#include<bits/stdc++.h>
using namespace std;
const int mod=1000000007;
int x,y;
int frac(int x)
{
	int ans=1;
	for(int i=2;i<=x;i++) ans=1LL*ans*i%mod;
	return ans;
}
int ksm(int a,int b)
{
	int ans=1;
	while(b)
	{
		if(b&1) ans=1LL*ans*a%mod;
		b>>=1;
		a=1LL*a*a%mod;
	}
	return ans;
}
int inv(int a)
{
	return ksm(a,mod-2);
}
int C(int a,int b)
{
	return 1LL*frac(b)*inv(frac(a))%mod*inv(frac(b-a))%mod;
}
int main()
{
	ios::sync_with_stdio(false);
	cin>>x>>y;
	if((x+y)%3||x<(x+y)/3||y<(x+y)/3)
	{
		cout<<0<<endl;
		return 0;
	}
	int n=(2*x-y)/3,m=(2*y-x)/3;
	cout<<C(n,n+m)<<endl;
	return 0;
}
### Prompt

Develop a solution in Cpp to the problem described below:

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;
const int mod=1000000007;
int x,y;
int frac(int x)
{
	int ans=1;
	for(int i=2;i<=x;i++) ans=1LL*ans*i%mod;
	return ans;
}
int ksm(int a,int b)
{
	int ans=1;
	while(b)
	{
		if(b&1) ans=1LL*ans*a%mod;
		b>>=1;
		a=1LL*a*a%mod;
	}
	return ans;
}
int inv(int a)
{
	return ksm(a,mod-2);
}
int C(int a,int b)
{
	return 1LL*frac(b)*inv(frac(a))%mod*inv(frac(b-a))%mod;
}
int main()
{
	ios::sync_with_stdio(false);
	cin>>x>>y;
	if((x+y)%3||x<(x+y)/3||y<(x+y)/3)
	{
		cout<<0<<endl;
		return 0;
	}
	int n=(2*x-y)/3,m=(2*y-x)/3;
	cout<<C(n,n+m)<<endl;
	return 0;
}
```