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 <iostream>
using namespace std;

typedef long long LL;
const int N = 3005;
LL mod = 1e9 + 7;

int n, m, r[N], pref[N];
LL dp[N][N];
char s[N];

inline void modadd(LL &x, LL y) {
  x += y;
  if (x >= mod) x -= mod;
}

int main() {
  scanf("%d%d", &n, &m);
  scanf("%s", s + 1);
  for (int i = 1; i <= n; i ++) {
    r[i] = i;
    pref[i] = pref[i - 1] + s[i] - '0';
  }
  for (int i = 1, x, y; i <= m; i ++) {
    scanf("%d%d", &x, &y);
    r[x] = max(r[x], y);
  }
  int c = 0, R = 0, t;
  dp[0][0] = 1;
  for (int i = 1; i <= n; i ++) {
    t = 0;
    if (R < r[i]) {
      c += (t = pref[r[i]] - pref[R]);
      R = r[i];
    }
    if (i == R)
      modadd(dp[i][0], dp[i - 1][0] + dp[i - 1][1]);
    else {
      for (int j = t - 1; j <= c && j <= R - i; j ++) {
  	if (j >= t) modadd(dp[i][j], dp[i - 1][j - t]);
  	if (j >= t - 1) modadd(dp[i][j], dp[i - 1][j - t + 1]);
      }
    }
  }
  printf("%lld\n", dp[n][0]);
  return 0;
}