#include <iostream>
#define mod 1000000007
using namespace std;
int x, y;
long long pow(long long a, int n)
{
	if (n==1)	return a%mod;
	long long tmp=pow(a,n/2);
	tmp=tmp*tmp%mod;
	if (n%2) tmp=tmp*a%mod;
	return tmp;
}
int main()
{
	cin>>x>>y;
	if ((x+y)%3!=0 || min(x,y)<(x+y)/3)	cout<<0;
	else{
		int m=(2*y-x)/3,	n=(2*x-y)/3;
		long long tu=1, mau=1;
		for(int i=m+1;i<=m+n;i++)	tu=tu*i%mod;
		for(int i=2;i<=n;i++)	mau=mau*i%mod;
		cout<<tu*pow(mau,mod-2)%mod;
	}	
	return 0;
}
### Prompt

Generate 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 <iostream>
#define mod 1000000007
using namespace std;
int x, y;
long long pow(long long a, int n)
{
	if (n==1)	return a%mod;
	long long tmp=pow(a,n/2);
	tmp=tmp*tmp%mod;
	if (n%2) tmp=tmp*a%mod;
	return tmp;
}
int main()
{
	cin>>x>>y;
	if ((x+y)%3!=0 || min(x,y)<(x+y)/3)	cout<<0;
	else{
		int m=(2*y-x)/3,	n=(2*x-y)/3;
		long long tu=1, mau=1;
		for(int i=m+1;i<=m+n;i++)	tu=tu*i%mod;
		for(int i=2;i<=n;i++)	mau=mau*i%mod;
		cout<<tu*pow(mau,mod-2)%mod;
	}	
	return 0;
}
```