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:
//Love and Freedom.
#include<cstdio>
#include<cmath>
#include<algorithm>
#include<cstring>
#define ll long long
#define inf 20021225
#define N 3100
#define mdn 1000000007
using namespace std;
int read()
{
	int s=0,t=1; char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')	t=-1; ch=getchar();}
	while(ch>='0' && ch<='9')	s=s*10+ch-'0',ch=getchar();
	return s*t;
}
int f[N][N],rt[N],sum[N],n,m;
char ch[N];
void upd(int &x,int y){x+=x+y>=mdn?y-mdn:y;}
int main()
{
	n=read(),m=read(); scanf("%s",ch+1);
	for(int i=1;i<=n;i++)	sum[i]=sum[i-1]+ch[i]-'0',rt[i]=i;
	rt[n+1]=n+1,sum[n+1]=sum[n];
	for(int i=1;i<=m;i++){int pos=read(); rt[pos]=max(read(),rt[pos]);}
	for(int i=1;i<=n;i++)	rt[i]=max(rt[i-1],rt[i]); f[1][sum[rt[1]]]=1;
	for(int i=1;i<=n;i++)	for(int j=0;j<n;j++)	if(f[i][j])
	{
		int l=rt[i]+1,r=rt[i+1],o=j,z=rt[i]+1-i-j;
		if(z)	upd(f[i+1][j+sum[r]-sum[l-1]],f[i][j]);
		if(o)	upd(f[i+1][j+sum[r]-sum[l-1]-1],f[i][j]);
	}
	printf("%d\n",f[n+1][0]);
	return 0;
}