#include<iostream>
using namespace std;
long mod=1e9+7;
long X,Y;
long power(long a,long b){return b?power(a*a%mod,b/2)*(b%2?a:1)%mod:1;}
long C(long a,long b)
{
	long x=1,y=1;
	for(int i=1;i<=b;i++)
	{
		x=x*(a-i+1)%mod;
		y=y*i%mod;
	}
	return x*power(y,mod-2)%mod;
}
int main()
{
	cin>>X>>Y;
	if((X+Y)%3)
	{
		cout<<0<<endl;
		return 0;
	}
	long T=(X+Y)/3;
	X-=T;
	Y-=T;
	if(X<0||Y<0)
	{
		cout<<0<<endl;
		return 0;
	}
	cout<<C(T,X)<<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<iostream>
using namespace std;
long mod=1e9+7;
long X,Y;
long power(long a,long b){return b?power(a*a%mod,b/2)*(b%2?a:1)%mod:1;}
long C(long a,long b)
{
	long x=1,y=1;
	for(int i=1;i<=b;i++)
	{
		x=x*(a-i+1)%mod;
		y=y*i%mod;
	}
	return x*power(y,mod-2)%mod;
}
int main()
{
	cin>>X>>Y;
	if((X+Y)%3)
	{
		cout<<0<<endl;
		return 0;
	}
	long T=(X+Y)/3;
	X-=T;
	Y-=T;
	if(X<0||Y<0)
	{
		cout<<0<<endl;
		return 0;
	}
	cout<<C(T,X)<<endl;
}

```