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 fact(n, r):
    calc_a = 1
    calc_b = 1
    for i in range(1, r + 1):
        calc_a = (calc_a * (n + 1 - i)) % p
        calc_b = (calc_b * i) % p
    ans = (calc_a * pow(calc_b, p - 2, p)) % p
    return ans


p = (10 ** 9) + 7
x, y = map(int, input().split())
if ((2 * y - x) % 3 == 0) & ((2 * x - y) % 3 == 0) & (2 * y > x) & (2 * x > y):
    a = (2 * y - x) // 3
    b = (2 * x - y) // 3
    print(fact(a + b, min(a, b)))
else:
    print(0)