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: Wrong Answer)

class Combi
  def initialize(max_n, mod = 10**9+7)
    @mod = mod
    @max_n = max_n
 
    @fac = Array.new(@max_n+1)
    @inv = Array.new(@max_n+1)
    @finv = Array.new(@max_n+1)
 
    @fac[0] = @fac[1] = 1
    @inv[1] = 1
    @finv[0] = @finv[1] = 1
    2.upto(@max_n) 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 nCk(n,k)
    @fac[n] * @finv[n - k] * @finv[k] % @mod
  end
end
 
x, y = gets.chomp.split.map(&:to_i)
 
x,y=y,x if x < y #=> y < x
 
if (x + y)%3!=0 || x/y > 2
  puts 0
  exit
end
 
layer = (x + y) / 3
num = x - layer
 
# p ['l', layer, num]
 
combi = Combi.new(10**6*3)
puts combi.nCk(layer, num)