Puzzle Lover

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, ..., c_k, such that:

• For all i from 1 to k the letter written in the cell c_i matches the letter w_i;
• All the cells in the sequence are pairwise distinct;
• For all i from 1 to k - 1 cells c_i and c_i + 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 c_i 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 c_j ≠ c'_j.