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 mod=1000000007,N=3010;
int n,m,a[N],b[N],f[N][N];
char s[N];
inline void reduce(int&x){x+=x>>31&mod;}
int main(){
	ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
	cin>>n>>m>>(s+1);
	for(int i=1;i<=n;++i)a[i]=i;
	for(int i=1;i<=m;++i){
		int x,y;cin>>x>>y;
		a[x]=max(a[x],y);
	}
	for(int i=1;i<=n;++i)a[i]=max(a[i-1],a[i]);
	for(int i=1;i<=n;++i)b[i]=b[i-1]+(s[i]&1);
	f[0][0]=1;
	for(int i=1;i<=n;++i){
		for(int j=0;j<i;++j)if(f[i-1][j]){
			int u=b[a[i]]-j,v=a[i]-i+1-u;
			if(v>0&&u>=0)reduce(f[i][j]+=f[i-1][j]-mod);
			if(u>0&&v>=0)reduce(f[i][j+1]+=f[i-1][j]-mod);
		}
	}
	cout<<f[n][b[n]]<<'\n';
	return 0;
}