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;
const int N=3005,M=1e9+7;
int n,m,x,y,f[N],a[N],r[N];
char s[N];
int main(){
	scanf("%d%d",&n,&m);
	scanf("%s",s+1);
	for (int i=1;i<=n;i++)r[i]=i,a[i]=a[i-1]+(s[i]=='1');
	while (m--){
		scanf("%d%d",&x,&y);
		r[x]=max(r[x],y);
	}
	f[0]=1;
	for (int i=1,R=0;i<=n;i++){
		R=r[i]>R?r[i]:R;
		for (int j=a[R]<i?a[R]:i;j>=0;j--)
			if (j<a[R]-R+i)f[j]=0;
			else if (j)(f[j]+=f[j-1])%=M;
	}
	printf("%d\n",f[a[n]]);
}