 = "TTFT", str2 = "uvw") == ""

Answer: assert Solution().generateString(str1 = "TTFTFFTFTFFTFT", str2 = "example") == ""

Answer: assert Solution().generateString(str1 = "FFFFFFFF", str2 = "abc") == "aaaaaaaaaa"

Answer: assert Solution().generateString(str1 = "TFFT", str2 = "lmnopqrstu") == ""

Answer: assert Solution().generateString(str1 = "FTFTFT", str2 = "def") == ""

Answer: assert Solution().generateString(str1 = "FFFFFF", str2 = "abcd") == "aaaaaaaaa"

Answer: assert Solution().generateString(str1 = "TFTFTFTFTFTFT", str2 = "abcdef") == ""

Answer: assert Solution().generateString(str1 = "TFFT", str2 = "vwxyz") == ""

Answer: assert Solution().generateString(str1 = "TTFTFTFTT", str2 = "world") == ""

Answer: assert Solution().generateString(str1 = "TFFFFFFFF", str2 = "wxyz") == "wxyzaaaaaaaa"

Answer: assert Solution().generateString(str1 = "TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT", str2 = "mnop") == ""

Answer: assert Solution().generateString(str1 = "TFT", str2 = "abcdef") == ""

Answer: assert Solution().generateString(str1 = "FTTFTFFT", str2 = "gggg") == ""

Answer: assert Solution().generateString(str1 = "TFFTFT", str2 = "abcd") == ""

Answer: assert Solution().generateString(str1 = "TTFTFTFFT", str2 = "lexicographically") == ""

Answer: assert Solution().generateString(str1 = "FTFTFTFTT", str2 = "stuv") == ""

Answer: assert Solution().generateString(str1 = "FFTFFT", str2 = "abc") == "aaabcabc"

Answer: assert Solution().generateString(str1 = "TTTTTTT", str2 = "abcd") == ""

Answer: assert Solution().generateString(str1 = "TF", str2 = "yz") == "yza"

Answer: assert Solution().generateString(str1 = "TTFT", str2 = "jklmno") == ""

Answer: assert Solution().generateString(str1 = "TFTFTFTFTFT", str2 = "mnopqrstuvw") == ""

Answer: assert Solution().generateString(str1 = "TFTF", str2 = "mnop") == ""

Answer: assert Solution().generateString(str1 = "TTTTTTTT", str2 = "a") == "aaaaaaaa"

Answer: assert Solution().generateString(str1 = "TFTFTF", str2 = "mnopqr") == ""

Answer: assert Solution().generateString(str1 = "TTT", str2 = "k") == "kkk"

Answer: assert Solution().generateString(str1 = "TFFTFF", str2 = "bcb") == "bcbbcbaa"

Answer: assert Solution().generateString(str1 = "TFTFTFTFTFTFTFTFTFT", str2 = "a") == "abababababababababa"

Answer: assert Solution().generateString(str1 = "FTFTFTFTFT", str2 = "uvw") == ""

Answer: assert Solution().generateString(str1 = "FTFTFT", str2 = "stuvwx") == ""

Answer: assert Solution().generateString(str1 = "FFTT", str2 = "abcd") == ""

Answer: assert Solution().generateString(str1 = "TTTTTTTTTTTTTTTTTT", str2 = "solution") == ""

Answer: assert Solution().generateString(str1 = "FTFTFTFFT", str2 = "example") == ""

Answer: assert Solution().generateString(str1 = "TFTFT", str2 = "efghij") == ""

Answer: assert Solution().generateString(str1 = "TFTFTFT", str2 = "wxyz") == ""

Answer: assert Solution().generateString(str1 = "TTTTTTTTT", str2 = "abcdefghi") == ""

Answer: assert Solution().generateString(str1 = "FTF", str2 = "abcd") == "aabcda"

Answer: assert Solution().generateString(str1 = "TFTFTFTFTFTFTF", str2 = "abcd") == ""

Answer: assert Solution().generateString(str1 = "TFTFTFTFTF", str2 = "uvw") == ""

Answer: assert Solution().generateString(str1 = "FTF", str2 = "zz") == "azza"

Answer: assert Solution().generateString(str1 = "TFT", str2 = "efghijkl") == ""

Answer: assert Solution().generateString(str1 = "TTTTTTTTTT", str2 = "yzab") == ""

Answer: assert Solution().generateString(str1 = "TTTTTTTTF", str2 = "mnopqr") == ""

Answer: assert Solution().generateString(str1 = "TFT", str2 = "def") == ""

Answer: assert Solution().generateString(str1 = "TFTFTF", str2 = "xyz") == ""

Answer: assert Solution().generateString(str1 = "TTTTTT", str2 = "aaa") == "aaaaaaaa"

Answer: assert Solution().generateString(str1 = "FTFT", str2 = "pqrstu") == ""

Answer: assert Solution().generateString(str1 = "FTFTFTFTFT", str2 = "mnopqrstuvwx") == ""

Answer: assert Solution().generateString(str1 = "FFFFFFFF", str2 = "abcd") == "aaaaaaaaaaa"

Answer: assert Solution().generateString(str1 = "TTFFTTFFTT", str2 = "abcdefgh") == ""

Answer: assert Solution().generateString(str1 = "FTFTFTFTFTFTFTFTFTFTFTFTFTFTFTFT", str2 = "defghijklm") == ""

Answer: assert Solution().generateString(str1 = "TFTFTF", str2 = "abcdefgh") == ""

Answer: assert Solution().generateString(str1 = "TF", str2 = "zzz") == "zzza"

Answer: assert Solution().generateString(str1 = "FTTFFTFF", str2 = "uvw") == ""

Answer: assert Solution().generateString(str1 = "FFFFFFFFF", str2 = "aaaa") == "aaabaaabaaab"

Answer: assert Solution().generateString(str1 = "TFTFT", str2 = "pqrstuvwx") == ""

Answer: assert Solution().generateString(str1 = "TFTFTFTFTFTFTFTFTFT", str2 = "abcdefghijklmnopqrstuvwxyz") == ""

Answer: assert Solution().generateString(str1 = "FFTTTFFFFTTFF", str2 = "abcdefghi") == ""

