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

int main(){
  long long Mod=1000000007;
  long long inv[1000000+10];
  inv[0]=0;
  inv[1]=1;
  for(int i=2; i<1000000+5; i++){
    inv[i]=((Mod/i)*(Mod-inv[Mod%i]))%Mod;
  }
  long long x,y;
  cin >> x >> y;
  long long ans=0;
  if((x+y)%3==0 && x<=2*y && y<=2*x){
    long long p=(2*y-x)/3;
    long long q=(2*x-y)/3;
    ans=1;
    for(int i=1; i<=q; i++){
      ans = (ans*(i+p))%Mod;
      ans = (ans*inv[i])%Mod;
    }
  }
  printf("%d", ans);
}

### Prompt

Create a solution in cpp for 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;

int main(){
  long long Mod=1000000007;
  long long inv[1000000+10];
  inv[0]=0;
  inv[1]=1;
  for(int i=2; i<1000000+5; i++){
    inv[i]=((Mod/i)*(Mod-inv[Mod%i]))%Mod;
  }
  long long x,y;
  cin >> x >> y;
  long long ans=0;
  if((x+y)%3==0 && x<=2*y && y<=2*x){
    long long p=(2*y-x)/3;
    long long q=(2*x-y)/3;
    ans=1;
    for(int i=1; i<=q; i++){
      ans = (ans*(i+p))%Mod;
      ans = (ans*inv[i])%Mod;
    }
  }
  printf("%d", ans);
}

```