B"Being 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} = 0 Wall-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 . First two lines contain two positive binary numbers A and B ( 1 <= q A <= q 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 <= q c_{00}, c_{01}, c_{10}, c_{11} <= q 100 ,000 ) representing the count of two-digit substrings 00, 01, 10 and 11 respectively. Output one integer number representing how many binary numbers in the interval [A, B] satisfy the constraints mod 10^9 + 7 . Example 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} ="...