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 $*c*_{1}$, $...$, $*c*_{*k*}$, 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 $10^{9} + 7$.

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 $*c*_{*j*} ≠ *c*'_{*j*}$.

Input

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 $2 000$.

Output

Print a single integer — the number of distinct solutions for the puzzle modulo $10^{9} + 7$.