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 maxn = 3e3 + 5;
const int mod = 1e9 + 7;
int n, m;

char s[maxn];

int sum[maxn];
int last[maxn];

long long dp[maxn][maxn], res;

int main()
{
    ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);

    cin >> n >> m;

    cin >> s + 1;

    for(int i=1;i<=n;++i)
    {
        sum[i] = sum[i-1];
        if( s[i] == '1' ) sum[i] ++;
    }

    for(int i=1;i<=n;++i) last[i] = i;

    for(int i=1;i<=m;++i)
    {
        int x, y;
        cin >> x >> y;
        last[x] = max(last[x], y);
    }
    for(int i=1;i<=n;++i) last[i] = max(last[i], last[i-1]);

    dp[0][0] = 1;

    for(int i=1;i<=n;++i)
    {
        int tung = last[i];
        if(tung - i + 1 > sum[tung] )  dp[i][0] = dp[i-1][0] % mod;

        for(int j=1;j<=i;++j)
        {
            if( tung - i + 1 > sum[tung] - j ) dp[i][j] = dp[i-1][j] % mod;
            if( sum[tung] >= j ) dp[i][j] = ( dp[i][j] + dp[i-1][j-1] ) % mod;
        }
    }

    for(int i=1;i<=n;++i) res = ( res + dp[n][i] ) % mod;

    cout << res;
}