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 ModComb
  def initialize(max, mod)
    @mod = mod
    @fac = Array.new(max + 1)
    @finv = Array.new(max + 1)
    @inv = Array.new(max + 1)
    @fac[0] = @fac[1] = 1
    @finv[0] = @finv[1] = 1
    @inv[1] = 1
    (2..max).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 comb(n, k)
    return 0 if n < k
    return 0 if n < 0 || k < 0
    @fac[n] * (@finv[k] * @finv[n - k] % @mod) % @mod
  end
end

MOD = 10 ** 9 + 7
X, Y = gets.split.map(&:to_i)
max = [X, Y].max
diff = (X - Y).abs
base = max - diff * 2
if base <= 0
  puts 0
  exit 0
end
if base % 3 != 0
  puts 0
  exit 0
end
c = base / 3
k = c + diff
n = c * 2 + diff
comb = ModComb.new(n, MOD)
puts comb.comb(n, k)