//PDF解説に倣って
#include<bits/stdc++.h>
using namespace std;

int64_t modinv(int64_t a, int64_t m){
	int64_t b=m, u=1, v=0;
	while (b){
		int64_t t=a/b;
		a-=t*b; swap(a,b);
		u-=t*v; swap(u,v);
	}
	u%=m;
	if (u<0) u+=m;
	return u;
}

int main(){
  int x,y,M=1e9+7;
  cin>> x >> y;
  int n=(2*y-x)/3,m=(2*x-y)/3;
  if ((x+y)%3!=0 || n<0 || m<0){
    cout<< 0 <<endl;
    return 0;
  }
  int64_t a=1,b=1;
  for (int i=n+m; i>max(n,m); i--) a=a*i%M;
  for (int i=min(n,m); i>0; i--) b=b*i%M;
  cout<< a*modinv(b,M)%M <<endl;
}
//modの逆元を学んだ
### 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
//PDF解説に倣って
#include<bits/stdc++.h>
using namespace std;

int64_t modinv(int64_t a, int64_t m){
	int64_t b=m, u=1, v=0;
	while (b){
		int64_t t=a/b;
		a-=t*b; swap(a,b);
		u-=t*v; swap(u,v);
	}
	u%=m;
	if (u<0) u+=m;
	return u;
}

int main(){
  int x,y,M=1e9+7;
  cin>> x >> y;
  int n=(2*y-x)/3,m=(2*x-y)/3;
  if ((x+y)%3!=0 || n<0 || m<0){
    cout<< 0 <<endl;
    return 0;
  }
  int64_t a=1,b=1;
  for (int i=n+m; i>max(n,m); i--) a=a*i%M;
  for (int i=min(n,m); i>0; i--) b=b*i%M;
  cout<< a*modinv(b,M)%M <<endl;
}
//modの逆元を学んだ
```