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)

def powermod(a, p, mod):
    if p == 0:
        return 1
    elif p % 2 == 0:
        return (powermod(a, p//2, mod) ** 2) % mod
    else:
        return ((powermod(a, (p-1)//2, mod) ** 2) % mod) * a % mod

def combinationmod(n,r):
    if r == 0 or n == r:
        return 1
    mod = 10 ** 9 + 7
    factorial = 1
    for i in range(n):
        factorial = (factorial * (i+1)) % mod
        if i+1 == r:
            fact_1 = factorial
        if i+1 == n-r:
            fact_2 = factorial
        if i+1 == n:
            fact_0 = factorial
    return fact_0 * powermod(fact_1,mod-2,mod) % mod * powermod(fact_2,mod-2,mod) % mod
    
X,Y = map(int,input().split())
if (X + Y) % 3 == 0 and X <= 2 * Y and 2 * X >= Y:
    turns = (X + Y) // 3
    print(combinationmod(turns, min(X,Y) - turns))
else:
    print(0)