#include <bits/stdc++.h>
using namespace std;

const int64_t MOD = 1e9+7;
void add(int64_t& a, int64_t b){
    a = (a+b) % MOD;
}

int64_t dp[3001][3001];

int main(){
    int N, M;
    string S;
    int L[3001], R[3001], sum[3001];

    cin >> N >> M >> S;
    for(int i=0; i<M; i++){
        cin >> L[i] >> R[i];
        L[i]--; R[i]--;
    }
    for(int i=0; i<N; i++){
        sum[i] = i>0 ? sum[i-1] : 0;
        if(S[i] == '1') sum[i]++;
    }

    dp[0][0] = 1;
    int pt = 0, right = 0;
    for(int i=0; i<N; i++){
        while(pt<M && L[pt] <= i){
            right = max(right, R[pt]);
            pt++;
        }
        right = max(right, i);

        int mn = max(0, sum[right] - (right-i));
        int mx = sum[right];
        for(int j=mn; j<=mx; j++){
            add(dp[i+1][j], dp[i][j]);
            if(j>0) add(dp[i+1][j], dp[i][j-1]);
        }
    }

    cout << dp[N][sum[N-1]] << endl;
    return 0;
}
### Prompt

Develop a solution in CPP to the problem described below:

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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;

const int64_t MOD = 1e9+7;
void add(int64_t& a, int64_t b){
    a = (a+b) % MOD;
}

int64_t dp[3001][3001];

int main(){
    int N, M;
    string S;
    int L[3001], R[3001], sum[3001];

    cin >> N >> M >> S;
    for(int i=0; i<M; i++){
        cin >> L[i] >> R[i];
        L[i]--; R[i]--;
    }
    for(int i=0; i<N; i++){
        sum[i] = i>0 ? sum[i-1] : 0;
        if(S[i] == '1') sum[i]++;
    }

    dp[0][0] = 1;
    int pt = 0, right = 0;
    for(int i=0; i<N; i++){
        while(pt<M && L[pt] <= i){
            right = max(right, R[pt]);
            pt++;
        }
        right = max(right, i);

        int mn = max(0, sum[right] - (right-i));
        int mx = sum[right];
        for(int j=mn; j<=mx; j++){
            add(dp[i+1][j], dp[i][j]);
            if(j>0) add(dp[i+1][j], dp[i][j-1]);
        }
    }

    cout << dp[N][sum[N-1]] << endl;
    return 0;
}
```