200893: [AtCoder]ARC089 F - ColoringBalls

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.

Input

Input is given from Standard Input in the following format:

$N$ $K$
$s$

Output

Print the number of the different possible sequences of colors of the balls after all the operations, modulo $10^9+7$.

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