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: Time Limit Exceeded)

import math

def comb(n, k, MOD, N):
    fact = [1]*(N+1)
    rfact = [1]*(N+1)
    r = 1
    for i in range(1, N+1):
        fact[i] = r = r * i % MOD
    rfact[N] = r = pow(fact[N], MOD-2, MOD)
    for i in range(N, 0, -1):
        rfact[i-1] = r = r * i % MOD
    return fact[n] * rfact[k] * rfact[n-k] % MOD

x, y = map(int, input().split())
mod = 10**9+7

diff = abs(x-y)
if (min(x, y) - diff) % 3 != 0:
    print(0)
else:
    count = (min(x, y) - diff) // 3
    print(comb(2*count+diff, count, mod, 10**7))