#include<bits/stdc++.h>
using namespace std;
const int N=3e3+10;
const int mod=1e9+7;

int gi() {
	int x=0,o=1;char ch=getchar();
	while(!isdigit(ch)&&ch!='-') ch=getchar();
	if(ch=='-') o=-1,ch=getchar();
	while(isdigit(ch)) x=x*10+ch-'0',ch=getchar();
	return x*o;
}

char s[N];
int n,m,f[N][N],R[N],sum[N][2];

void inc(int &a,int b) {
	a=a+b>=mod?a+b-mod:a+b;
}

int main() {
	cin>>n>>m;
	scanf("%s",s+1),n=strlen(s+1);
	for(int i=1;i<=n;i++) {
		R[i]=i;
		sum[i][0]=sum[i-1][0];
		sum[i][1]=sum[i-1][1];
		++sum[i][s[i]-'0'];
	}
	for(int i=1,l,r;i<=m;i++) l=gi(),r=gi(),R[l]=max(R[l],r);
	for(int i=2;i<=n;i++) R[i]=max(R[i],R[i-1]);
	f[0][0]=1;
	for(int i=0;i<n;i++)
		for(int j=0;j<=i;j++) {
			if(!f[i][j]) continue;
			if(j<sum[R[i+1]][0]) inc(f[i+1][j+1],f[i][j]);
			if(i-j<sum[R[i+1]][1]) inc(f[i+1][j],f[i][j]);
		}
	cout<<f[n][sum[n][0]];
	return 0;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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>
using namespace std;
const int N=3e3+10;
const int mod=1e9+7;

int gi() {
	int x=0,o=1;char ch=getchar();
	while(!isdigit(ch)&&ch!='-') ch=getchar();
	if(ch=='-') o=-1,ch=getchar();
	while(isdigit(ch)) x=x*10+ch-'0',ch=getchar();
	return x*o;
}

char s[N];
int n,m,f[N][N],R[N],sum[N][2];

void inc(int &a,int b) {
	a=a+b>=mod?a+b-mod:a+b;
}

int main() {
	cin>>n>>m;
	scanf("%s",s+1),n=strlen(s+1);
	for(int i=1;i<=n;i++) {
		R[i]=i;
		sum[i][0]=sum[i-1][0];
		sum[i][1]=sum[i-1][1];
		++sum[i][s[i]-'0'];
	}
	for(int i=1,l,r;i<=m;i++) l=gi(),r=gi(),R[l]=max(R[l],r);
	for(int i=2;i<=n;i++) R[i]=max(R[i],R[i-1]);
	f[0][0]=1;
	for(int i=0;i<n;i++)
		for(int j=0;j<=i;j++) {
			if(!f[i][j]) continue;
			if(j<sum[R[i+1]][0]) inc(f[i+1][j+1],f[i][j]);
			if(i-j<sum[R[i+1]][1]) inc(f[i+1][j],f[i][j]);
		}
	cout<<f[n][sum[n][0]];
	return 0;
}

```