E. Puzzle Lover
dp; hashing; strings
Oleg Petrov loves crossword puzzles and every Thursday he buys his favorite magazine with crosswords and other word puzzles. In the last magazine Oleg found a curious puzzle, and the magazine promised a valuable prize for it's solution. We give a formal description of the problem below.The puzzle field consists of two rows, each row contains n cells. Each cell contains exactly one small English letter. You also are given a word w, which consists of k small English letters. A solution of the puzzle is a sequence of field cells c1, ..., ck, such that: For all i from 1 to k the letter written in the cell ci matches the letter wi; All the cells in the sequence are pairwise distinct; For all i from 1 to k - 1 cells ci and ci + 1 have a common side.Oleg Petrov quickly found a solution for the puzzle. Now he wonders, how many distinct solutions are there for this puzzle. Oleg Petrov doesn't like too large numbers, so calculate the answer modulo 109 + 7.Two solutions ci and c'i are considered distinct if the sequences of cells do not match in at least one position, that is there is such j in range from 1 to k, such that cj ≠ c'j.
The first two lines contain the state of the field for the puzzle. Each of these non-empty lines contains exactly n small English letters.The next line is left empty.The next line is non-empty and contains word w, consisting of small English letters.The length of each line doesn't exceed 2 000.
Print a single integer — the number of distinct solutions for the puzzle modulo 109 + 7.