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;

const int maxn = 3010,mod = 1e9 + 7;
int n,m,sum[maxn],R[maxn],f[maxn][maxn];
char s[maxn];

int main()
{
    scanf("%d%d",&n,&m);
    scanf("%s",s + 1);
    for (int i = 1; i <= n; i++)
    {
        sum[i] = sum[i - 1] + s[i] - '0';
        R[i] = i;
    }
    R[n + 1] = n + 1;
    sum[n + 1] = sum[n];
    for (int i = 1; i <= m; i++)
    {
        int x,y;
        scanf("%d%d",&x,&y);
        R[x] = max(R[x],y);
    }
    for (int i = 2; i <= n + 1; i++)
        R[i] = max(R[i],R[i - 1]);
    f[1][sum[R[1]]] = 1;
    for (int i = 1; i <= n; i++)
        for (int j = 0; j <= n; j++)
        {
            if (!f[i][j])
                continue;
            int k = sum[R[i + 1]] - sum[R[i]];
            if (j)
                (f[i + 1][j - 1 + k] += f[i][j]) %= mod;
            if (i + j <= R[i])
                (f[i + 1][j + k] += f[i][j]) %= mod;
        }
    printf("%d\n",f[n + 1][0]);

    return 0;
}