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 (2.7.1) (judge verdict: Accepted)

MOD = 10 ** 9 + 7

x, y = gets.chomp.split.map(&:to_i)
if (2 * x - y) % 3 != 0 || (2 * y - x) % 3 != 0
  puts "0"
elsif 2 * x < y || 2 * y < x
  puts "0"
else
  h = (2 * x - y) / 3
  w = (2 * y - x) / 3
  m = 10 ** 6 - 1

  inv = Array.new(m + 1)
  m.times do |i|
    if i == 0
      inv[i + 1] = 1
    else
      inv[i + 1] = (- inv[MOD % (i + 1)] * (MOD / (i + 1))) % MOD
    end
  end
  
  r = [h, w].min
  comb = Array.new(r + 1)
  comb[0] = 1

  r.times do |i|
    comb[i + 1] = comb[i] * (h + w - i) * inv[i + 1] % MOD
  end

  puts comb[r]
end