Go around a Circle

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

inputFormat

Input

Input is given from Standard Input in the following format:

N M S

outputFormat

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

样例

4 7
RBRRBRR

2