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:
//Create Time: 2018-05-01 16:03:26
#include <iostream>
#include <cstdio>
#include <cstring>
#include <string>
#include <cmath>
#include <algorithm>
#include <vector>
#include <cstdlib>
#include <sstream>
#include <fstream>
#include <functional>
#include <list>
#include <deque>
#include <queue>
#include <stack>
#include <map>
#include <set>
#include <bitset>
#include <cctype>
#include <ctime>
#include <utility>
#include <complex>
#include <cassert>
#include <climits>
#include <iterator>
#include <tuple>
using namespace std;
#define snuke(i,x) for (__typeof((x).begin()) i = (x).begin(); i != (x).end(); ++i)
#define rep(i,a,n) for (int i=(a);i<(n);i++)
#define per(i,n,a) for (int i=(n)-1;i>=(a);i--)
// #define OUT(x) std::cout<<(#x)<<":"<<(x)<<std::endl
// #define TST(x) std::cout<<(#x)<<":"<<(x)<<" "
#define OUT(args...) {string _s=#args;replace(_s.begin(),_s.end(),',',' ');stringstream _ss(_s);istream_iterator<string> _it(_ss);OUT_TST("\n",_it,args);}
#define TST(args...) {string _s=#args;replace(_s.begin(),_s.end(),',',' ');stringstream _ss(_s);istream_iterator<string> _it(_ss);OUT_TST("",_it,args);}
#define SZ(v) ((int)(v).size())
#define all(v) (v).begin(), (v).end()
#define unq(x) sort(all(x)),(x).erase(unique(all(x)),(x).end())
#define mem(f,x) memset((f), (x), sizeof(f))
#define clr(f) mem(f,0)
#define x first
#define y second
#define mp make_pair
#define pb push_back
#define mt make_tuple
#define eb emplace_back
#define DEBUG
void OUT_TST(string s,istream_iterator<string> it) {cerr<<s;}
template<typename T, typename... Args> void OUT_TST(string s,istream_iterator<string> it,T a,Args... args){cerr<<*it<<"="<<a<<" ";OUT_TST(s,++it,args...);}
template<class T> void rd(T&ret){ret=0;bool ok=0,u=0;for(;;){int c=getchar();if(c>='0'&&c<='9')ret=(ret<<3)+(ret<<1)+c-'0',ok=1;else if(c=='-')u=1;else if(ok){if(u)ret*=-1;return;}}}
long long powmod(long long p,long long n,long long mod){long long ret=1;for(;n;n>>=1){if(n&1)ret=ret*p%mod;p=p*p%mod;}return ret;}
template <class T> bool chmin(T& a, const T &b) {return b < a? a = b, 1: 0;}
template <class T> bool chmax(T& a, const T &b) {return b > a? a = b, 1: 0;}
int gcd(int a,int b){return b?gcd(b,a%b):a;}
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<pii > vii;
typedef tuple<int,int,int> tp;
/****head****/
const ll mod=(ll)1e9+7;

template<int sz> struct Comb{
    const ll mod = ::mod;
    ll *fac, *ifac;
    ll mem_fac[sz+5],mem_ifac[sz+5];

    // long long powmod(long long p,long long n,long long mod){long long ret=1;for(;n;n>>=1){if(n&1)ret=ret*p%mod;p=p*p%mod;}return ret;}

    Comb(ll *fa=0,ll *ifa=0){
        fac=fa?fa:mem_fac;
        ifac=ifa?ifa:mem_ifac;
        fac[0]=ifac[0]=1;
        for(int i=1;i<sz;++i){
            fac[i]=i*fac[i-1]%mod;
            ifac[i]=powmod(fac[i],mod-2,mod);
        }
    }
    ll C(ll n,ll m){  // n >= m
        if(n<m)return 0;
        return (fac[n]*ifac[m]%mod)*ifac[n-m]%mod;
    }
    ll A(ll n,ll m){
        if(n<m)return 0;
        return fac[n]*ifac[n-m]%mod;
    }
};

