H. Self-explorationtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputBeing bored of exploring the Moon over and over again Wall-B decided to explore something he is made of — binary numbers. He took a binary number and decided to count how many times different substrings of length two appeared. He stored those values in c_{00}, c_{01}, c_{10} and c_{11}, representing how many times substrings 00, 01, 10 and 11 appear in the number respectively. For example: 10111100 \rightarrow c_{00} = 1, \ c_{01} = 1,\ c_{10} = 2,\ c_{11} = 3 10000 \rightarrow c_{00} = 3,\ c_{01} = 0,\ c_{10} = 1,\ c_{11} = 0 10101001 \rightarrow c_{00} = 1,\ c_{01} = 3,\ c_{10} = 3,\ c_{11} = 0 1 \rightarrow c_{00} = 0,\ c_{01} = 0,\ c_{10} = 0,\ c_{11} = 0Wall-B noticed that there can be multiple binary numbers satisfying the same c_{00}, c_{01}, c_{10} and c_{11} constraints. Because of that he wanted to count how many binary numbers satisfy the constraints c_{xy} given the interval [A, B]. Unfortunately, his processing power wasn't strong enough to handle large intervals he was curious about. Can you help him? Since this number can be large print it modulo 10^9 + 7.InputFirst two lines contain two positive binary numbers A and B (1 \leq A \leq B < 2^{100\,000}), representing the start and the end of the interval respectively. Binary numbers A and B have no leading zeroes.Next four lines contain decimal numbers c_{00}, c_{01}, c_{10} and c_{11} (0 \leq c_{00}, c_{01}, c_{10}, c_{11} \leq 100\,000) representing the count of two-digit substrings 00, 01, 10 and 11 respectively. OutputOutput one integer number representing how many binary numbers in the interval [A, B] satisfy the constraints mod 10^9 + 7.ExamplesInput1010010011Output1Input10100011234Output0NoteExample 1: The binary numbers in the interval [10,1001] are 10,11,100,101,110,111,1000,1001. Only number 110 satisfies the constraints: c_{00} = 0, c_{01} = 0, c_{10} = 1, c_{11} = 1.Example 2: No number in the interval satisfies the constraints
Input1010010011
Output1
['math', '*2400']