E - Go around a Circle

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

• 円周上の N 個の点のうち 1 つを任意に選び、その点上に駒を置く。
• 駒を時計回り、または反時計回りに隣合う点まで動かすことを M 回繰り返す。
• このとき最初にどの点を選んだとしても、うまく動かす向きを定めることで、i 回目に駒が通る円弧の色が S_i であるようにできる。

ただし、S_iR のとき赤を、B のとき青を指すものとします。 また駒を動かす向きは、最初に選ぶ点ごとに変えられることに注意してください。

ただし、回転して一致するような塗り方も区別して数えます。

### 制約

• 2 ≦ N ≦ 2 \times 10^5
• 1 ≦ M ≦ 2 \times 10^5
• |S|=M
• S_iR または B

### 入力

N M
S


### 入力例 1

4 7
RBRRBRR


### 出力例 1

2


### 入力例 2

3 3
BBB


### 出力例 2

4


### 入力例 3

12 10
RRRRBRRRRB


### 出力例 3

78


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.

### Sample Input 1

4 7
RBRRBRR


### Sample Output 1

2


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

### Sample Input 2

3 3
BBB


### Sample Output 2

4


### Sample Input 3

12 10
RRRRBRRRRB


### Sample Output 3

78