code: def extended_gcd(a, b):
      
  
      old_s, s = 1, 0
      old_t, t = 0, 1
      old_r, r = a, b
      
      while r != 0:
          quotient = old_r / r
          
          old_r, r = r, old_r - quotient * r
          old_s, s = s, old_s - quotient * s
          old_t, t = t, old_t - quotient * t
      
      return old_s, old_t, old_r
docs: Extended GCD algorithm.
      Return s, t, g
      such that a * s + b * t = GCD(a, b)
      and s and t are co-prime.