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>
#define forn(i, n) for(int i = 0; i < (int)(n); i++)
typedef long long ll;
using namespace std;

const int MAXN = 3000, MOD = 1000 * 1000 * 1000 + 7;
int dp[MAXN + 1][MAXN + 1], pr[MAXN + 1], ls[MAXN + 1];

void add(int& x, int y) {
    x += y;
    if(x >= MOD)
        x -= MOD;
}

int main() {
    //ios_base::sync_with_stdio(false);
    //freopen("input.txt", "r", stdin);
    //freopen("output.txt", "w", stdout);

    int n, m;
    cin >> n >> m;
    string s;
    cin >> s;
    s = "#" + s;
    for(int i = 1; i <= n; i++) {
        ls[i] = i;
        pr[i] = pr[i - 1] + s[i] - '0';
    }
    for(int i = 1; i <= m; i++) {
        int l, r;
        cin >> l >> r;
        for(int j = l; j <= r; j++)
            ls[j] = max(ls[j], r);
    }
    dp[0][0] = 1;
    for(int i = 0; i < n; i++) {
        int b = ls[i + 1];
        for(int j = 0; j <= i + 1; j++) {
            if(j < pr[b])
                add(dp[i + 1][j + 1], dp[i][j]);
            if((i - j) < b - pr[b])
                add(dp[i + 1][j], dp[i][j]);
        }
    }
    cout << dp[n][pr[n]] << endl;
    return 0;
}