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 N = 3e3 + 3;
const int mod = 1e9 + 7;
int n , m;
char str[N];
int sum[N];
int arr[N];
int a , b;
int dp[N][N];
int solve(int l , int r , int cnt){
    if(cnt > r - l + 1){
        return 0;
    }
    if(l > n){
        return 1;
    }
    if(arr[l] > r){
        cnt += sum[arr[l]] - sum[r];
        r = arr[l];
    }
    if(dp[l][cnt] != -1){
        return dp[l][cnt];
    }
    int res = 0;
    if(cnt){
        res += solve(l + 1 , r , cnt - 1);
    }
    res += solve(l + 1 , r , cnt);
    if(res >= mod){
        res -= mod;
    }
    return dp[l][cnt] = res;
}
int main(){
    scanf("%d %d" , &n , &m);
    scanf("%s" , str + 1);
    sum[0] = 0;
    for(int i = 1 ; i <= n ; ++i){
        sum[i] = sum[i - 1] + str[i] - '0';
    }
    for(int i = 1 ; i <= n ; ++i){
        arr[i] = i;
    }
    for(int i = 1 ; i <= n ; ++i){
        scanf("%d %d" , &a , &b);
        arr[a] = max(arr[a] , b);
    }
    memset(dp , -1 , sizeof(dp));
    printf("%d\n" , solve(1 , 0 , 0));
}