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 maxn=3e3+10;
const int mod=1e9+7;
char s[maxn];
int n,m,f[maxn][maxn],R[maxn],sum[maxn][2];
void check(int &a,int b) 
{
	a=a+b>=mod?a+b-mod:a+b;
}
int main() 
{
	cin>>n>>m;
	cin>>s+1;
	n=strlen(s+1);
	for(int i=1;i<=n;i++) 
	{
		R[i]=i;
		sum[i][0]=sum[i-1][0];
		sum[i][1]=sum[i-1][1];
		sum[i][s[i]-'0']++;
	}
	for(int i=1;i<=m;i++) 
	{
		int l,r;
		cin>>l>>r;
		R[l]=max(R[l],r);
	}
	for(int i=2;i<=n;i++) 
	{
		R[i]=max(R[i],R[i-1]);
	}
	f[0][0]=1;
	for(int i=0;i<n;i++)
	{
		for(int j=0;j<=i;j++) 
		{
			if(!f[i][j]) continue;
			if(j<sum[R[i+1]][0]) 
			{
				check(f[i+1][j+1],f[i][j]);
			}
			if(i-j<sum[R[i+1]][1]) 
			{
				check(f[i+1][j],f[i][j]);
			}
		}
	}
	cout<<f[n][sum[n][0]];
}