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 <cstdio>
const int mo=1000000007;
int f[3005],a[3005];
char s[3005];
void dp(int i,int &R){
	R=i>R?i:R;
	for (int j=i;j>=0;j--)
		if (j<a[R]-R+i || j>a[R]) f[j]=0;
			else if (j) (f[j]+=f[j-1])%=mo;
}
int main(){
	int n,m;
	scanf("%d%d\n%s",&n,&m,s+1);
	for (int i=1;i<=n;i++) a[i]=a[i-1]+s[i]-'0';
	int L=1,R=0;f[0]=1;
	for (int i=1;i<=m;i++){
		int l,r;
		scanf("%d%d\n",&l,&r);
		for (int j=L;j<l;j++) dp(j,R);
		L=l;R=r>R?r:R;
	}
	for (int i=L;i<=n;i++) dp(i,R);
	printf("%d\n",f[a[n]]);
}