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

int mod = 1000000007;

int mul(int x, int y){
	return (1ll*x*y)%mod;
}

int fact(int x){
	long long ret = 1;
	for(int i = 2; i<=x;i++)
		ret = (ret * i)%mod;
	return ret;
}

int power(int a, int p){
	if(p == 0)	return 1;
	int ret = power(a, p/2);
	ret = mul(ret, ret);
	if(p%2)	ret = mul(ret, a);
	return ret;
}

int inv(int a){
	return power(a, mod-2);
}

int main() {
	int x, y;
	cin>>x>>y;
	if((2*x - y)%3 != 0 || (2*y-x)%3 != 0 || 2*x < y || 2*y < x){
		cout<<0;
		return 0;
	}
	int b = (2*x-y)/3;
	int a = (2*y-x)/3;
	cout<<mul(fact(a+b),mul(inv(fact(a)),inv(fact(b))));
	return 0;
}
### Prompt

Construct a Cpp code solution to the problem outlined:

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;

int mod = 1000000007;

int mul(int x, int y){
	return (1ll*x*y)%mod;
}

int fact(int x){
	long long ret = 1;
	for(int i = 2; i<=x;i++)
		ret = (ret * i)%mod;
	return ret;
}

int power(int a, int p){
	if(p == 0)	return 1;
	int ret = power(a, p/2);
	ret = mul(ret, ret);
	if(p%2)	ret = mul(ret, a);
	return ret;
}

int inv(int a){
	return power(a, mod-2);
}

int main() {
	int x, y;
	cin>>x>>y;
	if((2*x - y)%3 != 0 || (2*y-x)%3 != 0 || 2*x < y || 2*y < x){
		cout<<0;
		return 0;
	}
	int b = (2*x-y)/3;
	int a = (2*y-x)/3;
	cout<<mul(fact(a+b),mul(inv(fact(a)),inv(fact(b))));
	return 0;
}
```