#include<bits/stdc++.h>
using namespace std;

const int MOD=1e9+7;

long long power(long long x, long long y){
	long long ret=1;
	while(y){
		if(y&1) ret=ret*x%MOD;
		y>>=1;
		x=x*x%MOD;
	}
	return ret;
}

int main()
{
	ios_base::sync_with_stdio(0);

	int x,y;
	cin >> x >> y;
	int n = x+y;
	if(n%3){
		cout << 0 << endl;
		return 0;
	}
	if(x>y*2 || y>x*2){
		cout << 0 << endl;
		return 0;
	}
	n/=3;
	int a = y-n;
	int b = x-n;
	long long ans=1,div=1;
	for(int i=2;i<=a+b;i++)
		ans=ans*i%MOD;
	for(int i=2;i<=a;i++)
		div=div*i%MOD;
	ans=ans*power(div,MOD-2)%MOD;
	div=1;
	for(int i=2;i<=b;i++)
		div=div*i%MOD;
	ans=ans*power(div,MOD-2)%MOD;
	cout << ans << 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=1e9+7;

long long power(long long x, long long y){
	long long ret=1;
	while(y){
		if(y&1) ret=ret*x%MOD;
		y>>=1;
		x=x*x%MOD;
	}
	return ret;
}

int main()
{
	ios_base::sync_with_stdio(0);

	int x,y;
	cin >> x >> y;
	int n = x+y;
	if(n%3){
		cout << 0 << endl;
		return 0;
	}
	if(x>y*2 || y>x*2){
		cout << 0 << endl;
		return 0;
	}
	n/=3;
	int a = y-n;
	int b = x-n;
	long long ans=1,div=1;
	for(int i=2;i<=a+b;i++)
		ans=ans*i%MOD;
	for(int i=2;i<=a;i++)
		div=div*i%MOD;
	ans=ans*power(div,MOD-2)%MOD;
	div=1;
	for(int i=2;i<=b;i++)
		div=div*i%MOD;
	ans=ans*power(div,MOD-2)%MOD;
	cout << ans << endl;

	return 0;
}
```