#include <iostream>
#define M ((ull)1e9+7)
#define ull unsigned long long
using namespace std;


ull fe(ull a, ull b) {
	if (b==0) return 1;
	ull half = fe(a, b/2);
	if (b%2==0) return (half*half)%M;
	else return (((half*half)%M) * a)%M;
}

ull mm, nn, ans;
int x, y;

int main() {
	cin>>x>>y;
	if ((2*y-x)%3||x==0||y==0)cout<<0<<endl;
	else {
		int n = (2*y-x)/3, m = (2*x-y)/3;
		if (n<0 or m<0) {cout<<0<<endl; return 0;}
		mm=nn=ans=1;
		for (ull i=2; i<=n+m; i++) {
			if (i<=n) nn=(nn*i +M)%M; 
			if (i<=m) mm=(mm*i +M)%M;
			ans=(ans*i)%M;
		}
		ans = (ans * fe(nn, M-2) + M) % M;
		ans = (ans * fe(mm, M-2) + M) % M;
		cout<<(long long)ans<<endl;
	}
}
### Prompt

In CPP, your task is to solve 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 M ((ull)1e9+7)
#define ull unsigned long long
using namespace std;


ull fe(ull a, ull b) {
	if (b==0) return 1;
	ull half = fe(a, b/2);
	if (b%2==0) return (half*half)%M;
	else return (((half*half)%M) * a)%M;
}

ull mm, nn, ans;
int x, y;

int main() {
	cin>>x>>y;
	if ((2*y-x)%3||x==0||y==0)cout<<0<<endl;
	else {
		int n = (2*y-x)/3, m = (2*x-y)/3;
		if (n<0 or m<0) {cout<<0<<endl; return 0;}
		mm=nn=ans=1;
		for (ull i=2; i<=n+m; i++) {
			if (i<=n) nn=(nn*i +M)%M; 
			if (i<=m) mm=(mm*i +M)%M;
			ans=(ans*i)%M;
		}
		ans = (ans * fe(nn, M-2) + M) % M;
		ans = (ans * fe(mm, M-2) + M) % M;
		cout<<(long long)ans<<endl;
	}
}
```