#include <bits/stdc++.h>
#define rep(i,n)for(int i=0;i<(n);i++)
#define MOD 1000000007
using namespace std;
typedef long long ll;
typedef pair<int,int>P;

int dp[4000][4000];
int b[4000];
int sum[4000];

int main(){
	int n,m;cin>>n>>m;
	string s;cin>>s;
	vector<P>v;
	rep(i,m){
		int l,r;scanf("%d%d",&l,&r);l--;r--;
		if(v.empty())v.push_back(P(l,r));
		else if(v.back().first==l)v.back().second=max(v.back().second,r);
		else if(v.back().second<r)v.push_back(P(l,r));
	}
	for(auto p:v)b[p.first]=p.second;
	for(int i=1;i<n;i++)b[i]=max({i,b[i],b[i-1]});
	int cnt=0;
	rep(i,n){
		if(s[i]=='1')cnt++;
		sum[i]=cnt;
	}
	dp[0][cnt]=1;
	rep(i,n)rep(j,cnt+1){
		if(dp[i][j]==0)continue;
		int a=j-(sum[n-1]-sum[b[i]]);
		if(a)(dp[i+1][j-1]+=dp[i][j])%=MOD;
		if(b[i]-i+1-a)(dp[i+1][j]+=dp[i][j])%=MOD;
	}
	cout<<dp[n][0]<<endl;
}
### Prompt

Your task is to create 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 rep(i,n)for(int i=0;i<(n);i++)
#define MOD 1000000007
using namespace std;
typedef long long ll;
typedef pair<int,int>P;

int dp[4000][4000];
int b[4000];
int sum[4000];

int main(){
	int n,m;cin>>n>>m;
	string s;cin>>s;
	vector<P>v;
	rep(i,m){
		int l,r;scanf("%d%d",&l,&r);l--;r--;
		if(v.empty())v.push_back(P(l,r));
		else if(v.back().first==l)v.back().second=max(v.back().second,r);
		else if(v.back().second<r)v.push_back(P(l,r));
	}
	for(auto p:v)b[p.first]=p.second;
	for(int i=1;i<n;i++)b[i]=max({i,b[i],b[i-1]});
	int cnt=0;
	rep(i,n){
		if(s[i]=='1')cnt++;
		sum[i]=cnt;
	}
	dp[0][cnt]=1;
	rep(i,n)rep(j,cnt+1){
		if(dp[i][j]==0)continue;
		int a=j-(sum[n-1]-sum[b[i]]);
		if(a)(dp[i+1][j-1]+=dp[i][j])%=MOD;
		if(b[i]-i+1-a)(dp[i+1][j]+=dp[i][j])%=MOD;
	}
	cout<<dp[n][0]<<endl;
}
```