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: Accepted)

X, Y = gets.chomp.split(" ").map(&:to_i)
ONE = '1'.freeze
MOD = (10**9) + 7

def inv(x)
    res = 1 
    beki = x
    (MOD - 2).to_s(2).reverse.chars do |digest|
      res = (beki * res) % MOD if digest == ONE
      beki = (beki * beki) % MOD
    end
    res
end

def fact(s, e)
    (s..e).reduce(1) { |r, i| (r * i) % MOD }
end

def nCk(n, k)
    (fact(k + 1, n) * inv(fact(1, n - k) % MOD)) % MOD
end

if (2 * Y - X) % 3 == 0 && (2 * X - Y) % 3 == 0 && 2 * Y >= X && 2 * X >= Y
    a = (2 * Y - X) / 3
    b = (2 * X - Y) / 3
    puts nCk(a + b, a)
else
    puts 0
end