#include<bits/stdc++.h>

using namespace std;

#define X   first
#define Y   second

const int   N   = 3e3 + 1;
const int   mod = 1e9 + 7;

int add(int &a,int b)   {
    a += b;
    if(a >= mod)a -= mod;
    return  a;
}

string s;
int n, q;
int r[N];
int c[N];

int f[N][N];

int cal(int L,int C)    {
    if (C < 0)
        return  0;
    if (C > r[L - 1] - L + 1)
        return  0;
    if (L == n)
        return  1;
    C += c[r[L]] - c[r[L - 1]];
    if (f[L][C] < 0)
        f[L][C] = 0,
        add(f[L][C],cal(L + 1,C)),
        add(f[L][C],cal(L + 1,C - 1));
    return  f[L][C];
}

int main()  {
    ios_base::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);

    cin >> n >> q;
    cin >> s;

    s = "#" + s;

    iota(r + 1,r + 1 + n,1);

    for(int i = 1 ; i <= q ; ++i)   {
        int L;  cin >> L;
        int R;  cin >> R;
        r[L] = max(r[L],R);
    }

    for(int i = 1 ; i <= n ; ++i)
        r[i] = max(r[i],r[i - 1]),
        c[i] = c[i - 1] + s[i] - '0';

    memset(f,-1,sizeof f);

    cout << cal(1,0);
}
### Prompt

Your task is to create 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 X   first
#define Y   second

const int   N   = 3e3 + 1;
const int   mod = 1e9 + 7;

int add(int &a,int b)   {
    a += b;
    if(a >= mod)a -= mod;
    return  a;
}

string s;
int n, q;
int r[N];
int c[N];

int f[N][N];

int cal(int L,int C)    {
    if (C < 0)
        return  0;
    if (C > r[L - 1] - L + 1)
        return  0;
    if (L == n)
        return  1;
    C += c[r[L]] - c[r[L - 1]];
    if (f[L][C] < 0)
        f[L][C] = 0,
        add(f[L][C],cal(L + 1,C)),
        add(f[L][C],cal(L + 1,C - 1));
    return  f[L][C];
}

int main()  {
    ios_base::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);

    cin >> n >> q;
    cin >> s;

    s = "#" + s;

    iota(r + 1,r + 1 + n,1);

    for(int i = 1 ; i <= q ; ++i)   {
        int L;  cin >> L;
        int R;  cin >> R;
        r[L] = max(r[L],R);
    }

    for(int i = 1 ; i <= n ; ++i)
        r[i] = max(r[i],r[i - 1]),
        c[i] = c[i - 1] + s[i] - '0';

    memset(f,-1,sizeof f);

    cout << cal(1,0);
}
```