Moo Decomposition

문제

You have a long string $S$ of Ms and Os and an integer $K \geq 1$. Count the number of ways of ways to decompose $S$ into subsequences such that each subsequence is MOOOO....O with exactly $K$ Os, modulo $10^9+7$.

Since the string is very long, you are not given it explicitly. Instead, you are given an integer $L$ ($1 \leq L \leq 10^{18}$), and a string $T$ of length $N$ ($1 \leq N \leq 10^6$). The string $S$ is the concatenation of $L$ copies of the string $T$.

입력

The first line contains $K$, $N$, and $L$.

The second line contains the string $T$ of length $N$. Every character is either an M or an O.

It is guaranteed that the number of decompositions of $S$ is nonzero.

출력

Output the number of decompositions of string $S$, modulo $10^9+7$.

예제 입력 1

2 6 1
MOOMOO

예제 출력 1

1

예제 입력 2

2 6 1
MMOOOO

예제 출력 2

6

예제 입력 3

1 4 2
MMOO

예제 출력 3

4

예제 입력 4

1 4 100
MMOO

예제 출력 4

976371285

점수

Inputs 5-7: $K=1$, $L = 1$Inputs 8-10: $K=2$, $N\leq 1000$, $L = 1$Inputs 11-13: $K=1$Inputs 14-19: $L = 1$Inputs 20-25: No additional constraints.