Problem Statement

Given two strings, $A$ and $B$, both of length $N$, which are composed of uppercase letters, and a string $S$ of length $M$.

A position is considered valid if the substring formed by selecting uppercase letters from $A$ and $B$ is equal to $S$.

Output the count of valid positions modulo $1007$.

We consider two strings to be different if there exists a position $i$ such that $S_i \neq S'_i$.

Constraints

• $1 \leq N \leq 2000$ and $1 \leq M \leq 2000$.
• The solution is guaranteed to exist.

Input

$N\ M$ $A_1A_2\cdots A_N$ $B_1B_2\cdots B_N$ $S_1S_2\cdots S_M$

• The first line contains two positive integers $N$ and $M$.
• The next two lines contain strings $A$ and $B$.
• The last line contains $M$ characters representing $S$.

Output

The count of valid positions modulo $1007$.

Sample Input 1

4 4
LOVE
EVOL
LOVE

Sample Output 1

4

• Possibility 1: $(1,1) \to (1,2) \to (1,3) \to (1,4)$;
• Possibility 2: $(1,1) \to (1,2) \to (2,2) \to (2,1)$;
• Possibility 3: $(2,4) \to (2,3) \to (2,2) \to (2,1)$;
• Possibility 4: $(2,4) \to (2,3) \to (1,3) \to (1,4)$.

Sample Input 2

1 3
Y
Y
YYY

Sample Output 2

2

• Possibility 1: $(1,1) \to (1,2) \to (1,1)$;
• Possibility 2: $(1,2) \to (1,1) \to (1,2)$.