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 il inline
#define Max 3005
#define int long long
#define Mod 1000000007
using namespace std;
il int read()
{
	char c=getchar();
	int x=0,f=1;
	while(c>'9'||c<'0')
	{
		if(c=='-') f=-1;
		c=getchar();
	}
	while(c>='0'&&c<='9')
	{
		x=x*10+c-'0';
		c=getchar();
	}
	return x*f;
}
char s[Max];
int n,m,r[Max],l[Max],cnt;
int f[Max][Max];
signed main()
{
	n=read(),m=read();
	scanf("%s",s+1);
	for(int i=1;i<=n+1;i++)
	{
		l[i]=l[i-1]+(s[i]=='1');
		r[i]=i;
		cnt+=(s[i]=='1');
	}
	for(int i=1;i<=m;i++)
	{
		int x=read(),y=read();
		r[x]=max(y,r[x]);
	}
	for(int i=1;i<=n;i++) r[i]=max(r[i],r[i-1]);
	f[1][l[r[1]]]=1;
	for(int i=1;i<=n;i++)
	{
		for(int j=0;j<=n;j++)
		{
			if(f[i][j])
			{
				int a=l[r[i]],b=l[r[i+1]];
				if(r[i]-i+1-j) (f[i+1][j+b-a]+=f[i][j])%=Mod;//,puts("qwq1");
				if(j) (f[i+1][j+b-a-1]+=f[i][j])%=Mod;//,puts("qwq2");
				//cout<<i<<' '<<j<<endl;
			}
		}
	}
	cout<<(f[n+1][0]+Mod)%Mod<<endl;
}