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 <cstdio>
#include <numeric>
#include <algorithm>
#include <functional>

const int N = 3000 + 10, MOD = 1000000007;

int n;
char s[N];

int a[N], b[N];

int main() {
  int m;
  scanf("%d%d %s", &n, &m, s + 1);
  for (int i = 1; i <= n; ++i) a[i] = b[i] = s[i] - '0';
  while (m--) {
    int l, r;
    scanf("%d%d", &l, &r);
    std::sort(a + l, a + r + 1);
    std::sort(b + l, b + r + 1, std::greater<int>());
  }
  for (int i = 1; i <= n; ++i) a[i] += a[i - 1], b[i] += b[i - 1];
  static int f[N][N];
  f[1][0] = 1;
  for (int i = 1; i <= n; ++i) {
    for (int j = 0; j <= n; ++j) {
      int cur = f[i][j];
      if (!cur) continue;
      if (a[i] <= j && j <= b[i]) (f[i + 1][j] += cur) %= MOD;
      if (a[i] <= j + 1 && j + 1 <= b[i]) (f[i + 1][j + 1] += cur) %= MOD;
    }
  }
  printf("%d\n", f[n + 1][a[n]]);
  return 0;
}