Problem Statement

There are N white balls arranged in a row, numbered 1,2,..,N from left to right. AtCoDeer the deer is thinking of painting some of these balls red and blue, while leaving some of them white.

You are given a string s of length K. AtCoDeer performs the following operation for each i from 1 through K in order:

• The i-th operation: Choose a contiguous segment of balls (possibly empty), and paint these balls red if the i-th character in s is r; paint them blue if the character is b.

Here, if a ball which is already painted is again painted, the color of the ball will be overwritten. However, due to the properties of dyes, it is not possible to paint a white, unpainted ball directly in blue. That is, when the i-th character in s is b, the chosen segment must not contain a white ball.

After all the operations, how many different sequences of colors of the balls are possible? Since the count can be large, find it modulo 10^9+7.

Constraints

• 1 ≤ N ≤ 70
• 1 ≤ K ≤ 70
• |s| = K
• s consists of r and b.
• N and K are integers.

Sample Input 1

2 2
rb

Sample Output 1

9

There are nine possible sequences of colors of the balls, as follows:

ww, wr, rw, rr, wb, bw, bb, rb, br.

Here, r represents red, b represents blue and wrepresents white.

Sample Input 2

5 2
br

Sample Output 2

16

Since we cannot directly paint white balls in blue, we can only choose an empty segment in the first operation.

Sample Input 3

7 4
rbrb

Sample Output 3

1569

Sample Input 4

70 70
bbrbrrbbrrbbbbrbbrbrrbbrrbbrbrrbrbrbbbbrbbrbrrbbrrbbbbrbbrbrrbbrrbbbbr

Sample Output 4

841634130