Problem: There is a string S of length N consisting of characters `0` and `1`. You will perform the following operation for each i = 1, 2, ..., m:

* Arbitrarily permute the characters within the substring of S starting at the l_i-th character from the left and extending through the r_i-th character.



Here, the sequence l_i is non-decreasing.

How many values are possible for S after the M operations, modulo 1000000007(= 10^9+7)?

Constraints

* 2≦N≦3000
* 1≦M≦3000
* S consists of characters `0` and `1`.
* The length of S equals N.
* 1≦l_i < r_i≦N
* l_i ≦ l_{i+1}

Input

The input is given from Standard Input in the following format:


N M
S
l_1 r_1
:
l_M r_M


Output

Print the number of the possible values for S after the M operations, modulo 1000000007.

Examples

Input

5 2
01001
2 4
3 5


Output

6


Input

9 3
110111110
1 4
4 6
6 9


Output

26


Input

11 6
00101000110
2 4
2 3
4 7
5 6
6 10
10 11


Output

143

Solution (in CPP):

Solution:
#include<bits/stdc++.h>

using namespace std;

using lli = long long int;
using pii = pair<int,int>;

const int maxn = 3e3 + 5;
const int mod = 1e9 + 7;

int n,m;
char s[maxn],t[maxn];
int f[maxn][maxn]={};

int main(){
    ios::sync_with_stdio(false);cin.tie(nullptr);
    //freopen("t.inp","r",stdin);freopen("t.out","w",stdout);
    cin>>n>>m>>(s+1);
    strcpy(t+1,s+1);
    for(int i=1,u,v;i<=m;i++){
        cin>>u>>v;
        sort(s+u,s+v+1);
        sort(t+u,t+v+1,greater<char>());
    }
    int cnt[2]={};
    f[0][0]=1;
    for(int i=1;i<=n;i++){
        cnt[0]+=(s[i]=='1');
        cnt[1]+=(t[i]=='1');
        for(int j=cnt[0];j<=cnt[1];j++){
            f[i][j]=f[i-1][j];
            if (j) f[i][j]+=f[i-1][j-1];
            if (f[i][j]>=mod) f[i][j]-=mod;
        }
    }
    int res=0;
    for(int j=cnt[0];j<=cnt[1];j++){
        res+=f[n][j];
        if (res>=mod) res-=mod;
    }
    cout<<res;
    return 0;
}