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 mod = 1e9+7;
int dp[3002][3002], sum[3002];
int R[3002];
char s[3002];
int main(){
    int n, m;
    scanf("%d%d", &n, &m);
    scanf("%s", s+1);
    for(int i=1;i<=n;i++){
        if(s[i] == '1') sum[i]++;
        sum[i] += sum[i-1];
        R[i] = i;
    }
    for(int i=1;i<=m;i++){
        int l, r;
        scanf("%d%d", &l, &r);
        R[l] = max(R[l], r);
    }
    dp[1][0] = 1;
    int last = 0;
    for(int i=1;i<=n;i++){
        int add = 0;
        if(R[i] > last) add += sum[R[i]] - sum[last];
        last = max(last, R[i]);
        for(int j=0;j<=n;j++){
            if(dp[i][j] == 0) continue;

            int one = j + add;
            int zero = last-i+1 - one;

            if(one > 0){
                dp[i+1][one-1] = (dp[i+1][one-1] + dp[i][j])%mod;
            }
            if(zero > 0){
                dp[i+1][one] = (dp[i+1][one] + dp[i][j])%mod;
            }
        }
    }
    printf("%d\n", dp[n+1][0]);
}