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<iostream>
#include<algorithm>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<vector>
#include<queue>
#include<map>
using namespace std;
typedef long long ll;
#define N 1000015
const int p=1e9+7;
int n,m,dp[3002][3002],mx[N],s[N];
char ch[N];
inline int ksm(int d,int tk){int ret=1;while(tk){if(tk&1)ret=1ll*ret*d%p;d=1ll*d*d%p;tk>>=1;}return ret;}
int main()
{
    scanf("%d%d",&n,&m);
    scanf("%s",ch+1);
    for(int i=1;i<=n;i++)s[i]=s[i-1]+ch[i]-'0',mx[i]=i;s[n+1]=s[n];
    for(int i=1;i<=m;i++)
    {
    	int l,r;scanf("%d%d",&l,&r);
    	mx[l]=max(mx[l],r);
	}
	for(int i=1;i<=n;i++)mx[i]=max(mx[i],mx[i-1]);mx[n+1]=mx[n];
	dp[0][s[mx[1]]]=1;
	for(int i=0;i<n;i++)for(int j=0;j<=n;j++)
	{
		if(j)(dp[i+1][j+s[mx[i+2]]-s[mx[i+1]]-1]+=dp[i][j])%=p;
		if(mx[i+1]-i-j>0)(dp[i+1][j+s[mx[i+2]]-s[mx[i+1]]]+=dp[i][j])%=p;
	}
	printf("%d\n",dp[n][0]);
}