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>
using namespace std;
typedef long long lli;
lli n,m;
string s;
vector<lli> rightend;
vector<vector<lli> > dp;
vector<lli> sum;
int main(){
    cin >> n >> m;
    cin >> s;
    rightend = vector<lli> (n+1);
    for(lli i = 1;i <= n;i++) rightend[i] = i;
    for(lli i = 0;i < m;i++){
        lli l,r;
        cin >> l >> r;
        rightend[l] = max(rightend[l],r);
    }
    sum = vector<lli> (n+1);
    for(lli i = 1;i <= n;i++) sum[i] = s[i-1] - '0';
    for(lli i = 0;i < n;i++) sum[i+1] += sum[i];
    for(lli i = 0;i < n;i++) rightend[i+1] = max(rightend[i+1],rightend[i]);
    dp = vector<vector<lli> > (n+2,vector<lli>(n+2));
    dp[0][0] = 1;
    for(lli i = 0;i < n;i++){
        lli b,e;
        b = max(0ll,i - (rightend[i] - sum[rightend[i]]));
        e = min(i,sum[rightend[i]]);
        for(lli j = b;j <= e;j++){
            dp[i+1][j] += dp[i][j];dp[i+1][j] %= 1000000007;
            dp[i+1][j+1] += dp[i][j];dp[i+1][j] %= 1000000007;
        }
    }
    cout << dp[n][sum[n]] << endl;
}