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;
const long long mod=1000000007;

long long modpow(long long a, long long n, long long mod){
  long long res =1;
  while(n>0){
    if(n &1) res= res* a % mod;
    a= a* a%mod;
    n>>=1;
  }
  return res;
}
long long modinv(long long x, long long mod){
  return modpow(x, mod -2, mod);
}

int main() {
  long long x,y;
  cin>>x>>y;
  if((x+y)%3!=0) {
    cout<<0<<endl;
    return 0;
  }
  int a,b;
  a=(-x+2*y)/3;
  b=(2*x-y)/3;
  if(a<0||b<0){
    cout<<0<<endl;
    return 0;
  }
  if(a>b) swap(a,b);
  long long ans=1;
  for(int i=a+b; i>b; i--){
    ans =ans*i%mod;
    if(ans<0) ans+=mod;
  }
  for(int i=1; i<=a; i++){
    ans =ans* modinv(i, mod)%mod;
    if(ans<0) ans+=mod;
  }
  cout<<ans<<endl;
  
}