# https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm

def extended_euclidean_gcd(a, b)

  x0, x1 = a, b
  s, t = 1, 0
  until x1.zero?
    q, x2 = x0.divmod(x1)
    x0, x1 = x1, x2
    s, t = t, s - q * t
  end
  gcd = x0
  return gcd
end

puts "GCD(3, 5) = " + extended_euclidean_gcd(3, 5).to_s
# GCD(3, 6) = 3
puts "GCD(3, 6) = " + extended_euclidean_gcd(3, 6).to_s
# GCD(3, 6) = 3
puts "GCD(6, 3) = " + extended_euclidean_gcd(6, 3).to_s
# GCD(6, 3) = 3

=begin

Dynamic driver code:

a = gets.to_i
b = gets.to_i
puts "GCD (#{a}, #{b} ) = #{extended_euclidean_gcd(a, b)}"

=end