Answer: assert Solution().generateString(str1 = "FTFTFTFT", str2 = "efghijkl") == ""

Answer: assert Solution().generateString(str1 = "TTFFFFTT", str2 = "xyz") == ""

Answer: assert Solution().generateString(str1 = "FT", str2 = "mnopqr") == "amnopqr"

Answer: assert Solution().generateString(str1 = "FF", str2 = "abcdef") == "aaaaaaa"

Answer: assert Solution().generateString(str1 = "TTT", str2 = "yz") == ""

Answer: assert Solution().generateString(str1 = "TTTT", str2 = "aaa") == "aaaaaa"

Answer: assert Solution().generateString(str1 = "FTFTFTFTFTFT", str2 = "yz") == "ayzyzyzyzyzyz"

Answer: assert Solution().generateString(str1 = "TFFT", str2 = "rstuv") == ""

Answer: assert Solution().generateString(str1 = "FFTFTFTFF", str2 = "mnop") == ""

Answer: assert Solution().generateString(str1 = "TFT", str2 = "abcd") == ""

Answer: assert Solution().generateString(str1 = "FFFFFFFFF", str2 = "abcde") == "aaaaaaaaaaaaa"

Answer: assert Solution().generateString(str1 = "FFTFFT", str2 = "xyz") == "aaxyzxyz"

Answer: assert Solution().generateString(str1 = "TFTFT", str2 = "abcde") == ""

Answer: assert Solution().generateString(str1 = "FFFFFFFF", str2 = "abcdefgh") == "aaaaaaaaaaaaaaa"

Answer: assert Solution().generateString(str1 = "TTTFFFF", str2 = "aaaa") == "aaaaaabaaa"

Answer: assert Solution().generateString(str1 = "TFTFTF", str2 = "abc") == ""

Answer: assert Solution().generateString(str1 = "FTFTFTFT", str2 = "a") == "babababa"

Answer: assert Solution().generateString(str1 = "TTTTTTTTTTTTTTTT", str2 = "xyz") == ""

Answer: assert Solution().generateString(str1 = "TFTFFT", str2 = "xyz") == ""

Answer: assert Solution().generateString(str1 = "FFFFFFFFFT", str2 = "qrstuv") == "aaaaaaaaaqrstuv"

Answer: assert Solution().generateString(str1 = "TTTTTTTT", str2 = "aaaa") == "aaaaaaaaaaa"

Answer: assert Solution().generateString(str1 = "FFFFFFFFFFFFFFFF", str2 = "hijklmnop") == "aaaaaaaaaaaaaaaaaaaaaaaa"

Answer: assert Solution().generateString(str1 = "TFTFFTFTFTFFT", str2 = "xyzxyz") == ""

Answer: assert Solution().generateString(str1 = "TTTTTTTTT", str2 = "mnopqrst") == ""

Answer: assert Solution().generateString(str1 = "FFFTTFFT", str2 = "qrstu") == ""

Answer: assert Solution().generateString(str1 = "TTTTT", str2 = "ab") == ""

Answer: assert Solution().generateString(str1 = "FFFF", str2 = "abcdefgh") == "aaaaaaaaaaa"

Answer: assert Solution().generateString(str1 = "TFTFTFTFTFTFTFT", str2 = "abcdefg") == ""

Answer: assert Solution().generateString(str1 = "FFFFFFFFFT", str2 = "cdefgh") == "aaaaaaaaacdefgh"

Answer: assert Solution().generateString(str1 = "FFFFFFFFFF", str2 = "zyxwvut") == "aaaaaaaaaaaaaaaa"

Answer: assert Solution().generateString(str1 = "TFFTFTF", str2 = "abcd") == ""

Answer: assert Solution().generateString(str1 = "TTTTF", str2 = "mnop") == ""

Answer: assert Solution().generateString(str1 = "FTFT", str2 = "abcdefghijk") == ""

Answer: assert Solution().generateString(str1 = "TFTFTFTFT", str2 = "abcde") == ""

Answer: assert Solution().generateString(str1 = "FFTT", str2 = "yz") == ""

Answer: assert Solution().generateString(str1 = "TFFTTF", str2 = "abc") == ""

Answer: assert Solution().generateString(str1 = "TTFFTTFFT", str2 = "solution") == ""

Answer: assert Solution().generateString(str1 = "FFTTFF", str2 = "xyz") == ""

Answer: assert Solution().generateString(str1 = "FTFTF", str2 = "qrst") == ""

Answer: assert Solution().generateString(str1 = "FFTFTFTFT", str2 = "yz") == "aayzyzyzyz"

Answer: assert Solution().generateString(str1 = "TTFFTT", str2 = "abc") == ""

Answer: assert Solution().generateString(str1 = "FFFFFFFFFFFFFFFFFFFFFFFF", str2 = "mnopqrstuvwxyz") == "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"

Answer: assert Solution().generateString(str1 = "TTTTF", str2 = "abcde") == ""

Answer: assert Solution().generateString(str1 = "FTFT", str2 = "zz") == ""

Answer: assert Solution().generateString(str1 = "TFTFTFTFTFT", str2 = "abcdabcd") == ""

Answer: assert Solution().generateString(str1 = "FTTFFTFTT", str2 = "possible") == ""

Answer: assert Solution().generateString(str1 = "TFFFTF", str2 = "mnop") == "mnopmnopa"

Answer: assert Solution().generateString(str1 = "FFTFFTTFT", str2 = "output") == ""

Answer: assert Solution().generateString(str1 = "TTT", str2 = "qrstuv") == ""

Answer: assert Solution().generateString(str1 = "TTF", str2 = "abcd") == ""

Answer: assert Solution().generateString(str1 = "FFFFFFFFFFFF", str2 = "abcde") == "aaaaaaaaaaaaaaaa"

Answer: assert Solution().generateString(str1 = "FFFFFFFFTT", str2 = "abcd") == ""

Answer: assert Solution().generateString(str1 = "TTFF", str2 = "yz") == ""

Answer: assert Solution().generateString(str1 = "FFFFFFFF", str2 = "zz") == "aaaaaaaaa"

