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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <math.h>

long modpow(long a, long n, long mod){
  long size;
  for (long i = 1; ; i++) {
    if (pow(2,i) > n) {
      size = i;
      break;
    }
  }
  long bit[size];
  bit[0] = n;
  for (long i = 1; i < size; i++) {
    bit[i] = bit[i-1]/2;
    bit[i-1] %= 2;
  }
  long powa[size];
  powa[0] = a;
  for (long i = 1; i < size; i++) {
    powa[i] = powa[i-1]*powa[i-1];
    powa[i] %= mod;
  }
  long answer = 1;
  for (long i = 0; i < size; i++) {
    if (bit[i] == 1) {
      answer *= bit[i]*powa[i];
      answer %= mod;
    }
  }
  return answer;
}
long modCombination(long n, long r, long mod) {
  long answer;
  if (n-r < r) {
    r = n-r;
  }
  long nu = 1;
  long de = 1;
  for (long i = 1; i <= r; i++) {
    nu *= n+1-i;
    nu %= mod;
    de *= i;
    de %= mod;
  }
  answer = nu;
  answer *= modpow(de,mod-2,mod);
  answer %= mod;
  return answer;
}

int main(void) {

  long x,y;
  scanf("%ld %ld", &x, &y);
  long mod = pow(10,9)+7;
  if ((x+y)%3 != 0) {
    printf("0\n");
    return 0;
  }
  long move = (x+y)/3;
  long move_a = y-move;
  printf("%ld\n", modCombination(move,move_a,mod));

  return 0;
}