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 = 3030;
const int mod = 1e9 + 7;

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

int n, m;
char s[N];
int go[N];
int f[N][N];

int main() {
   scanf("%d %d %s", &n, &m, s + 1);
   for (int i = 1; i <= n; ++i) {
      go[i] = i;
   }
   for (int i = 0; i < m; ++i) {
      int l, r;
      scanf("%d %d", &l, &r);
      go[l] = max(go[l], r);
   }
   for (int i = 1; i <= n; ++i) {
      go[i] = max(go[i], go[i - 1]);
   }
   f[0][0] = 1;
   for (int i = 1; i <= n; ++i) {
      int ad = 0;
      for (int j = go[i - 1] + 1; j <= go[i]; ++j) {
         ad += (s[j] - '0');
      }
      for (int j = 0; j <= n; ++j) {
         if (!f[i - 1][j]) continue;
         if ((j + ad)) {
            add(f[i][j + ad - 1], f[i - 1][j]);
         }
         if (go[i] - i + 1 - (j + ad)) {
            add(f[i][j + ad], f[i - 1][j]);
         }
      }
   }
   printf("%d\n", f[n][0]);
}