Answer: assert Solution().generateString(str1 = "FFFF", str2 = "xyz") == "aaaaaa"

Answer: assert Solution().generateString(str1 = "TTFT", str2 = "yz") == ""

Answer: assert Solution().generateString(str1 = "FFFF", str2 = "zzz") == "aaaaaa"

Answer: assert Solution().generateString(str1 = "FFFFFF", str2 = "zzz") == "aaaaaaaa"

Answer: assert Solution().generateString(str1 = "FFTFTFTFT", str2 = "complex") == ""

Answer: assert Solution().generateString(str1 = "TT", str2 = "qrstuv") == ""

Answer: assert Solution().generateString(str1 = "FFFFFFFF", str2 = "z") == "aaaaaaaa"

Answer: assert Solution().generateString(str1 = "FTF", str2 = "mnop") == "amnopa"

Answer: assert Solution().generateString(str1 = "FFTFFT", str2 = "qrst") == ""

Answer: assert Solution().generateString(str1 = "TFT", str2 = "efghijklmno") == ""

Answer: assert Solution().generateString(str1 = "FTFTFTFT", str2 = "pqrstuvwx") == ""

Answer: assert Solution().generateString(str1 = "FFTFFTFFT", str2 = "string") == ""

Answer: assert Solution().generateString(str1 = "FTFTFTFT", str2 = "ab") == "aabababab"

Answer: assert Solution().generateString(str1 = "FFTFTF", str2 = "bcd") == ""

Answer: assert Solution().generateString(str1 = "FTFTFTFT", str2 = "qrst") == ""

Answer: assert Solution().generateString(str1 = "TFTFTF", str2 = "uvw") == ""

Answer: assert Solution().generateString(str1 = "FTT", str2 = "efghijkl") == ""

Answer: assert Solution().generateString(str1 = "TFTFTFTFTFTFTFTFT", str2 = "abc") == ""

Answer: assert Solution().generateString(str1 = "TFFFFT", str2 = "def") == "defaadef"

Answer: assert Solution().generateString(str1 = "TFTTFF", str2 = "hello") == ""

Answer: assert Solution().generateString(str1 = "FFFFFFFFFFFFFFFF", str2 = "challenge") == "aaaaaaaaaaaaaaaaaaaaaaaa"

Answer: assert Solution().generateString(str1 = "TFTFFTFF", str2 = "ffff") == ""

Answer: assert Solution().generateString(str1 = "FTFTFT", str2 = "zzz") == ""

Answer: assert Solution().generateString(str1 = "TTTTTTTT", str2 = "abcdefghijk") == ""

Answer: assert Solution().generateString(str1 = "FTFTFTFTFTFT", str2 = "abcd") == ""

Answer: assert Solution().generateString(str1 = "FFTFT", str2 = "wxyz") == ""

Answer: assert Solution().generateString(str1 = "FTFTFFTTT", str2 = "smaller") == ""

Answer: assert Solution().generateString(str1 = "FTFTFTFTFTFTFTFT", str2 = "mnopqr") == ""

Answer: assert Solution().generateString(str1 = "TTTTTTTTTT", str2 = "mnop") == ""

Answer: assert Solution().generateString(str1 = "TTTFTF", str2 = "abc") == ""

Answer: assert Solution().generateString(str1 = "FTFTFTFTFT", str2 = "ab") == "aababababab"

Answer: assert Solution().generateString(str1 = "TFTFTFTFTFT", str2 = "ijklmn") == ""

Answer: assert Solution().generateString(str1 = "FFTTFFTT", str2 = "stuv") == ""

Answer: assert Solution().generateString(str1 = "FTFTFTFTFT", str2 = "jklmnop") == ""

Answer: assert Solution().generateString(str1 = "FTFTFFTTT", str2 = "input") == ""

Answer: assert Solution().generateString(str1 = "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", str2 = "zzzzzzzzzz") == "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"

Answer: assert Solution().generateString(str1 = "FFFFFFFFFT", str2 = "mnopqr") == "aaaaaaaaamnopqr"

Answer: assert Solution().generateString(str1 = "FFFFFFT", str2 = "bbbb") == "aaaaaabbbb"

Answer: assert Solution().generateString(str1 = "FTTFFTFTF", str2 = "hello") == ""

Answer: assert Solution().generateString(str1 = "FFTFTFT", str2 = "qrst") == ""

Answer: assert Solution().generateString(str1 = "FFFFFFFF", str2 = "lmnop") == "aaaaaaaaaaaa"

Answer: assert Solution().generateString(str1 = "FFFFFFFFFFFFFFFF", str2 = "zzzzzzzzzzzzzzzzzzzzzzzzzzzz") == "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"

Answer: assert Solution().generateString(str1 = "TFTFTFTFT", str2 = "stuv") == ""

Answer: assert Solution().generateString(str1 = "FFTFFTFFT", str2 = "qrst") == ""

Answer: assert Solution().generateString(str1 = "FFFFFFFF", str2 = "mnopqr") == "aaaaaaaaaaaaa"

Answer: assert Solution().generateString(str1 = "TTFFFFTT", str2 = "uvwxy") == ""

Answer: assert Solution().generateString(str1 = "FFFF", str2 = "vwxyz") == "aaaaaaaa"

Answer: assert Solution().generateString(str1 = "TT", str2 = "abcdef") == ""

Answer: assert Solution().generateString(str1 = "TTFFTTF", str2 = "mnop") == ""

Answer: assert Solution().generateString(str1 = "FFFF", str2 = "abcdefghijklmno") == "aaaaaaaaaaaaaaaaaa"

Answer: assert Solution().generateString(str1 = "TTFFTT", str2 = "mnop") == ""

Answer: assert Solution().generateString(str1 = "TTT", str2 = "abc") == ""

Answer: assert Solution().generateString(str1 = "TTTTTTTFT", str2 = "stuvwx") == ""

Answer: assert Solution().generateString(str1 = "FFFFFFFFFT", str2 = "uvwxyz") == "aaaaaaaaauvwxyz"

Answer: assert Solution().generateString(str1 = "TFTFTFTFTFTFT", str2 = "abcdabcd") == ""

Answer: assert Solution().generateString(str1 = "FFTTF", str2 = "xyz") == ""

