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: Accepted)

#include<bits/stdc++.h>
using namespace std;
constexpr int64_t mod=1e9+7;

int64_t bin_pow(int64_t a,int64_t n)
{
  int64_t ans=1;
  while(n>0){
    if(n&1) ans=ans*a%mod;
    a=a*a%mod;
    n>>=1;
  }
  return ans%mod;
}

int64_t inv_mod(int64_t a)
{
  return bin_pow(a,mod-2);
}

int64_t fact(int64_t a)
{
  int64_t ans=1;
  for (int i = 2; i <= a; ++i)
  {
    ans*=i;
    ans%=mod;
  }
  return ans;
}

int64_t comb(int64_t n,int64_t r)
{
  return fact(n)*inv_mod(fact(r)*fact(n-r)%mod)%mod;
}

int main()
{
  int64_t x,y;
  cin>>x>>y;
  double a=(2*y-x)/3.0,b=(2*x-y)/3.0;
  if(a<0 || b<0 || (x+y)%3!=0 )
  {
    cout<<0<<endl;
    return 0;
  }
  cout<<comb((a+b),a);
}