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 mod = 1e9 + 7;

int main() {
  int N, M, R[3000];
  memset(R, -1, sizeof(R));

  string S;

  cin >> N >> M;
  cin >> S;
  for(int i = 0; i < M; i++) {
    int l, r;
    cin >> l >> r;
    --l, --r;
    R[l] = max(R[l], r);
  }
  for(int i = 0; i < N; i++) {
    if(i > 0) R[i] = max(R[i], R[i - 1]);
    R[i] = max(R[i], i);
  }

  vector< int > sum(N + 1);
  int one = 0;
  for(int i = 0; i < N; i++) {
    one += S[i] == '1';
    sum[i] = one;
  }

  vector< int > dp(3001);
  dp[0] = 1;
  for(int i = 0; i < N; i++) {
    vector< int > dp2(3001);
    for(int j = 0; j < dp.size(); j++) {
      int rest = sum[R[i]] - j;
      if(dp[j] == 0) continue;
      if(rest > 0) (dp2[j + 1] += dp[j]) %= mod;
      if(R[i] - i + 1 != rest) (dp2[j] += dp[j]) %= mod;
    }
    dp.swap(dp2);
  }
  cout << dp[sum[N - 1]] << endl;
}