Answer: assert Solution().generateString(str1 = "FFFFFFFFF", str2 = "a") == "bbbbbbbbb"

Answer: assert Solution().generateString(str1 = "TFTFT", str2 = "ijkl") == ""

Answer: assert Solution().generateString(str1 = "TFFTFT", str2 = "bca") == ""

Answer: assert Solution().generateString(str1 = "FTFTFT", str2 = "ijklmnop") == ""

Answer: assert Solution().generateString(str1 = "FFFFFT", str2 = "zyxwvut") == "aaaaazyxwvut"

import random
import functools
import collections
import string
import math
import datetime

from typing import *
from functools import *
from collections import *
from itertools import *
from heapq import *
from bisect import *
from string import *
from operator import *
from math import *

inf = float('inf')

class ListNode:
    def __init__(self, val=0, next=None):
        self.val = val
        self.next = next

def list_node(values: list):
    if not values:
        return None
    head = ListNode(values[0])
    p = head
    for val in values[1:]:
        node = ListNode(val)
        p.next = node
        p = node
    return head

def is_same_list(p1, p2):
    if p1 is None and p2 is None:
        return True
    if not p1 or not p2:
        return False
    return p1.val == p2.val and is_same_list(p1.next, p2.next)

class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def tree_node(values: list):
    if not values:
        return None
    root = TreeNode(values[0])
    i = 1
    queue = deque()
    queue.append(root)
    while queue:
        node = queue.popleft()
        if i < len(values) and values[i] is not None:
            node.left = TreeNode(values[i])
            queue.append(node.left)
        i += 1
        if i < len(values) and values[i] is not None:
            node.right = TreeNode(values[i])
            queue.append(node.right)
        i += 1
    return root

def is_same_tree(p, q):
    if not p and not q:
        return True
    elif not p or not q:
        return False
    elif p.val != q.val:
        return False
    else:
        return is_same_tree(p.left, q.left) and is_same_tree(p.right, q.right)

class Solution:
  def generateString(self, str1: str, str2: str) -> str:
    n = len(str1)
    m = len(str2)
    sz = n + m - 1
    ans = [None] * sz
    modifiable = [True] * sz

    # 1. Handle all 'T' positions first.
    for i, tf in enumerate(str1):
      if tf == 'T':
        for j, c in enumerate(str2):
          pos = i + j
          if ans[pos] and ans[pos] != c:
            return ''
          ans[pos] = c
          modifiable[pos] = False

    # 2. Fill all remaining positions with 'a'.
    for i in range(sz):
      if not ans[i]:
        ans[i] = 'a'

    # 3. Handle all 'F' positions.
    for i in range(n):
      if str1[i] == 'F' and self._match(ans, i, str2):
        modifiablePos = self._lastModifiablePosition(i, m, modifiable)
        if modifiablePos == -1:
          return ''
        ans[modifiablePos] = 'b'
        modifiable[modifiablePos] = False

    return ''.join(ans)

  def _match(self, ans: list, i: int, s: str) -> bool:
    """Returns True if the substring of ans starting at `i` matches `s`."""
    for j, c in enumerate(s):
      if ans[i + j] != c:
        return False
    return True

  def _lastModifiablePosition(self, i: int, m: int, modifiable: list) -> int:
    """
    Finds the last modifiable position in the substring of ans starting at `i`.
    """
    modifiablePos = -1
    for j in range(m):
      pos = i + j
      if modifiable[pos]:
        modifiablePos = pos
    return modifiablePos

class Solution:
    def generateString(self, str1: str, str2: str) -> str:


