#include<bits/stdc++.h>
using namespace std;
long long mod=1e9+7;
long long qpow(long long a,long long b){
	long long res=1;
	while(b){
		if(b&1) res=res*a%mod;
		a=a*a%mod;
		b/=2;
	}
	return res%mod;
}
int main(){
	long long r,c;
	cin>>r>>c;
	if((r+c)%3!=0||max(r,c)>min(r,c)*2) cout<<0<<endl;
	else{
		long long a=(r+c)/3,x=r-a,y=c-a,ans=1,num=1;
		for(long long i=x;i>=1;i--){
			ans=(ans*(a-i+1))%mod;
		}
		for(long long i=x;i>=1;i--){
			num=(num*i)%mod;
		}
		cout<<ans%mod*qpow(num,mod-2)%mod<<endl;
	}
}
### Prompt

Your challenge is to write a CPP solution to the following problem:

There is a knight - the chess piece - at the origin (0, 0) of a two-dimensional grid.

When the knight is at the square (i, j), it can be moved to either (i+1,j+2) or (i+2, j+1).

In how many ways can the knight reach the square (X, Y)?

Find the number of ways modulo 10^9 + 7.

Constraints

* 1 \leq X \leq 10^6
* 1 \leq Y \leq 10^6
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


X Y


Output

Print the number of ways for the knight to reach (X, Y) from (0, 0), modulo 10^9 + 7.

Examples

Input

3 3


Output

2


Input

2 2


Output

0


Input

999999 999999


Output

151840682

### Response

```cpp
#include<bits/stdc++.h>
using namespace std;
long long mod=1e9+7;
long long qpow(long long a,long long b){
	long long res=1;
	while(b){
		if(b&1) res=res*a%mod;
		a=a*a%mod;
		b/=2;
	}
	return res%mod;
}
int main(){
	long long r,c;
	cin>>r>>c;
	if((r+c)%3!=0||max(r,c)>min(r,c)*2) cout<<0<<endl;
	else{
		long long a=(r+c)/3,x=r-a,y=c-a,ans=1,num=1;
		for(long long i=x;i>=1;i--){
			ans=(ans*(a-i+1))%mod;
		}
		for(long long i=x;i>=1;i--){
			num=(num*i)%mod;
		}
		cout<<ans%mod*qpow(num,mod-2)%mod<<endl;
	}
}
```