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;

using ll = long long;

const int MAXN = 3010;
int N, M;
char S[MAXN];
int pref[MAXN];

int to[MAXN];
ll dp[MAXN][MAXN];

const ll MOD = 1e9 + 7;

int main() {
	scanf("%d %d", &N, &M);
	scanf("%s", S);
	for (int i = 0; i < N; i++) {
		pref[i+1] = pref[i] + S[i] - '0';
	}

	for (int i = 0; i <= N; i++) {
		to[i] = i;
	}
	for (int i = 0; i < M; i++) {
		int l, r;
		scanf("%d %d", &l, &r);
		to[l] = max(r, to[l]);
	}
	for (int i = 1; i <= N; i++) {
		to[i] = max(to[i], to[i-1]);
	}

	dp[0][0] = 1;
	for (int i = 0; i < N; i++) {
		int add = pref[to[i+1]] - pref[to[i]];
		for (int j = 0; j <= N; j++) {
			int newj = j + add;
			if (newj > 0) {
				dp[i+1][newj-1] = (dp[i+1][newj-1] + dp[i][j]) % MOD;
			}
			if (to[i+1] - i - newj > 0) {
				dp[i+1][newj] = (dp[i+1][newj] + dp[i][j]) % MOD;
			}
		}
	}

	printf("%lld\n", dp[N][0]);
}