You are an expert Python programmer. Write correct, efficient Python 3 code that solves the problem and passes all tests. Output the code in the following format: ```python
<code>
```

PROBLEM:
You are given two integer arrays, nums1 and nums2, both of length n, along with a positive integer k.
For each index i from 0 to n - 1, perform the following:

Find all indices j where nums1[j] is less than nums1[i].
Choose at most k values of nums2[j] at these indices to maximize the total sum.

Return an array answer of size n, where answer[i] represents the result for the corresponding index i.

Example 1:

Input: nums1 = [4,2,1,5,3], nums2 = [10,20,30,40,50], k = 2
Output: [80,30,0,80,50]
Explanation:

For i = 0: Select the 2 largest values from nums2 at indices [1, 2, 4] where nums1[j] < nums1[0], resulting in 50 + 30 = 80.
For i = 1: Select the 2 largest values from nums2 at index [2] where nums1[j] < nums1[1], resulting in 30.
For i = 2: No indices satisfy nums1[j] < nums1[2], resulting in 0.
For i = 3: Select the 2 largest values from nums2 at indices [0, 1, 2, 4] where nums1[j] < nums1[3], resulting in 50 + 30 = 80.
For i = 4: Select the 2 largest values from nums2 at indices [1, 2] where nums1[j] < nums1[4], resulting in 30 + 20 = 50.

Example 2:

Input: nums1 = [2,2,2,2], nums2 = [3,1,2,3], k = 1
Output: [0,0,0,0]
Explanation:
Since all elements in nums1 are equal, no indices satisfy the condition nums1[j] < nums1[i] for any i, resulting in 0 for all positions.

Constraints:

n == nums1.length == nums2.length
1 <= n <= 105
1 <= nums1[i], nums2[i] <= 106
1 <= k <= n

Your solution to the problem should be a method of the class Solution called findMaxSum and should pass all tests. Use the following starter code:
```python
class Solution:
    def findMaxSum(self, nums1: List[int], nums2: List[int], k: int) -> List[int]:
        # Add your code here
```

SOLUTION:

Question:
PROBLEM:
You are given two integer arrays, nums1 and nums2, both of length n, along with a positive integer k.
For each index i from 0 to n - 1, perform the following:

Find all indices j where nums1[j] is less than nums1[i].
Choose at most k values of nums2[j] at these indices to maximize the total sum.

Return an array answer of size n, where answer[i] represents the result for the corresponding index i.

Example 1:

Input: nums1 = [4,2,1,5,3], nums2 = [10,20,30,40,50], k = 2
Output: [80,30,0,80,50]
Explanation:

For i = 0: Select the 2 largest values from nums2 at indices [1, 2, 4] where nums1[j] < nums1[0], resulting in 50 + 30 = 80.
For i = 1: Select the 2 largest values from nums2 at index [2] where nums1[j] < nums1[1], resulting in 30.
For i = 2: No indices satisfy nums1[j] < nums1[2], resulting in 0.
For i = 3: Select the 2 largest values from nums2 at indices [0, 1, 2, 4] where nums1[j] < nums1[3], resulting in 50 + 30 = 80.
For i = 4: Select the 2 largest values from nums2 at indices [1, 2] where nums1[j] < nums1[4], resulting in 30 + 20 = 50.

Example 2:

Input: nums1 = [2,2,2,2], nums2 = [3,1,2,3], k = 1
Output: [0,0,0,0]
Explanation:
Since all elements in nums1 are equal, no indices satisfy the condition nums1[j] < nums1[i] for any i, resulting in 0 for all positions.

Constraints:

n == nums1.length == nums2.length
1 <= n <= 105
1 <= nums1[i], nums2[i] <= 106
1 <= k <= n

Your solution to the problem should be a method of the class Solution called findMaxSum and should pass all tests. Use the following starter code:
```python
class Solution:
    def findMaxSum(self, nums1: List[int], nums2: List[int], k: int) -> List[int]:
        # Add your code here
```

SOLUTION:

Answer: assert Solution().findMaxSum(nums1 = [10,20,30,40,50], nums2 = [50,40,30,20,10], k = 2) == [0, 50, 90, 90, 90]

Answer: assert Solution().findMaxSum(nums1 = [100000, 90000, 80000, 70000, 60000], nums2 = [1, 2, 3, 4, 5], k = 4) == [14, 12, 9, 5, 0]

Answer: assert Solution().findMaxSum(nums1 = [1,1,1,1,1], nums2 = [5,5,5,5,5], k = 5) == [0, 0, 0, 0, 0]

Answer: assert Solution().findMaxSum(nums1 = [5,4,3,2,1], nums2 = [1,2,3,4,5], k = 2) == [9, 9, 9, 5, 0]

Answer: assert Solution().findMaxSum(nums1 = [5,5,5,5,5], nums2 = [1,2,3,4,5], k = 5) == [0, 0, 0, 0, 0]

Answer: assert Solution().findMaxSum(nums1 = [1,2,3,4,5], nums2 = [5,4,3,2,1], k = 3) == [0, 5, 9, 12, 12]

Answer: assert Solution().findMaxSum(nums1 = [10,20,30,40,50], nums2 = [1,1,1,1,1], k = 5) == [0, 1, 2, 3, 4]

Answer: assert Solution().findMaxSum(nums1 = [1,3,5,7,9], nums2 = [9,7,5,3,1], k = 3) == [0, 9, 16, 21, 21]

Answer: assert Solution().findMaxSum(nums1 = [4,2,1,5,3], nums2 = [10,20,30,40,50], k = 2) == [80, 30, 0, 80, 50]

Answer: assert Solution().findMaxSum(nums1 = [2,2,2,2], nums2 = [3,1,2,3], k = 1) == [0, 0, 0, 0]

Answer: assert Solution().findMaxSum(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], k = 2) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().findMaxSum(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], nums2 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], k = 3) == [0, 10, 30, 60, 90, 120, 150, 180, 210, 240]

Answer: assert Solution().findMaxSum(nums1 = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5], nums2 = [5, 5, 4, 4, 3, 3, 2, 2, 1, 1], k = 3) == [0, 0, 10, 10, 14, 14, 14, 14, 14, 14]

Answer: assert Solution().findMaxSum(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], nums2 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], k = 10) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

Answer: assert Solution().findMaxSum(nums1 = [100, 200, 300, 400, 500], nums2 = [5, 10, 15, 20, 25], k = 1) == [0, 5, 10, 15, 20]

Answer: assert Solution().findMaxSum(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], nums2 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19], k = 10) == [0, 1, 4, 9, 16, 25, 36, 49, 64, 81]

Answer: assert Solution().findMaxSum(nums1 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], k = 5) == [0, 1, 3, 6, 10, 15, 20, 25, 30, 35]

Answer: assert Solution().findMaxSum(nums1 = [100000, 100000, 100000, 100000, 100000], nums2 = [50000, 60000, 70000, 80000, 90000], k = 3) == [0, 0, 0, 0, 0]

Answer: assert Solution().findMaxSum(nums1 = [5, 4, 3, 2, 1, 0, 6, 7, 8, 9], nums2 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], k = 3) == [150, 150, 150, 110, 60, 0, 150, 180, 210, 240]

