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)

class Fractional
    attr_reader :mod

    def initialize(max, mod)
        @max = max
        @mod = mod
        @frac     = { 0 => 1, 1 => 1 }
        @frac_inv = { 0 => 1, 1 => 1 }
        @inv      = {         1 => 1 }

        pre_calc(max)
    end

    def pre_calc(max)
        2.upto(max) do |i|
            @frac[i] = @frac[i - 1] * i % @mod;
            @inv[i] = @mod - @inv[@mod % i] * (@mod / i) % @mod
            @frac_inv[i] = @frac_inv[i - 1] * @inv[i] % @mod
        end
    end

    def at(i)
        @frac[i]
    end

    def inv_at(i)
        @frac_inv[i]
    end
end

class Combination
  def initialize(fraction)
      @fraction = fraction
  end

  def calc(n, r)
      return 0 if n < r
      return 0 if (n < 0 || r < 0)

      denom_inv = (@fraction.inv_at(r) * @fraction.inv_at(n - r) % @fraction.mod)
      return @fraction.at(n) * denom_inv % @fraction.mod
  end
end

x, y = gets.chomp!.split(" ").map(&:to_i)
min, max = [x, y].minmax

if min * 2 < max
  puts 0
  exit 0
end

if (x + y) % 3 != 0
  puts 0
  exit 0
end

frac = Fractional.new(10 ** 6 - 1, 10 ** 9 + 7)
comb = Combination.new(frac)

p = (x + y) / 3
r = 
  if p % 2 == 0
    p / 2 - (max - min) / 2
  else
    p / 2 - ((max - min) / 2)
  end

puts comb.calc(p, r)