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 <cstdio>
#define MOD 1000000007
using namespace std;
const int MAXN = 3005;
int f[MAXN][MAXN],n,m,r[MAXN];
int sum[MAXN];
char s[MAXN];
inline void add(int &x,int a)
{
	x+=a;
	if(x>=MOD)x-=MOD;
}
int main()
{
	scanf("%d%d",&n,&m);
	scanf("%s",s+1);
	for(int i=1;i<=n;++i)r[i]=i,sum[i]=sum[i-1]+s[i]-'0';
	for(int i=1,x,y;i<=m;++i){
		scanf("%d%d",&x,&y);
		r[x]=max(r[x],y);
	}
	for(int i=1;i<=n;++i)r[i]=max(r[i],r[i-1]);
	f[1][sum[r[1]]]=1;
	for(int i=1;i<=n;++i){
		for(int j=0;j<=n;++j){
			if(!f[i][j])continue;
			int baseline=sum[r[i+1]]-sum[r[i]];
			if(j<r[i]-i+1)add(f[i+1][baseline+j],f[i][j]);
			if(j>=1)add(f[i+1][baseline+j-1],f[i][j]);
		}
	}
	cout<<(f[n][0]+f[n][1])%MOD<<endl;
	return 0;
}