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)

x, y = map(int, input().split())
a = (- x + 2 * y) // 3
b = (2 * x - y) // 3
p = 1000000007
if (x + y) % 3 != 0 or a < 0 or b < 0:
    print(0)
else:
    fact = [1] * 700000
    for i in range(2, a + b + 1):
        fact[i] = fact[i - 1] * i % p

    def pow(a, n):
        if n == 0:
            return 1
        elif n == 1:
            return a
        elif n % 2 == 0:
            return pow(a, n // 2) ** 2 % p
        else:
            return a * pow(a, n // 2) ** 2 % p

    print(fact[a + b] * pow(fact[a], p - 2) * pow(fact[b], p - 2) % p)