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>
#define int long long
using namespace std;
const int mod = 1e9 + 7;
const int N = 3005;
int n, m;
int mx[N], mn[N];
int dp[N][N];
string s;

signed main()
{
	int cnt = 0;
	cin >> n >> m;
	cin >> s;
	s = "a" + s;
	for(int i = 1; i <= n; i++)
	{
		cnt += (s[i] == '1');
		mn[i] = cnt,
		mx[i] = cnt;
	}

	for(int i = 1; i <= m; i++)
	{
		int l, r;
		cin >> l >> r;
		int tmp1 = mn[r] - mn[l - 1],
			tmp2 = mx[r] - mx[l - 1];

		for(int j = l; j <= r; j++)
		{
			mn[j] = min(mn[j], mn[l - 1] + max(0LL, tmp1 - r + j));
			mx[j] = max(mx[j], mx[l - 1] + min(j - l + 1, tmp2));
		}
	}

	dp[0][0] = 1;
	for(int i = 1; i <= n; i++)
	{
		for(int j = mn[i]; j <= mx[i]; j++)
		{
			if(j > 0)
			 	dp[i][j] = dp[i - 1][j] + dp[i - 1][j - 1];
			 else
			 	dp[i][j] = dp[i - 1][j];
			dp[i][j] %= mod;
		}
		
	}
	cout << dp[n][cnt];
}