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)

require 'prime'
class NCK_mod
  def initialize(mod)
    raise "incompatible error" unless mod.prime?
    @MOD = mod
    @fac = [1,1]
    @finv = [1,1]
    @inv = [0,1]
    @n = 1
  end

  def prepare(n)
    return if @n >= n
    (@n+1..n).each{|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;
    }
    @n = n
  end

  def calc(n,k)
    raise "range error" if n < 0 || k < 0
    raise "incompatible error" if n >= @MOD
    return 0 if n < k
    prepare(n)
    return @fac[n] * (@finv[k] * @finv[n - k] % @MOD) % @MOD;
  end
end

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

kkk = [(2*x-y),(2*y-x)].min
if kkk < 0 || kkk % 3 != 0 
  p 0
  exit
end

k = kkk/3
n = (x+y)/3
nCk = NCK_mod.new(1000000007)

p nCk.calc(n,k)