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:
// Crt. 2019-11-04  19:01:50
#include <algorithm>
#include <iostream>
#include <cstdio>
#define N 3100
using namespace std;
const int Mod = 1e9 + 7;

inline void inc(int &x, int y) {
    x += y, x -= x >= Mod ? Mod : 0;
}

int n, m, r[N], sum[N], f[N][N];
char s[N];

int main() {
#ifdef whyqx
    freopen("work.in", "r", stdin);
    freopen("work.out", "w", stdout);
#endif

    cin >> n >> m;
    scanf("%s", s + 1);
    for (int i = 1; i <= n + 1; ++i)
        sum[i] = sum[i - 1] + (s[i] == '1'), r[i] = i;

    for (int i = 1, l, x; i <= m; ++i) {
        scanf("%d%d", &l, &x);
        r[l] = max(r[l], x);
    }

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

    f[0][0] = 1;
    for (int i = 0; i <= n; ++i)
        for (int j = 0; j <= n; ++j) {
            if (!f[i][j]) continue;
            int r1 = r[i], r2 = r[i + 1];
            if (j) inc(f[i + 1][sum[r2] - sum[r1] + j - 1], f[i][j]);
            if (r[i] - (i - 1) - j) inc(f[i + 1][sum[r2] - sum[r1] + j], f[i][j]);
        }

    cout << f[n + 1][0] << endl;

    return 0;
}