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: Wrong Answer)

import math

def main():
    X,Y = map(int,input().split())
    MOD = 10**9+7
    K = (2*X-Y)/3
    L = (2*Y-X)/3
    if K == int(K) and L == int(L):
        A = int(K)+int(L)
        B = min(int(K),int(L))
        num = num_ = 1
        for i in range(1,B+1):
            num = num * (A+1-i) % MOD
            num_ = num_ * i % MOD
        ans = num * pow(num_,MOD-2,MOD) % MOD
        print(ans)

    else:
        print(0)

if __name__ == "__main__":
    main()