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 Python (3.4.3) (judge verdict: Accepted)

#!/usr/bin/env python3


M = 10 ** 9 + 7


def solve(n, m, s, lst):

    cnt = [0] * n
    t = 0
    for i in range(n):
        if s[i] == '1':
            t += 1
        cnt[i] = t


    dp = [[0] * (n + 1) for _ in range(n + 1)]
    dp[0][0] = 1
    r = 0
    j = 0
    for i in range(n):
        while j < m:
            lj, rj = lst[j]
            if lj <= i:
                r = max(r, rj)
                j += 1
            else:
                break
        if r <= i:
            c = cnt[i]
            if 0 < c:
                dp[i + 1][cnt[i]] = (dp[i][c] + dp[i][c - 1]) % M
            else:
                dp[i + 1][0] = dp[i][0]
        else:
            for k in range(max(0, cnt[r] - r + i), min(i + 1, cnt[r]) + 1):
                if 0 < k:
                    dp[i + 1][k] = (dp[i][k] + dp[i][k - 1]) % M
                else:
                    dp[i + 1][0] = dp[i][0]

    return dp[n][cnt[n - 1]]


def main():
    n, m = input().split()
    n = int(n)
    m = int(m)
    s = input()
    lst = []
    for _ in range(m):
        l, r = input().split()
        l = int(l) - 1
        r = int(r) - 1
        lst.append((l, r))

    print(solve(n, m, s, lst))


if __name__ == '__main__':
    main()