#include<bits/stdc++.h>
using namespace std;
#define N 3000 + 5
#define Mod 1000000007
#define rep(i, l, r) for(int i = l; i <= r; ++i)
char s[N];
int n, m, tot, L, R, r[N], sum[N], dp[N][N];
int read(){
    char c; int x = 0, f = 1;
    c = getchar();
    while(c > '9' || c < '0'){ if(c == '-') f = -1; c = getchar();}
    while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = getchar();
    return x * f;
}
int Inc(int a, int b){
    return (a += b) >= Mod ? a - Mod : a;
}
int main(){
    n = read(), m = read(), scanf("%s", s + 1);
    rep(i, 1, n) sum[i] = sum[i - 1] + s[i] - '0';
    rep(i, 1, m) L = read(), R = read(), r[L] = max(r[L], R);
    dp[0][0] = 1, R = 0;
    rep(i, 1, n){
        int D = 0; if(r[i] > R) D = sum[r[i]] - sum[R];
        R = max(R, max(r[i], i));
        rep(j, max(D - 1, 0), R - i){
            if(j >= D) dp[i][j] = Inc(dp[i][j], dp[i - 1][j - D]);
            dp[i][j] = Inc(dp[i][j], dp[i - 1][j - D + 1]);
        }   
    } 
    printf("%d", dp[n][0]);
    return 0;
}
### Prompt

Generate a Cpp solution to the following 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

### Response

```cpp
#include<bits/stdc++.h>
using namespace std;
#define N 3000 + 5
#define Mod 1000000007
#define rep(i, l, r) for(int i = l; i <= r; ++i)
char s[N];
int n, m, tot, L, R, r[N], sum[N], dp[N][N];
int read(){
    char c; int x = 0, f = 1;
    c = getchar();
    while(c > '9' || c < '0'){ if(c == '-') f = -1; c = getchar();}
    while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = getchar();
    return x * f;
}
int Inc(int a, int b){
    return (a += b) >= Mod ? a - Mod : a;
}
int main(){
    n = read(), m = read(), scanf("%s", s + 1);
    rep(i, 1, n) sum[i] = sum[i - 1] + s[i] - '0';
    rep(i, 1, m) L = read(), R = read(), r[L] = max(r[L], R);
    dp[0][0] = 1, R = 0;
    rep(i, 1, n){
        int D = 0; if(r[i] > R) D = sum[r[i]] - sum[R];
        R = max(R, max(r[i], i));
        rep(j, max(D - 1, 0), R - i){
            if(j >= D) dp[i][j] = Inc(dp[i][j], dp[i - 1][j - D]);
            dp[i][j] = Inc(dp[i][j], dp[i - 1][j - D + 1]);
        }   
    } 
    printf("%d", dp[n][0]);
    return 0;
}
```