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 Python (3.4.3) (judge verdict: Accepted)

import math
import sys
input = sys.stdin.readline

def main():
    mod = 10 ** 9 + 7
    x, y = map(int, input().split())
    if (2 * y - x) % 3 != 0:
        print(0)
        return None

    n = (2 * y - x) // 3
    m = y - 2 * n

    if n < 0 or m < 0:
        print(0)
    elif n == 0 and m == 0:
        print(0)
    elif n == 0 or m == 0:
        print(1)
    else:
        s = n + m + 1
        f = [1] * s

        for i in range(1, s):
            f[i] = f[i-1] * i % mod

        ans = f[n+m]
        ans = ans * modinv(f[n]) % mod
        ans = ans * modinv(f[m]) % mod
        print(ans)

def modinv(a, mod=10**9+7):
    return pow(a, mod-2, mod)

if __name__ == '__main__':
    main()