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 math

def cmb(n, r, mod):
    r = min(r, n-r)

    a = 1
    b = 1
    for i in range(r):
        a = (a * (n-i)) % mod
        b = (b * (i+1)) % mod
    
    return a * pow(b, mod-2, mod) % mod

X, Y = [int(i) for i in input().split()]
mod = 10**9+7 
x_tmp = 2*X - Y
y_tmp = 2*Y - X

if x_tmp < 0 or y_tmp < 0:
    ans = 0
elif x_tmp % 3 != 0 or y_tmp % 3 != 0:
    ans = 0
else:
    x = x_tmp // 3
    y = y_tmp // 3
    ans = cmb(x + y, y, mod)

print(ans)