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<iostream>
#include<vector>
#include<algorithm>
#define MOD 1000000007
using namespace std;
typedef long long ll;
typedef pair<int, int>P;

int dp[4000][4000];
int b[4000];
int sum[4000];

int main() {
	int n, m; cin >> n >> m;
	string s; cin >> s;
	vector<P>v;
	for (int i = 0; i < m; i++) {
		int l, r; scanf("%d%d", &l, &r); l--; r--;
		if (v.empty())v.push_back(P(l, r));
		else if (v.back().first == l)v.back().second = max(v.back().second, r);
		else if (v.back().second < r)v.push_back(P(l, r));
	}
	for (auto p : v)b[p.first] = p.second;
	for (int i = 1; i < n; i++)b[i] = max({ i,b[i],b[i - 1] });
	int cnt = 0;
	for (int i = 0; i < n; i++) {
		if (s[i] == '1')cnt++;
		sum[i] = cnt;
	}
	dp[0][cnt] = 1;
	for (int i = 0; i < n; i++)for (int j = 0; j < cnt + 1; j++) {
		if (dp[i][j] == 0)continue;
		int a = j - (sum[n - 1] - sum[b[i]]);
		if (a)(dp[i + 1][j - 1] += dp[i][j]) %= MOD;
		if (b[i] - i + 1 - a)(dp[i + 1][j] += dp[i][j]) %= MOD;
	}
	cout << dp[n][0] << endl;

	return 0;
}