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)

def nCk(n, k, mod=10 ** 9 + 7):
    def xgcd(a, b):
        if b == 0:
            return (a, 1, 0)
        g, x, y = xgcd(b, a % b)
        return (g, y, x - (a // b) * y)
    p, q = 1, 1
    for i in range(n - k + 1, n + 1):
        p = (p * i) % mod
    for i in range(2, k + 1):
        q = (q * i) % mod
    return p * (xgcd(q, mod)[1] % mod) % mod


X, Y = map(int, input().split())

b = (2 * X - Y) // 3
a = (-X + 2 * Y) // 3

if X % 3 != 0 or Y % 3 != 0 or a < 0 or b < 0:
    print(0)
else:
    print(nCk(a + b, a))