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)

mod = 10**9 + 7


def pwr(p, q):
    if q == 1:
        return p%mod
    elif q % 2 == 0:
        return (pwr(p, q//2)%mod)**2%mod
    else:
        return (pwr(p, q//2)%mod)**2*p%mod

x, y = map(int,input().split())
if (2*x-y)%3 != 0 or (2*y-x)%3 != 0:
    print(0)
elif x == 2 and y == 1:
    print(1)
elif x == 1 and y == 2:
    print(1)
else:
    n = (2*x-y)//3
    m = (2*y-x)//3

    s1 = 1
    s2 = 1
    for i in range(m+1, n+m+1):
        s1 *= i
        s1 %= mod
    for i in range(n):
        s2 *= (i+1)
        s2 %= mod

    print(s1*pwr(s2, mod-2)%mod)