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)

import numpy as np
MOD = 10**9 + 7
def extgcd(a, b):
    r = np.array([1,0,a], dtype=int)
    w = np.array([0,1,b], dtype=int)
    while w[2] != 1:
        q = r[2] // w[2]
        r, w = w, r - q*w
    return w[:2]

def mod_inverse(a, m):
    x, y = extgcd(a, m)
    return (m + x % m) % m

def solve(x, y):
    a = -y + 2*x
    b = 2*y - x
    if a % 3 != 0:
        return 0
    if b % 3 != 0:
        return 0
    a //= 3
    b //= 3
    n, k = a+b, a
    p, q = 1, 1
    for i in range(k):
        p = p * (n-i) % MOD
        q = q * (i+1) % MOD
    return (p * mod_inverse(q, MOD)) % MOD

x, y = map(int, input().split())
print(solve(x, y))