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)
mod = 1000000007
ans = 0
max_num = 1000010

class Combination_mod_p
  def initialize(mod,max_num)
    @max_num = max_num
    @mod = mod

    @fac = Array.new(@max_num,0)
    @finv = Array.new(@max_num,0)
    @inv = Array.new(@max_num,0)

    @fac[0] = @fac[1] = 1
    @finv[0] = @finv[1] = 1
    @inv[1] = 1
    (2..@max_num-1).each do |i|
      @fac[i] = @fac[i-1]*i % @mod
      @inv[i] = @mod - @inv[@mod % i] * (@mod / i) % @mod
      @finv[i] = @finv[i - 1] * @inv[i] % @mod 
    end
  end

  def com(n,k)
    return 0 if n < k || (n < 0 || k < 0)

    return @fac[n] * (@finv[k] * @finv[n-k] % @mod) % @mod
  end
end

if (-x + 2*y) % 3 == 0 && (2*x - y) % 3 == 0
  combination = Combination_mod_p.new(mod,max_num)
  r_n = (-x + 2*y)/3
  u_n = (2*x - y)/3
  sum = r_n + u_n
  if r_n > u_n
    ans = combination.com(sum,u_n)
  else
    ans = combination.com(sum,r_n)
  end
end

puts ans