Answer: assert Solution().findMaxSum(nums1 = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5], nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], k = 2) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().findMaxSum(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], nums2 = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000], k = 2) == [0, 100, 300, 500, 700, 900, 1100, 1300, 1500, 1700]

Answer: assert Solution().findMaxSum(nums1 = [1, 3, 2, 4, 5], nums2 = [5, 3, 8, 2, 7], k = 2) == [0, 13, 5, 13, 13]

Answer: assert Solution().findMaxSum(nums1 = [10, 20, 30, 40, 50, 10, 20, 30, 40, 50], nums2 = [50, 40, 30, 20, 10, 50, 40, 30, 20, 10], k = 4) == [0, 100, 180, 180, 180, 0, 100, 180, 180, 180]

Answer: assert Solution().findMaxSum(nums1 = [1000000, 999999, 999998, 999997, 999996, 999995, 999994, 999993, 999992, 999991], nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], k = 5) == [40, 40, 40, 40, 40, 34, 27, 19, 10, 0]

Answer: assert Solution().findMaxSum(nums1 = [100, 1, 200, 2, 300, 3, 400, 4, 500, 5], nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], k = 2) == [18, 0, 18, 2, 18, 6, 18, 10, 18, 14]

Answer: assert Solution().findMaxSum(nums1 = [10, 10, 10, 10, 10], nums2 = [1000, 1001, 1002, 1003, 1004], k = 3) == [0, 0, 0, 0, 0]

Answer: assert Solution().findMaxSum(nums1 = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0], nums2 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], k = 5) == [400, 400, 400, 400, 400, 340, 270, 190, 100, 0]

Answer: assert Solution().findMaxSum(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], nums2 = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000], k = 2) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().findMaxSum(nums1 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29], nums2 = [29, 27, 25, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1], k = 7) == [0, 29, 56, 81, 104, 125, 144, 161, 161, 161, 161, 161, 161, 161, 161]

Answer: assert Solution().findMaxSum(nums1 = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], k = 3) == [27, 27, 27, 27, 27, 27, 27, 19, 10, 0]

Answer: assert Solution().findMaxSum(nums1 = [50000, 40000, 30000, 20000, 10000, 60000, 70000, 80000, 90000, 100000], nums2 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], k = 5) == [140, 120, 90, 50, 0, 150, 200, 250, 300, 350]

Answer: assert Solution().findMaxSum(nums1 = [1,2,3,4,5,6,7,8,9,10], nums2 = [100,90,80,70,60,50,40,30,20,10], k = 3) == [0, 100, 190, 270, 270, 270, 270, 270, 270, 270]

Answer: assert Solution().findMaxSum(nums1 = [1, 3, 2, 4, 5, 3, 4, 5, 6, 7], nums2 = [100, 200, 300, 400, 500, 100, 200, 300, 400, 500], k = 3) == [0, 400, 100, 600, 900, 400, 600, 900, 1200, 1300]

Answer: assert Solution().findMaxSum(nums1 = [1, 3, 2, 4, 6, 5, 8, 7, 10, 9], nums2 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], k = 4) == [0, 40, 10, 60, 150, 100, 230, 180, 310, 260]

Answer: assert Solution().findMaxSum(nums1 = [500000, 500000, 500000, 500000, 500000, 500000, 500000, 500000, 500000, 500000], nums2 = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000], k = 2) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().findMaxSum(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], nums2 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], k = 1) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().findMaxSum(nums1 = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20], nums2 = [20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1], k = 5) == [0, 20, 39, 57, 74, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90]

Answer: assert Solution().findMaxSum(nums1 = [10, 15, 20, 25, 30, 35, 40, 45, 50, 55], nums2 = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000], k = 2) == [0, 100, 300, 500, 700, 900, 1100, 1300, 1500, 1700]

Answer: assert Solution().findMaxSum(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], nums2 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], k = 2) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().findMaxSum(nums1 = [100, 200, 300, 400, 500], nums2 = [500, 400, 300, 200, 100], k = 3) == [0, 500, 900, 1200, 1200]

Answer: assert Solution().findMaxSum(nums1 = [5, 4, 3, 2, 1], nums2 = [100, 200, 300, 400, 500], k = 1) == [500, 500, 500, 500, 0]

Answer: assert Solution().findMaxSum(nums1 = [20, 20, 20, 20, 20, 20, 20, 20, 20, 20], nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], k = 5) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().findMaxSum(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], nums2 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], k = 5) == [0, 10, 30, 60, 100, 150, 200, 250, 300, 350]

Answer: assert Solution().findMaxSum(nums1 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], nums2 = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10], k = 5) == [0, 100, 190, 270, 340, 400, 400, 400, 400, 400]

Answer: assert Solution().findMaxSum(nums1 = [5,4,3,2,1,6,7,8,9,10], nums2 = [1,2,3,4,5,6,7,8,9,10], k = 5) == [14, 12, 9, 5, 0, 15, 20, 25, 30, 35]

Answer: assert Solution().findMaxSum(nums1 = [1000000, 999999, 999998, 999997, 999996, 999995, 999994, 999993, 999992, 999991], nums2 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], k = 10) == [540, 520, 490, 450, 400, 340, 270, 190, 100, 0]

Answer: assert Solution().findMaxSum(nums1 = [5, 3, 8, 6, 2, 7, 4, 10, 9, 1], nums2 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], k = 4) == [240, 150, 280, 240, 100, 260, 170, 320, 280, 0]

Answer: assert Solution().findMaxSum(nums1 = [5, 3, 8, 6, 2, 7, 4, 1, 9, 10], nums2 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], k = 3) == [200, 130, 210, 200, 80, 200, 150, 0, 210, 240]

Answer: assert Solution().findMaxSum(nums1 = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000], nums2 = [1000, 900, 800, 700, 600, 500, 400, 300, 200, 100], k = 3) == [0, 1000, 1900, 2700, 2700, 2700, 2700, 2700, 2700, 2700]

Answer: assert Solution().findMaxSum(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], nums2 = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10], k = 4) == [0, 100, 190, 270, 340, 340, 340, 340, 340, 340]

Answer: assert Solution().findMaxSum(nums1 = [5, 4, 3, 2, 1], nums2 = [10, 20, 30, 40, 50], k = 5) == [140, 120, 90, 50, 0]

Answer: assert Solution().findMaxSum(nums1 = [1, 1, 1, 1, 1], nums2 = [5, 4, 3, 2, 1], k = 2) == [0, 0, 0, 0, 0]

Answer: assert Solution().findMaxSum(nums1 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19], nums2 = [19, 17, 15, 13, 11, 9, 7, 5, 3, 1], k = 5) == [0, 19, 36, 51, 64, 75, 75, 75, 75, 75]

