Score : $1500$ points

Problem Statement

Consider a circle whose perimeter is divided by $N$ points into $N$ arcs of equal length, and each of the arcs is painted red or blue. Such a circle is said to generate a string S from every point when the following condition is satisfied:

• We will arbitrarily choose one of the $N$ points on the perimeter and place a piece on it.
• Then, we will perform the following move $M$ times: move the piece clockwise or counter-clockwise to an adjacent point.
• Here, whatever point we choose initially, it is always possible to move the piece so that the color of the $i$-th arc the piece goes along is $S_i$, by properly deciding the directions of the moves.

Assume that, if $S_i$ is R, it represents red; if $S_i$ is B, it represents blue. Note that the directions of the moves can be decided separately for each choice of the initial point.

You are given a string $S$ of length $M$ consisting of R and B. Out of the $2^N$ ways to paint each of the arcs red or blue in a circle whose perimeter is divided into $N$ arcs of equal length, find the number of ways resulting in a circle that generates $S$ from every point, modulo $10^9+7$.

Note that the rotations of the same coloring are also distinguished.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq M \leq 2 \times 10^5$
• $|S|=M$
• $S_i$ is R or B.

Input

Input is given from Standard Input in the following format:

$N$ $M$

$S$

Output

Print the number of ways to paint each of the arcs that satisfy the condition, modulo $10^9+7$.

4 7
RBRRBRR

2

The condition is satisfied only if the arcs are alternately painted red and blue, so the answer here is $2$.

3 3
BBB

4

12 10
RRRRBRRRRB

78