#!/usr/bin/env python3
with open('input.txt') as f:
  input_string = f.read().split('\n')

def twos_comp(num, length):
  if num == 0:
    return 0
  num ^= ((1 << length) - 1)
  return num + 1

def logical_shiftr(num, length, times):
  for t in range(times):
    num = (num >> 1) | ((1 << length) & num)
  return num

def convert_if_twoscomp(num, length):
  if num & (1 << length - 1):
    return (-1 * twos_comp(num, length))
  return num & (1 << length) - 1

def debug(multiplicand_b, multiplier_b, length):
  sign = 0
  multiplicand = convert_if_twoscomp(multiplicand_b, length)
  multiplier = convert_if_twoscomp(multiplier_b, length)
  
  result = multiplicand * multiplier
  result_bin = (twos_comp(result, length * 2), result) [result > 0]

  print("expected result:\t{}\t*\t{}\t=\t{}\t=\t{}".format(multiplicand, multiplier, bin(result_bin), multiplicand * multiplier))
  #print("booths result:\t\t{}\t*\t{}\t=\t{}".format(bin(multiplicand), bin(multiplier), bin(result_booth)))

  
def booth(multiplier, multiplicand, length):
  multiplicand_twos_comp = twos_comp(multiplicand, length)
  result = multiplier << 1 # extended bit
  for i in range(length):
    op = result & 0b11
    if op == 0b01:
      result += multiplicand << (length + 1)
    if op == 0b10:
      result += multiplicand_twos_comp << (length + 1)
    result &= (1 << (length * 2) + 1) - 1 # get rid of any overflows
    result = logical_shiftr(result, length * 2, 1)
  result = result >> 1
  return result

def booth_mod(multiplier, multiplicand, length):
  multiplicand_twos_comp = twos_comp(multiplicand, length)
  result = multiplier << 1 # extended bit
  for i in range(int(length / 2)):
    match result & 0b111:
      case 0b010 | 0b001: # add
        result += multiplicand << (length + 1)
      case 0b011:         # add * 2
        result += multiplicand << (length + 2) # extra shift is multiplying multiplicand by 2
      case 0b100:         # sub * 2
        result += multiplicand_twos_comp << (length + 2)
      case 0b101 | 0b110: # sub
        result += multiplicand_twos_comp << (length + 1)
    result &= (1 << (length * 2) + 1) - 1 # get rid of any overflows
    result = logical_shiftr(result, length * 2, 2)
  result = result >> 1
  return result




for operation in input_string:
  if operation == '' or operation[0] == '#':
    continue
  length = len(operation.split(" ")[0])
  multiplicand = int(operation.split(" ")[0], 2)
  multiplier = int(operation.split(" ")[1], 2)

  
  debug(multiplicand, multiplier, length)
  result_booth = booth(multiplier, multiplicand, length)
  result_mod_booth = booth_mod(multiplier, multiplicand, length)
  print("booths:\t\t\t", bin(result_booth))
  print("modified booths:\t", bin(result_mod_booth))