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)

X, Y = map(int,input().split())
MOD = 10 ** 9 + 7


def calc_comb(n, k, mod):
    '''
        n が大きい場合に使う
    '''
    a = 1
    b = 1
    for i in range(1,k+1):
        a *= i
        a %= mod
        b *= n
        n -= 1
        b %= mod
    return b * pow(a, mod-2, mod) % mod

if (X+Y) % 3 != 0:
    print(0)
else:
    total_move = (X+Y) // 3
    # 右に2つ動くことを選択しなければいけない回数
    right_move =  min(X,Y) - total_move
    if right_move * 2 + total_move - right_move in (X, Y):
        print(calc_comb(total_move, right_move, MOD))
    else:
        print(0)