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>
#define maxn 3010
#define mod 1000000007
using namespace std;
int dp[maxn][maxn],n,m,l[maxn],r[maxn],tp,s[maxn],C[maxn][maxn];
char ss[maxn];
int main(){
	scanf("%d%d",&n,&m);
	scanf("%s",ss+1);
	for(int i=1;i<=n;++i)
		s[i]=s[i-1]+(ss[i]=='1');
	for(int i=1;i<=m;++i){
		scanf("%d%d",&l[i],&r[i]);
		if(l[i]==l[tp])r[tp]=max(r[tp],r[i]);
		else if(r[tp]<r[i])l[++tp]=l[i],r[tp]=r[i];
	}
	dp[1][s[r[1]]-s[l[1]-1]]=1;
	for(int i=0;i<=n;++i)
		for(int j=*C[i]=1;j<=i;++j)
			C[i][j]=(C[i-1][j-1]+C[i-1][j])%mod;
	for(int i=2;i<=tp;++i){
		int k=s[r[i]]-s[max(l[i]-1,r[i-1])],A=min(r[i-1]+1,l[i])-l[i-1],len=r[i-1]-l[i-1]+1,len2=r[i]-l[i]+1;
		for(int j=k;j<=len2&&j<=max(0,r[i-1]-l[i]+1)+k;++j)
			for(int a=0;a<=A&&a+j-k<=len;++a)
				dp[i][j]=(dp[i][j]+1ll*dp[i-1][a+j-k]*C[A][a])%mod;
	}
	int ans=0;
	for(int i=0;i<=r[tp]-l[tp]+1;++i)
		ans=(ans+1ll*dp[tp][i]*C[r[tp]-l[tp]+1][i])%mod;
	printf("%d",ans);
}