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<iostream>
#include<vector>

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;
}

// a^{-1} mod を計算する
long long modinv(long long a, long long mod) {
  return modpow(a, mod - 2, mod);
}

long long int combination(long long int n, long long int r) {
  if ( r * 2 > n ) r = n - r;
  long long int dividend = 1;
  long long int  divisor  = 1;
  for ( long long  int i = 1; i <= r; ++i ) {
    dividend *= (n-i+1);
    divisor  *= modinv(i, 1000000007);
    divisor  = divisor%(1000000007);
    dividend = dividend%(1000000007);
    //divisor = modinv(divisor, 1000000007);
  }
  //std::cout << divisor << " "<<dividend<<std::endl;
  return dividend * divisor % 1000000007;
}

int main(void){
  long long int X, Y;
  std::cin >> X >>Y;
  long long int Z=X+Y;
  long long int turn =Z/3;
  if(Z%3!=0){
    std::cout << 0;
    return 0;
  }else if(X<turn||Y<turn){
    std::cout << 0;
    return 0;    
  }
  //std::vector<std::vector<long long int> > v=comb(turn, Y-turn);
  std::cout << combination(turn,Y-turn);
  return 0; 
}