Answer: assert Solution().findMaxSum(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], nums2 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], k = 5) == [0, 1, 2, 3, 4, 5, 5, 5, 5, 5]

Answer: assert Solution().findMaxSum(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], nums2 = [100000, 90000, 80000, 70000, 60000, 50000, 40000, 30000, 20000, 10000], k = 5) == [0, 100000, 190000, 270000, 340000, 400000, 400000, 400000, 400000, 400000]

Answer: assert Solution().findMaxSum(nums1 = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], k = 2) == [19, 19, 19, 19, 19, 19, 19, 19, 10, 0]

Answer: assert Solution().findMaxSum(nums1 = [1000000, 500000, 250000, 125000, 62500], nums2 = [62500, 125000, 250000, 500000, 1000000], k = 2) == [1500000, 1500000, 1500000, 1000000, 0]

Answer: assert Solution().findMaxSum(nums1 = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], nums2 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], k = 2) == [190, 190, 190, 190, 190, 190, 190, 190, 100, 0]

Answer: assert Solution().findMaxSum(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], nums2 = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], k = 4) == [0, 10, 19, 27, 34, 34, 34, 34, 34, 34]

Answer: assert Solution().findMaxSum(nums1 = [1, 2, 2, 3, 4, 4, 5, 5, 5, 6], nums2 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], k = 2) == [0, 10, 10, 50, 70, 70, 110, 110, 110, 170]

Answer: assert Solution().findMaxSum(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], nums2 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], k = 3) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().findMaxSum(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], nums2 = [100, 99, 98, 97, 96, 95, 94, 93, 92, 91], k = 5) == [0, 100, 199, 297, 394, 490, 490, 490, 490, 490]

Answer: assert Solution().findMaxSum(nums1 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], k = 4) == [0, 1, 3, 6, 10, 14, 18, 22, 26, 30]

Answer: assert Solution().findMaxSum(nums1 = [1, 2, 3, 4, 5], nums2 = [5, 4, 3, 2, 1], k = 5) == [0, 5, 9, 12, 14]

Answer: assert Solution().findMaxSum(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], nums2 = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10], k = 2) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().findMaxSum(nums1 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], nums2 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], k = 3) == [0, 1, 2, 3, 3, 3, 3, 3, 3, 3]

Answer: assert Solution().findMaxSum(nums1 = [5, 4, 3, 2, 1, 0], nums2 = [100, 200, 300, 400, 500, 600], k = 3) == [1500, 1500, 1500, 1100, 600, 0]

Answer: assert Solution().findMaxSum(nums1 = [100, 99, 98, 97, 96, 95, 94, 93, 92, 91], nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], k = 3) == [27, 27, 27, 27, 27, 27, 27, 19, 10, 0]

Answer: assert Solution().findMaxSum(nums1 = [5, 4, 3, 2, 1], nums2 = [10, 20, 30, 40, 50], k = 2) == [90, 90, 90, 50, 0]

Answer: assert Solution().findMaxSum(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], nums2 = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], k = 1) == [0, 10, 10, 10, 10, 10, 10, 10, 10, 10]

Answer: assert Solution().findMaxSum(nums1 = [1, 10, 2, 9, 3, 8, 4, 7, 5, 6], nums2 = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], k = 3) == [0, 25, 10, 24, 18, 24, 24, 24, 24, 24]

Answer: assert Solution().findMaxSum(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], k = 10) == [0, 1, 3, 6, 10, 15, 21, 28, 36, 45]

Answer: assert Solution().findMaxSum(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], nums2 = [100000, 90000, 80000, 70000, 60000, 50000, 40000, 30000, 20000, 10000], k = 1) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().findMaxSum(nums1 = [5, 3, 8, 6, 2, 7, 4, 10, 1], nums2 = [9, 1, 8, 7, 2, 6, 3, 10, 4], k = 3) == [9, 6, 22, 16, 4, 20, 7, 24, 0]

Answer: assert Solution().findMaxSum(nums1 = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000], nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], k = 3) == [0, 1, 3, 6, 9, 12, 15, 18, 21, 24]

Answer: assert Solution().findMaxSum(nums1 = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], nums2 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], k = 4) == [340, 340, 340, 340, 340, 340, 270, 190, 100, 0]

Answer: assert Solution().findMaxSum(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], nums2 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], k = 2) == [0, 10, 30, 50, 70, 90, 110, 130, 150, 170]

Answer: assert Solution().findMaxSum(nums1 = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], k = 1) == [10, 10, 10, 10, 10, 10, 10, 10, 10, 0]

Answer: assert Solution().findMaxSum(nums1 = [1, 1, 1, 1, 1], nums2 = [1, 2, 3, 4, 5], k = 1) == [0, 0, 0, 0, 0]

Answer: assert Solution().findMaxSum(nums1 = [1, 2, 2, 3, 3, 3, 4, 4, 5, 5], nums2 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], k = 3) == [0, 10, 10, 60, 60, 60, 150, 150, 210, 210]

Answer: assert Solution().findMaxSum(nums1 = [1, 2, 3, 4, 5], nums2 = [5, 5, 5, 5, 5], k = 3) == [0, 5, 10, 15, 15]

Answer: assert Solution().findMaxSum(nums1 = [9, 8, 7, 6, 5, 4, 3, 2, 1], nums2 = [1, 3, 5, 7, 9, 11, 13, 15, 17], k = 4) == [56, 56, 56, 56, 56, 45, 32, 17, 0]

Answer: assert Solution().findMaxSum(nums1 = [5, 4, 3, 2, 1], nums2 = [1, 1, 1, 1, 1], k = 3) == [3, 3, 2, 1, 0]

Answer: assert Solution().findMaxSum(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], nums2 = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], k = 3) == [0, 15, 29, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42]

Answer: assert Solution().findMaxSum(nums1 = [1, 3, 2, 5, 4, 7, 6, 9, 8, 10], nums2 = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], k = 4) == [0, 18, 10, 33, 27, 34, 34, 34, 34, 34]

Answer: assert Solution().findMaxSum(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], nums2 = [1000000, 999999, 999998, 999997, 999996, 999995, 999994, 999993, 999992, 999991], k = 3) == [0, 1000000, 1999999, 2999997, 2999997, 2999997, 2999997, 2999997, 2999997, 2999997]

Answer: assert Solution().findMaxSum(nums1 = [10,9,8,7,6,5,4,3,2,1], nums2 = [1,2,3,4,5,6,7,8,9,10], k = 10) == [54, 52, 49, 45, 40, 34, 27, 19, 10, 0]

Answer: assert Solution().findMaxSum(nums1 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], nums2 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], k = 5) == [0, 1, 2, 3, 4, 5, 5, 5, 5, 5]

Answer: assert Solution().findMaxSum(nums1 = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], nums2 = [1, 10, 2, 20, 3, 30, 4, 40, 5, 50], k = 4) == [140, 140, 140, 125, 125, 99, 95, 55, 50, 0]

