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 <string>
#include <iostream>
#include <algorithm>
using namespace std;
const int mod = 1000000007;
int N, M, lp, rp, sum[3009], r[3009], dp[3009][3009]; string s;
int main() {
	cin >> N >> M >> s;
	for (int i = 0; i < N; i++) sum[i + 1] = sum[i] + s[i] - 48;
	for (int i = 0; i < M; i++) {
		cin >> lp >> rp;
		r[lp] = max(r[lp], rp);
	}
	for (int i = 1; i <= N; i++) r[i] = max({ r[i], r[i - 1], i });
	dp[0][0] = 1;
	for (int i = 1; i <= N; i++) {
		int pl = max(sum[r[i]] - r[i] + i, 0), pr = min(sum[r[i]], i);
		for (int j = pl; j <= pr; j++) {
			dp[i][j] = dp[i - 1][j];
			if (j != 0) {
				dp[i][j] += dp[i - 1][j - 1];
				if (dp[i][j] >= mod) dp[i][j] -= mod;
			}
		}
	}
	int ret = 0;
	for (int i = 0; i <= N; i++) {
		ret += dp[N][i];
		if (ret >= mod) ret -= mod;
	}
	cout << ret << endl;
	return 0;
}