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>
using namespace std;

long long kMod = 1e9+7;

/*
long long modinv(long long a, long long m)
{
  long long b = m;
  long long x = 1;
  long long y = 0;
  while (b != 0) {
    long long t = a /b;
    a = a - t * b;
    x = x - t * y;
    swap(a, b);
    swap(x, y);
  }
  x %= m;
  if (x < 0) {
    x += m;
  }
  assert(0 <= x);
  return x;
}
*/
long long modinv(long long a, long long m) {
  long long b = m, u = 1, v = 0;
  while (b) {
    long long t = a / b;
    a -= t * b; swap(a, b);
    u -= t * v; swap(u, v);
  }
  u %= m;
  if (u < 0) u += m;
  return u;
}

int main()
{
  long long x, y;
  cin >> x >> y;
  if ((x + y) % 3 != 0 || 2 * x < y || 2 * y < x) {
    cout << "0\n";
    return 0;
  }
  long long n = (x + y) / 3;
  long long r = n - (n / 2 + abs(x - y));
  long long res = 1;
  //cout << n << 'C' << r << '\n';
  for (long long i = 1; i <= r; i++) {
    res *= (n-i+1) % kMod;
    res %= kMod;
    res *= modinv(i, kMod);
    res %= kMod;
  }
  cout << res << '\n';
  return 0;
}