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>
using namespace std;
const int N=3e3+2;
const int mod=1e9+7;
int sum[N],dp[N],max1[N],dp1[N];
int main(){
	ios::sync_with_stdio(0);
	cin.tie(0);
	int n,i,j,k,l,m,now=0;
	string s;
	cin>>n>>m>>s;
	s=' '+s;
	for(i=1;i<=n;i++){
		sum[i]=sum[i-1];
		if(s[i]=='1'){
			sum[i]++;
		}
	}
	for(i=1;i<=m;i++){
		cin>>j>>k;
		max1[j]=max(max1[j],k);
	}
	dp[0]=1;
	for(i=1;i<=n;i++){
		if(max1[i]){
			now=max(now,max1[i]);
		}
		now=max(now,i);
		for(j=0;j<=min(sum[now],i);j++){
			if(j){
				dp1[j]=dp[j-1];
			}
			else{
				dp1[j]=0;
			}
			if(i-j<=now-sum[now]){
				dp1[j]+=dp[j];
				if(dp1[j]>=mod){
					dp1[j]-=mod;
				}
			}
		}
		for(j=0;j<=sum[now];j++){
			dp[j]=dp1[j];
		}
	}
	cout<<dp[sum[n]];
}