Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

3 3

Sample Output 1

2

There are two ways: (0,0) \to (1,2) \to (3,3) and (0,0) \to (2,1) \to (3,3).

Sample Input 2

2 2

Sample Output 2

0

The knight cannot reach (2,2).

Sample Input 3

999999 999999

Sample Output 3

151840682

Print the number of ways modulo 10^9 + 7.

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
#define r(i,n) for(long long i = 0; i<n; i++)
typedef long long ll;
using namespace std;

int main() {
  ll x,y,a,b,A=1,B=1,j=2,ans=1,mod1=66666667,mod2=1000000007;
  cin >> x >>y;
  a=(2*y-x)/3;	b=(2*x-y)/3;
  r(i,a)A=A*(i+1)%mod2;
  r(i,b)B=B*(i+1)%mod2;
  if(a+2*b!=x||2*a+b!=y)cout<<0<<endl;
  else {
    r(i,a+b){
      ans*=(i+1);
      ans%=mod2;
    }
    r(i,15){
      A*=A;
      B*=B;
      A%=mod2;
      B%=mod2;
    }
    r(i,mod1){
      ans*=A;
      ans%=mod2;
      ans*=B;
      ans%=mod2;
    }
  cout<<ans<<endl;
  }
}