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)

# frozen_string_literal: true

x, y = gets.split.map(&:to_i)

if (2 * x - y) % 3 != 0 || (-x + 2 * y) % 3 != 0
  puts 0
  exit
end

n = (2 * x - y) / 3
m = (-x + 2 * y) / 3

MOD = 10**9 + 7
N = (n + m) * 3

def ncrmod(n, r)
  return 0 if r < 0 || r > n

  r = [r, n - r].min
  $g1[n] * $g2[r] * $g2[n - r] % MOD
end

$g1 = [1, 1]
$g2 = [1, 1]
$inverse = [0, 1]

2.upto(N + 1) do |i|
  $g1.push(($g1[-1] * i) % MOD)
  $inverse.push((-$inverse[MOD % i] * (MOD / i)) % MOD)
  $g2.push(($g2[-1] * $inverse[-1]) % MOD)
end

puts ncrmod(n + m, m)