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>
#define ll long long
#define N 3005
#define mod 1000000007
using namespace std;
inline int read(){
	int x=0; bool f=1; char c=getchar();
	for(;!isdigit(c); c=getchar()) if(c=='-') f=0;
	for(; isdigit(c); c=getchar()) x=(x<<3)+(x<<1)+(c^'0');
	if(f) return x;
	return 0-x;
}
int n,m; char s[N];
int R[N],sum[N],f[N][N];
int main(){
    n=read(), m=read(); scanf("%s",s+1);
    for(int i=1; i<=n; ++i) sum[i]=s[i]-'0';
    for(int i=1; i<=n+1; ++i) sum[i]+=sum[i-1];
    for(int i=1; i<=n+1; ++i) R[i]=i;
    int l,r;
    for(int i=1; i<=m; ++i){
        l=read(), r=read();
        R[l]=max(R[l],r);
    }
    for(int i=1; i<=n; ++i) R[i]=max(R[i],R[i-1]);
    f[1][sum[R[1]]]=1;
    int flag0,flag1;
    for(int i=1; i<=n; ++i)
        for(int j=0; j<=n; ++j)
            if(f[i][j]){
                l=R[i]+1, r=R[i+1];
                flag1=j, flag0=R[i]-(i-1)-flag1;
                if(flag0) (f[i+1][j+sum[r]-sum[l-1]]+=f[i][j])%=mod;
                if(flag1) (f[i+1][j-1+sum[r]-sum[l-1]]+=f[i][j])%=mod;
            }
    printf("%d\n",f[n+1][0]);
    return 0;
}