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)

import sys

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

# 直交座標に直す
if X > 2 * Y or Y > 2 * X or \
        (2 * X - Y) % 3 != 0 or (2 * Y - X) % 3 != 0:
    print(0)
    sys.exit()
x, y = (2 * X - Y) // 3, (2 * Y - X) // 3


def comb_inv(n, k, mod):
    f = [1 for _ in range(n + 1)]
    inv = [1 for _ in range(n + 1)]
    finv = [1 for _ in range(n + 1)]

    for i in range(2, n + 1):
        f[i] = f[i - 1] * i % mod
        inv[i] = mod - inv[mod % i] * (mod // i) % mod
        finv[i] = finv[i - 1] * inv[i] % mod
    return f[n] * (finv[k] * finv[n - k] % mod) % mod


print(comb_inv(x + y, x, 10 ** 9 + 7))