const int N=87;
ll fac[N],ifac[N];
Comb<N> comb(fac,ifac);

vector<vii> trans;
int n,m,dp[77][77],pos[77],pos_top,clk,cnt_r,cnt_b,flag[77],can[77],can_top;
ll ans;
string s;
vector<vi> state;
void add(int &a,int b){
    a+=b;if(a>=mod)a-=mod;
}
void DP(){
    if(pos_top==0){
        ++ans;return;
    }
    clr(dp);
    dp[pos_top][0]=1;
    int up=1,nxt,dn=0,ndn,nup;
    per(i,pos_top,0){
        ndn=100;
        nup=up;
        rep(j,dn,up)if(dp[i+1][j]){
            for(auto k:trans[pos[i]]){
                if(j==0){
                    nxt=k.x;
                    add(dp[i][nxt],(ll)dp[i+1][j]*k.y%mod);
                    add(dp[i][nxt+1],(ll)2*dp[i+1][j]*k.y%mod);
                    add(dp[i][nxt+2],(ll)dp[i+1][j]*k.y%mod);
                    chmax(nup,nxt+3);
                    chmin(ndn,nxt);
                } else {
                    nxt=j+k.x+1;
                    add(dp[i][nxt],(ll)dp[i+1][j]*k.y%mod);
                    // OUT(i+1,j,dp[i+1][j],nxt,dp[i][nxt]);
                    chmax(nup,nxt+1);
                    chmin(ndn,nxt);
                }
                if(nup>n)nup=n+1;
            }
        }
        dn=ndn;up=nup;
    }

    ll xi=fac[pos_top];
    int c=0;
    rep(i,0,pos_top){
        if(!i || pos[i]==pos[i-1])++c;
        else {
            xi=xi*ifac[c]%mod;
            c=1;
        }
        if(i==pos_top-1)xi=xi*ifac[c]%mod;
    }
    // ll tmp;
    rep(i,0,up)if(dp[0][i]){
        // OUT(i,dp[0][i],xi,comb.C(n-1,i-1));
        // tmp=xi*dp[0][i]%mod;
        // "R" could be "WRW","
        // if(i<=n) ans+=tmp*comb.C(n-1,i-1)%mod;
        // if(i+1<=n) ans+=tmp*comb.C(n-1,i)*2ll%mod;
        // if(i+2<=n) ans+=tmp*comb.C(n-1,i+1)%mod;
        ans+=xi*comb.C(n-1,i-1)%mod *dp[0][i]%mod;
        if(ans>=mod)ans-=mod;
    }
}
/*
bool check(){
    if(top==0)return 1;
    clk++;
    int cr=top,c1=0;
    rep(i,0,top){
        if(pos[i]==1)c1++;
        if(pos[i]>=2)break;
    }
    int cb=top-c1;
    if(cr>cnt_r)return 0;
    if(cb>cnt_b)return 0;
    // TST("139",c1,cb,cr);

    if(c1==top)return 1;

