Problem: 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.

Examples

Input

2 2
rb


Output

9


Input

5 2
br


Output

16


Input

7 4
rbrb


Output

1569


Input

70 70
bbrbrrbbrrbbbbrbbrbrrbbrrbbrbrrbrbrbbbbrbbrbrrbbrrbbbbrbbrbrrbbrrbbbbr


Output

841634130

Solution (in CPP):

Solution:
#include<stdio.h>
#include<iostream>
#include<vector>
#include<algorithm>
#include<string>
#include<string.h>

#ifdef LOCAL
#define eprintf(...) fprintf(stderr, __VA_ARGS__)
#else
#define NDEBUG
#define eprintf(...) do {} while (0)
#endif
#include<cassert>

using namespace std;

typedef long long LL;
typedef vector<int> VI;

#define REP(i,n) for(int i=0, i##_len=(n); i<i##_len; ++i)
#define EACH(i,c) for(__typeof((c).begin()) i=(c).begin(),i##_end=(c).end();i!=i##_end;++i)

template<class T> inline void amin(T &x, const T &y) { if (y<x) x=y; }
template<class T> inline void amax(T &x, const T &y) { if (x<y) x=y; }
template<class Iter> void rprintf(const char *fmt, Iter begin, Iter end) {
    for (bool sp=0; begin!=end; ++begin) { if (sp) putchar(' '); else sp = true; printf(fmt, *begin); }
    putchar('\n');
}
template<unsigned MOD> struct ModInt {
    static const unsigned static_MOD = MOD;
    unsigned x;
    void undef() { x = (unsigned)-1; }
    bool isnan() const { return x == (unsigned)-1; }
    inline int geti() const { return (int)x; }
    ModInt() { x = 0; }
    ModInt(const ModInt &y) { x = y.x; }
    ModInt(int y) { if (y<0 || (int)MOD<=y) y %= (int)MOD; if (y<0) y += MOD; x=y; }
    ModInt(unsigned y) { if (MOD<=y) x = y % MOD; else x = y; }
    ModInt(long long y) { if (y<0 || MOD<=y) y %= MOD; if (y<0) y += MOD; x=y; }
    ModInt(unsigned long long y) { if (MOD<=y) x = y % MOD; else x = y; }
    ModInt &operator+=(const ModInt y) { if ((x += y.x) >= MOD) x -= MOD; return *this; }
    ModInt &operator-=(const ModInt y) { if ((x -= y.x) & (1u<<31)) x += MOD; return *this; }
    ModInt &operator*=(const ModInt y) { x = (unsigned long long)x * y.x % MOD; return *this; }
    ModInt &operator/=(const ModInt y) { x = (unsigned long long)x * y.inv().x % MOD; return *this; }
    ModInt operator-() const { return (x ? MOD-x: 0); }

    ModInt inv() const {
	unsigned a = MOD, b = x; int u = 0, v = 1;
	while (b) {
	    int t = a / b;
	    a -= t * b; swap(a, b);
	    u -= t * v; swap(u, v);
	}
	if (u < 0) u += MOD;
	return ModInt(u);
    }
    ModInt pow(long long y) const {
	ModInt b = *this, r = 1;
	if (y < 0) { b = b.inv(); y = -y; }
	for (; y; y>>=1) {
	    if (y&1) r *= b;
	    b *= b;
	}
	return r;
    }
    friend ModInt operator+(ModInt x, const ModInt y) { return x += y; }
    friend ModInt operator-(ModInt x, const ModInt y) { return x -= y; }
    friend ModInt operator*(ModInt x, const ModInt y) { return x *= y; }
    friend ModInt operator/(ModInt x, const ModInt y) { return x *= y.inv(); }
    friend bool operator<(const ModInt x, const ModInt y) { return x.x < y.x; }
    friend bool operator==(const ModInt x, const ModInt y) { return x.x == y.x; }
    friend bool operator!=(const ModInt x, const ModInt y) { return x.x != y.x; }
};

const LL MOD = 1000000007;
//const LL MOD = 998244353;
typedef ModInt<MOD> Mint;

const int MAX = 1000;
Mint inv[MAX+1], fact[MAX+1], fact_inv[MAX+1];

void init() {
    inv[1] = 1;
    for (int i=2; i<=MAX; i++) inv[i] = inv[MOD%i] * (MOD-MOD/i);

    fact[0] = fact_inv[0] = 1;
    for (int i=1; i<=MAX; i++) {
	fact[i] = fact[i-1] * i;
	fact_inv[i] = fact_inv[i-1] * inv[i];
    }
}

Mint nCk(int n, int k) {
    return fact[n] * fact_inv[k] * fact_inv[n-k];
}

int N, K;
char S[211];
int D[211];
Mint ans;
void calc(const VI &v) {
    memset(D, -1, sizeof D);
    int cnt = 0;
    REP (k, K) {
	if (S[k] == 'r' && cnt < (int)v.size()) {
	    D[k] = cnt++;
	}
    }
    if (cnt < (int)v.size()) return;

    int b_size = 0;
    EACH (e, v) if (*e >= 1) b_size++;

    int ma = -1;
    cnt = 0;
    REP (k, K) {
	amax(ma, D[k]);
	if (S[k] == 'b' && cnt < b_size && cnt <= ma) {
	    D[k] = cnt++;
	}
    }
    if (cnt < b_size) return;

    int idx = 0;
    ma = -1;
    cnt = 0;
    REP (k, K) {
	if (S[k] == 'b' && D[k] != -1) amax(ma, D[k]);
	else if (D[k] == -1 && idx < (int)v.size() && v[idx] >= 2 && idx <= ma) {
	    cnt++;
	    if (v[idx] == cnt + 1) {
		idx++;
		cnt = 0;
	    }
	}
    }
    if (idx < (int)v.size() && v[idx] >= 2) return;

    Mint tmp = 0;
    if (v.empty()) {
	tmp = 1;
    } else {
	Mint x = fact[v.size()];
	for (int i=0; i<(int)v.size();) {
	    int j = i;
	    while (j < (int)v.size() && v[i] == v[j]) j++;
	    x *= fact_inv[j-i];
	    i = j;
	}

	int use_len = v.size()-1;
	int color_cnt = v.size()+1;
	REP (i, v.size()) {
	    if (v[i] == 0) {
		use_len++;
		color_cnt++;
	    } else {
		use_len += v[i]*2 - 1;
		color_cnt += v[i]*2 + 1;
	    }
	}

	int rest = N - use_len;
	if (rest < 0) exit(-1);
	assert(rest >= 0);
	tmp = nCk(rest + color_cnt - 1, rest) * x;
    }

    ans += tmp;
}

void rec(int len, VI &v) {
    calc(v);
    int high;
    if (len) {
	high = v.back();
    } else {
	high = N;
    }

    v.push_back(0);
    REP (i, high+1) {
	int add = 0;
	add += (i? i*2-1: 1);
	if (v.size() > 1u) add += 1;
	if (len + add > N) break;
	v.back() = i;
	rec(len+add, v);
    }
    v.pop_back();
}

void MAIN() {
    init();
    scanf("%d%d%s", &N, &K, S);
    VI v;
    rec(0, v);
    printf("%d\n", ans.geti());
}

int main() {
    int TC = 1;
//    scanf("%d", &TC);
    REP (tc, TC) MAIN();
    return 0;
}