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 <algorithm>
#include<cmath>
#include<cstring>
#include<cstdio>
#include<cstdlib>
#include<vector>
#include<iomanip>
#define sqr(x) (x)*(x)
using namespace std;
long long n,m,i,j,dp[3005][3005],l[3005],r[3005],mod=1000000007,cnt[3005],x,y;
string st;
int main()
{
	cin>>n>>m>>st;
	st=" "+st;
	for (i=1;i<=n;i++) 
	{
		cnt[i]=cnt[i-1]+st[i]-'0';
	}
	for (i=1;i<=n;i++)
	{
		l[i]=i;
		r[i]=i;
	}
	for (i=1;i<=m;i++)
	{
		cin>>x>>y;
		r[x]=max(r[x],y);
	}
	for (i=1;i<=n;i++)
	{
		r[i]=max(r[i],r[i-1]);
	}
	dp[0][0]=1;
	for (i=1;i<=n;i++)
	{
		for (j=0;j<=r[i];j++)
		{
			if (j>cnt[r[i]]) break;
			if (j>=cnt[r[i]]-r[i]+i)
			{
				dp[i][j]=dp[i-1][j]+dp[i-1][j-1];
				dp[i][j]%=mod;
			}
		}
	}
	cout<<dp[n][cnt[n]];
	return 0;
}