    static int stk[77],stk_top;
    stk_top=0;
    int i=0,j=0;
    for(int _=0;_<top-c1;++_){
        while(i<m && s[i]!='r')++i;
        while(j<m && (j<=i || s[j]!='b')){
            if(s[j]=='b' && _==0)flag[j]=clk;
            ++j;
        }
        // TST(i,j);
        if(j>=m)return 0;
        flag[i]=flag[j]=clk;
        stk[stk_top++]=j;
        ++i;++j;
    }
    stk[stk_top++]=m;
    for(i=0;c1>0;--c1){
        while(i<m && !(flag[i]!=clk && s[i]=='r'))++i;
        if(i>=m)return 0;
        flag[i]=clk;
    }
    ll sum=0;
    for(int i=c1,j=stk_top-2;j>=0 && i<top;++i,--j){
        rep(k,stk[j],stk[j+1])if(flag[k]!=clk)++sum;
        sum-=pos[i]-2;
        if(sum<0)return 0;
    }
    return 1;
}
int ok_cnt;
void dfs(int p,int s,int cr,int cb){
    if(p+s>m){
        if(check()){
            // TST(top);rep(i,0,top)TST(pos[i]);printf("YES ");
            // TST(ans);
            // DP();
            ++ok_cnt;
            // OUT(ans);
        } else{
            // TST(top);rep(i,0,top)TST(pos[i]);puts("NO");
        } return;
    }
    for(int i=0;;++i){
        if(s+i*p>m)break;
        rep(j,0,i)pos[top++]=p;
        dfs(p+1,s+i*p);
        top-=i;
    }
}
*/
int ok_cnt;
vector<vi > output;
bool output_flag;
void dfs(int p,int ci,int yu,int ns){
    // if(output_flag && ci==5)OUT(p,ci,yu,ns);
    if(ns>n)return;
    if(ci==can_top){
        ++ok_cnt;
        // TST(ns);
        // rep(i,0,pos_top)TST(pos[i]);
        // puts("");
        // vi tmp;
        // rep(i,0,pos_top)tmp.pb(pos[i]);
        // output.pb(tmp);
        DP();
        return;
    }
    if(p-2>yu+can[ci])return;
    dfs(p+1,ci,yu,ns);
    pos[pos_top++]=p;
    dfs(p,ci+1,can[ci]+yu-(p-2),ns+2*p-2);
    pos_top--;
}
int main(){
    trans.resize(71);
    trans[1]={{1,1}};
    trans[2]={{1,1},{2,2},{3,1}};
    rep(i,3,71){
        trans[i].clear();
        trans[i].eb(i*2-3,1);
        trans[i].eb(i*2-2,2);
        trans[i].eb(i*2-1,1);
    }

    cin>>n>>m>>s;
    m=SZ(s);
    rep(i,0,m){
        if(s[i]=='r')++cnt_r;
        if(s[i]=='b')++cnt_b;
    }
    static int stk[77],stk_top;
    rep(i,0,cnt_r+1)rep(j,0,min(cnt_b,cnt_r-i)+1){
        if(!i && !j){
            ++ans;continue;
        }
        ++clk;
        pos_top=0;
        rep(k,0,i)pos[pos_top++]=1;
        int t1=0,t2=0;
        stk_top=0;
        bool gg=0;
        rep(_,0,j){
            while(t1<m && s[t1]!='r')++t1;
            while(t2<m && !(t2>t1 && s[t2]=='b')){
                if(s[t2]=='b' && _==0)flag[t2]=clk;
                ++t2;
            }
            if(t2>=m){gg=1;break;}
            stk[stk_top++]=t2;
            flag[t1]=flag[t2]=clk;
            ++t1;++t2;
        }
        // if(i==0 && j==1)OUT(gg);
        // if(i==1 && j==0)OUT(gg);
        t1=0;
        rep(k,0,i){
            while(t1<m && !(flag[t1]!=clk && s[t1]=='r'))++t1;
            flag[t1]=clk;
        }

        if(gg)continue;
        stk[stk_top++]=m;
        // if(i==1&&j==6){
            // OUT("debug");
            // rep(i,0,stk_top)TST(stk[i]);puts("");
            // OUT(clk);
            // rep(i,0,m)TST(flag[i]);puts("");
            // OUT(flag[12]);OUT(flag[13]);
        // }
        can_top=0;
        per(k,stk_top-1,0){
            int c=0;
            rep(t,stk[k],stk[k+1])if(flag[t]!=clk)++c;
            can[can_top++]=c;
        }
        // if(i==1 && j==6){
            // output_flag=1;
            // rep(i,0,can_top)TST(can[i]);
            // dfs(2,0,0,2*i-1);
            // assert(false);
        // }
        dfs(2,0,0,2*i-1);
    }
    ans%=mod;
    cout<<ans<<endl;
    OUT(ok_cnt);

    // sort(all(output));
    // for(auto i:output){
        // for(int j:i)printf("%d ",j);
        // puts("");
    // }
    return 0;
}