Problem:
Score : 900 points

Problem Statement

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.

Sample Input 1

5 2
01001
2 4
3 5

Sample Output 1

6

After the first operation, S can be one of the following three: 01001, 00101 and 00011.

After the second operation, S can be one of the following six: 01100, 01010, 01001, 00011, 00101 and 00110.

Sample Input 2

9 3
110111110
1 4
4 6
6 9

Sample Output 2

26

Sample Input 3

11 6
00101000110
2 4
2 3
4 7
5 6
6 10
10 11

Sample Output 3

143

Solution in C (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <string.h>

#define N	3000
#define MD	1000000007

int max(int a, int b) { return a > b ? a : b; }

int main() {
	static char cc[N + 1];
	static int dp[N + 1];
	int n, m, k, k0, l_, r_;

	scanf("%d%d%s", &n, &m, cc);
	l_ = 0, r_ = -1, k0 = 0;
	dp[0] = 1;
	while (m--) {
		int l, r;

		scanf("%d%d", &l, &r), l--, r--;
		if (r_ < r) {
			if (r_ < l)
				l_ = l, r_ = l - 1;
			else
				while (l_ < l) {
					for (k = k0; k > 0; k--)
						dp[k] = (dp[k] + dp[k - 1]) % MD;
					if (k0 >= r_ - l_ + 1)
						dp[k0 - (r_ - l_ + 1)] = 0;
					l_++;
				}
			while (r_ < r)
				if (cc[++r_] == '0')
					k0++;
		}
	}
	while (l_ <= r_) {
		for (k = k0; k > 0; k--)
			dp[k] = (dp[k] + dp[k - 1]) % MD;
		if (k0 >= r_ - l_ + 1)
			dp[k0 - (r_ - l_ + 1)] = 0;
		l_++;
	}
	printf("%d\n", dp[k0]);
	return 0;
}