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<string>
#include<vector>
#include<set>
#include<map>
#include<queue>
using namespace std;
 
typedef long long ll;
typedef pair<ll,ll> P;
 
#define pb push_back
#define fr first
#define sc second

const ll Mod = 1000000007;

int main(){
	static int N,M;
	static string S;
	static int l[3002],r[3002];
	scanf("%d%d",&N,&M);
	cin >> S;
	for(int i = 1 ; i <= M ; i ++){
		scanf("%d%d",&l[i],&r[i]);
	}
	
	static int cnt[3002] = {};
	for(int i = 1 ; i <= N ; i ++){
		cnt[i] = cnt[i-1] + S[i-1]-'0';
	}
	static int R[3002] = {};
	for(int i = 1 ; i <= N ; i ++){
		R[i] = i;
	}
	for(int i = 1 ; i <= M ; i ++){
		for(int j = l[i] ; j <= r[i] ; j ++){
			R[j] = max( R[j] , r[i] );
		}
	}
	
	static ll dp[3002][3002] = {};
	dp[0][0] = 1;
	for(int i = 1 ; i <= N ; i ++){
		if(cnt[R[i]]-R[i]+i <= 0)dp[i][0] = dp[i-1][0];
		for(int j = max(cnt[R[i]]-R[i]+i,1) ; j <= cnt[R[i]] ; j ++){
			dp[i][j] = dp[i-1][j]+dp[i-1][j-1];
			if(dp[i][j] >= Mod)dp[i][j] -= Mod;
		}
	}
	cout << dp[N][cnt[N]] << endl;
}