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 Ruby (2.3.3) (judge verdict: Runtime Error)

require 'openssl'
X, Y = gets.split.map(&:to_i)

num_moves = (X+Y)/3

for i in 0..num_moves
    if [X, Y] == [i + 2 * (num_moves - i), (num_moves - i) + 2 * i]
        num_a = i
        break
    end
end

if !num_a || (X + Y) % 3 != 0
    p 0
    exit
end

a = ((num_a + 1)..(num_moves)).inject{|prod, n| prod * n % (10**9+7)}
b = (1..(num_moves - num_a)).inject{|prod, n| prod * n % (10**9+7)}
p a * OpenSSL::BN.new(b).mod_inverse(10**9+7) % (10**9+7)