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;
typedef long long lint;
const int mod= 1e9 + 7;

int r[3005];
int n, l;
char str[3005];
int ps[3005];
int sum(int s, int e){
	return ps[e] - ps[s-1];
}

int dp[3005][3005];

lint f(int x, int y){
	if(y < 0 || y > r[x] - x + 1) return 0;
	if(x == n+1) return y == 0;
	if(~dp[x][y]) return dp[x][y];
	int ret = 0;
	if(y < r[x] - x + 1) ret += f(x+1, y + sum(r[x]+1, r[x+1]));
	if(y) ret += f(x+1, y-1 + sum(r[x]+1, r[x+1]));
	return dp[x][y] = ret % mod;
}

int main(){
	memset(dp, -1, sizeof(dp));
	cin >> n >> l >> (str + 1);
	for(int i=1; i<=n; i++) r[i] = i, ps[i] = (str[i] == '1');
	for(int i=0; i<l; i++){
		int s, e;
		cin >> s >> e;
		r[s] = max(r[s], e);
	}
	r[n+1] = n;
	for(int i=2; i<=n; i++){
		r[i] = max(r[i], r[i-1]);
		ps[i] += ps[i-1];
	}
	cout << f(1, sum(1, r[1])) << endl;
}