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>
using namespace std;
const int N = 3005, MOD = 1e9 + 7;

int n, m, r[N], rightend[N], cnt1[N], f[N][N];
string s;

int main() {
  ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
  cin >> n >> m >> s;
  int curl, curr;
  cin >> curl >> curr;
  for (int i = 2, nxl, nxr; i <= m; ++i) {
    cin >> nxl >> nxr;
    if (nxl == curl) curr = max(curr, nxr);
    else if (nxr > curr) {
      r[curl] = curr;
      curl = nxl;
      curr = nxr;
    }
  }
  r[curl] = curr;
  for (int i = 1; i <= n; ++i) {
    cnt1[i] = cnt1[i - 1] + (s[i - 1] == '1');
    rightend[i] = max(rightend[i - 1], r[i - 1]);
    r[i] = max({rightend[i], r[i], i});
  }
  f[0][0] = 1;
  for (int i = 0; i <= n; ++i) {
    for (int j = 0; j <= n; ++j) {
      if (f[i][j] == 0) continue;
      int one = j + ((rightend[i] < r[i]) ? (cnt1[r[i]] - cnt1[rightend[i]]) : 0);
      if (one) (f[i + 1][one - 1] += f[i][j]) %= MOD;
      if (r[i] - i + 1 > one) (f[i + 1][one] += f[i][j]) %= MOD;
    }
  }
  cout << f[n + 1][0];
  return 0;
}