#include<bits/stdc++.h> 
#define fo(i,a,b) for(i=a;i<=b;i++)
#define fd(i,a,b) for(i=a;i>=b;i--)
#define min(a,b) (a<b?a:b)
#define max(a,b) (a>b?a:b)
typedef long long ll;
using namespace std;
const int maxn=3e3+5,mo=1e9+7;
int i,j,n,a,b,m,ri[maxn];
int sum[maxn],f[maxn][maxn];
char s[maxn];
void mod(int &x){
	x-=(x>=mo)?mo:0;
}
int main(){
	scanf("%d%d",&n,&m);
	scanf("%s",s+1);
	fo(i,1,n) sum[i]=sum[i-1]+(s[i]=='1'),ri[i]=i;
	fo(i,1,m){
		scanf("%d%d",&a,&b);
		ri[a]=max(ri[a],b);
	}
	fo(i,1,n) ri[i]=max(ri[i-1],ri[i]);
	f[1][sum[ri[1]]]=1,ri[n+1]=n;
	fo(i,1,n){
		int ad=sum[ri[i+1]]-sum[ri[i]];
		fo(j,0,n-i+1) if (f[i][j]){
			int s=f[i][j];
			if (j)mod(f[i+1][j-1+ad]+=s);
			if (ri[i]-i+1>j)mod(f[i+1][j+ad]+=s);
		}
	}
	printf("%d\n",f[n+1][0]);
}
### Prompt

Please formulate a cpp solution to the following 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

### Response

```cpp
#include<bits/stdc++.h> 
#define fo(i,a,b) for(i=a;i<=b;i++)
#define fd(i,a,b) for(i=a;i>=b;i--)
#define min(a,b) (a<b?a:b)
#define max(a,b) (a>b?a:b)
typedef long long ll;
using namespace std;
const int maxn=3e3+5,mo=1e9+7;
int i,j,n,a,b,m,ri[maxn];
int sum[maxn],f[maxn][maxn];
char s[maxn];
void mod(int &x){
	x-=(x>=mo)?mo:0;
}
int main(){
	scanf("%d%d",&n,&m);
	scanf("%s",s+1);
	fo(i,1,n) sum[i]=sum[i-1]+(s[i]=='1'),ri[i]=i;
	fo(i,1,m){
		scanf("%d%d",&a,&b);
		ri[a]=max(ri[a],b);
	}
	fo(i,1,n) ri[i]=max(ri[i-1],ri[i]);
	f[1][sum[ri[1]]]=1,ri[n+1]=n;
	fo(i,1,n){
		int ad=sum[ri[i+1]]-sum[ri[i]];
		fo(j,0,n-i+1) if (f[i][j]){
			int s=f[i][j];
			if (j)mod(f[i+1][j-1+ad]+=s);
			if (ri[i]-i+1>j)mod(f[i+1][j+ad]+=s);
		}
	}
	printf("%d\n",f[n+1][0]);
}
```