#include <bits/stdc++.h>

using namespace std;

const int N=2e6+6;
const int MOD=1e9+7;

long long fac[N],infac[N];

long long poww(long long b,long long p)
{
	if(p==0) return 1;
	if(p%2) return (b*poww(b,p-1))%MOD;
	return poww((b*b)%MOD,p/2);
}

int main()
{
	fac[0]=1; infac[0]=1;
	for(int i=1;i<N;i++)
	{
		fac[i]=(i*fac[i-1])%MOD;
		infac[i]=poww(fac[i],MOD-2);
	}
	int x,y;
	cin >> x >> y;
	if((2*y-x)%3)
	{
		cout << 0 << endl;
		return 0;
	}
	int a=(2*y-x)/3;
	int b=y-2*a;
	if(a<0||b<0)
	{
		cout << 0 << endl;
		return 0;
	}
	long long ans=(((fac[a+b]*infac[a])%MOD)*infac[b])%MOD;
	cout << ans << endl;
}
### Prompt

Please create a solution in CPP 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;

const int N=2e6+6;
const int MOD=1e9+7;

long long fac[N],infac[N];

long long poww(long long b,long long p)
{
	if(p==0) return 1;
	if(p%2) return (b*poww(b,p-1))%MOD;
	return poww((b*b)%MOD,p/2);
}

int main()
{
	fac[0]=1; infac[0]=1;
	for(int i=1;i<N;i++)
	{
		fac[i]=(i*fac[i-1])%MOD;
		infac[i]=poww(fac[i],MOD-2);
	}
	int x,y;
	cin >> x >> y;
	if((2*y-x)%3)
	{
		cout << 0 << endl;
		return 0;
	}
	int a=(2*y-x)/3;
	int b=y-2*a;
	if(a<0||b<0)
	{
		cout << 0 << endl;
		return 0;
	}
	long long ans=(((fac[a+b]*infac[a])%MOD)*infac[b])%MOD;
	cout << ans << endl;
}
```