old_contents: def gcf(a, b):
      while b:
          a, b = b, a % b
  
      return a
  
  
  def xgcf(a, b):
      s1, s2 = 1, 0
      t1, t2 = 0, 1
  
      while b:
          q, r = divmod(a, b)
          a, b = b, r
          s2, s1 = s1 - q * s2, s2
          t2, t1 = t1 - q * t2, t2
  
      return a, s1, t1
  
new_contents: def gcf(a, b):
      while b:
          a, b = b, a % b
  
      return a
  
  
  def xgcf(a, b):
      s1, s2 = 1, 0
      t1, t2 = 0, 1
  
      while b:
          q, r = divmod(a, b)
          a, b = b, r
          s2, s1 = s1 - q * s2, s2
          t2, t1 = t1 - q * t2, t2
  
      # Bézout's identity says: s1 * a + t1 * b == gcd(a, b)
      return a, s1, t1
  
subject: Add Bézout's identity into comments