Answer: assert Solution().findMaxSum(nums1 = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20], nums2 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19], k = 5) == [0, 1, 4, 9, 16, 25, 35, 45, 55, 65]

Answer: assert Solution().findMaxSum(nums1 = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5], nums2 = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], k = 1) == [0, 0, 10, 10, 10, 10, 10, 10, 10, 10]

Answer: assert Solution().findMaxSum(nums1 = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], k = 10) == [54, 52, 49, 45, 40, 34, 27, 19, 10, 0]

Answer: assert Solution().findMaxSum(nums1 = [5, 4, 3, 2, 1], nums2 = [500, 400, 300, 200, 100], k = 1) == [400, 300, 200, 100, 0]

Answer: assert Solution().findMaxSum(nums1 = [500000, 400000, 300000, 200000, 100000], nums2 = [50000, 40000, 30000, 20000, 10000], k = 2) == [70000, 50000, 30000, 10000, 0]

Answer: assert Solution().findMaxSum(nums1 = [100000, 90000, 80000, 70000, 60000, 50000, 40000, 30000, 20000, 10000], nums2 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], k = 5) == [400, 400, 400, 400, 400, 340, 270, 190, 100, 0]

Answer: assert Solution().findMaxSum(nums1 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], nums2 = [90, 80, 70, 60, 50, 40, 30, 20, 10, 0], k = 5) == [0, 90, 170, 240, 300, 350, 350, 350, 350, 350]

Answer: assert Solution().findMaxSum(nums1 = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], nums2 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], k = 1) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 0]

Answer: assert Solution().findMaxSum(nums1 = [500000, 400000, 300000, 200000, 100000], nums2 = [10, 20, 30, 40, 50], k = 5) == [140, 120, 90, 50, 0]

Answer: assert Solution().findMaxSum(nums1 = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5], nums2 = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000], k = 4) == [0, 0, 300, 300, 1000, 1000, 1800, 1800, 2600, 2600]

Answer: assert Solution().findMaxSum(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], nums2 = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10], k = 3) == [0, 100, 190, 270, 270, 270, 270, 270, 270, 270]

Answer: assert Solution().findMaxSum(nums1 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19], nums2 = [20, 18, 16, 14, 12, 10, 8, 6, 4, 2], k = 5) == [0, 20, 38, 54, 68, 80, 80, 80, 80, 80]

Answer: assert Solution().findMaxSum(nums1 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], nums2 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], k = 5) == [0, 10, 30, 60, 100, 150, 200, 250, 300, 350]

Answer: assert Solution().findMaxSum(nums1 = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5], nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], k = 2) == [0, 0, 3, 3, 7, 7, 11, 11, 15, 15]

Answer: assert Solution().findMaxSum(nums1 = [1,1,1,1,1,1,1,1,1,1], nums2 = [10,20,30,40,50,60,70,80,90,100], k = 2) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

Answer: assert Solution().findMaxSum(nums1 = [100, 50, 75, 25, 150, 125, 200, 175, 225, 15], nums2 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], k = 4) == [190, 140, 160, 100, 230, 190, 290, 250, 310, 0]

Answer: assert Solution().findMaxSum(nums1 = [1, 2, 3, 4, 5, 1, 2, 3, 4, 5], nums2 = [10, 20, 30, 40, 50, 10, 20, 30, 40, 50], k = 3) == [0, 20, 50, 80, 110, 0, 20, 50, 80, 110]

Answer: assert Solution().findMaxSum(nums1 = [1000000, 999999, 999998, 999997, 999996, 999995, 999994, 999993, 999992, 999991], nums2 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], k = 5) == [400, 400, 400, 400, 400, 340, 270, 190, 100, 0]

Answer: assert Solution().findMaxSum(nums1 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19], nums2 = [19, 17, 15, 13, 11, 9, 7, 5, 3, 1], k = 2) == [0, 19, 36, 36, 36, 36, 36, 36, 36, 36]

Answer: assert Solution().findMaxSum(nums1 = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50], nums2 = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10], k = 5) == [0, 100, 190, 270, 340, 400, 400, 400, 400, 400]

Answer: assert Solution().findMaxSum(nums1 = [5, 4, 3, 2, 1, 1, 2, 3, 4, 5], nums2 = [10, 20, 30, 40, 50, 10, 20, 30, 40, 50], k = 2) == [90, 90, 90, 60, 0, 0, 60, 90, 90, 90]

import random
import functools
import collections
import string
import math
import datetime

from typing import *
from functools import *
from collections import *
from itertools import *
from heapq import *
from bisect import *
from string import *
from operator import *
from math import *

inf = float('inf')

class ListNode:
    def __init__(self, val=0, next=None):
        self.val = val
        self.next = next

def list_node(values: list):
    if not values:
        return None
    head = ListNode(values[0])
    p = head
    for val in values[1:]:
        node = ListNode(val)
        p.next = node
        p = node
    return head

def is_same_list(p1, p2):
    if p1 is None and p2 is None:
        return True
    if not p1 or not p2:
        return False
    return p1.val == p2.val and is_same_list(p1.next, p2.next)

class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def tree_node(values: list):
    if not values:
        return None
    root = TreeNode(values[0])
    i = 1
    queue = deque()
    queue.append(root)
    while queue:
        node = queue.popleft()
        if i < len(values) and values[i] is not None:
            node.left = TreeNode(values[i])
            queue.append(node.left)
        i += 1
        if i < len(values) and values[i] is not None:
            node.right = TreeNode(values[i])
            queue.append(node.right)
        i += 1
    return root

def is_same_tree(p, q):
    if not p and not q:
        return True
    elif not p or not q:
        return False
    elif p.val != q.val:
        return False
    else:
        return is_same_tree(p.left, q.left) and is_same_tree(p.right, q.right)

class Solution:
    def findMaxSum(self, nums1: List[int], nums2: List[int], k: int) -> List[int]:
        arr = [(x, i) for i, x in enumerate(nums1)]
        arr.sort()
        pq = []
        s = j = 0
        n = len(arr)
        ans = [0] * n
        for h, (x, i) in enumerate(arr):
            while j < h and arr[j][0] < x:
                y = nums2[arr[j][1]]
                heappush(pq, y)
                s += y
                if len(pq) > k:
                    s -= heappop(pq)
                j += 1
            ans[i] = s
        return ans