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.

Examples

Input

4 7
RBRRBRR


Output

2


Input

3 3
BBB


Output

4


Input

12 10
RRRRBRRRRB


Output

78
#include<bits/stdc++.h>
const int N=200005,M=1000000007;
using namespace std;
int n,m,l=1,k=N,ls,f[N],s[N];
char S[N],fi;
int main(){
	scanf("%d%d%s",&n,&m,S);
	fi=S[0];
	for(int i=1;i<m;i++)
	if(S[i]!=S[i-1])
	if(S[i]^fi){
		if(ls==0||i-ls&1)
		k=min(k,i-ls);
	}else ls=i;
	if(k<N){
		if(n&1)return puts("0"),0;
		k=k+2>>1,n>>=1;
	}else l++;
	for(int i=l;i<=n;i++)
	f[i]=(s[i-l]+(i>k?-s[i-k-1]:(3ll-l)*i))%M,s[i]=(s[i-1]+f[i])%M;
	printf("%d",(f[n]+l-1+M)%M);
}