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;
#define M 3010
#define MOD 1000000007
#define rep(i, x, y) for(int i = (x) ; i <= (y); i ++) 
inline int read() {
	char ch = getchar(); int x = 0, f = 1;
	while(ch < '0' || ch > '9') {
		if(ch == '-') f = -1;
		ch = getchar();
	} while('0' <= ch && ch <= '9') {
		x = x * 10 + ch - '0';
		ch = getchar();
	} return x * f;
}
char s[M]; int sum[M];
int r[M];
int f[M][M];
int main() {
	int n = read(), m = read();
	scanf("%s", s + 1);
	rep(i, 1, n) sum[i] = sum[i - 1] + (s[i] == '1');
	rep(i, 1, n) r[i] = i;
	rep(i, 1, m) {
		int x = read(), y = read();
		r[x] = max(r[x], y);
	} rep(i, 1, n) r[i] = max(r[i - 1], r[i]);
	f[0][0] = 1;
	rep(i, 1, n) {
		rep(j, 0, sum[r[i - 1]]) if(f[i - 1][j]) {
			if(sum[r[i]] > j) (f[i][j + 1] += f[i - 1][j]) %= MOD;
			if(sum[r[i]] - j < r[i] - i + 1) (f[i][j] += f[i - 1][j]) %= MOD;
		}
	} cout << f[n][sum[n]];
	return 0;
}