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],r[3005],a[3005];
char s[3005];
int main(){
	int n,m;
	scanf("%d%d\n%s",&n,&m,s+1);
	for (int i=1;i<=n;i++) r[i]=i,a[i]=a[i-1]+s[i]-'0';
	for (int i=1;i<=m;i++){
		int x,y;
		scanf("%d%d\n",&x,&y);
		if (y>r[x]) 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])%=mo;
	}
	printf("%d\n",f[a[n]]);
}