






"""simple docstring"""
from __future__ import annotations






def 			lowerCamelCase_    (		_lowerCamelCase							):
 for r in range(1     ,  _lowerCamelCase							):
  lowerCamelCase__	:     Tuple								=		[]
  for x in range(n - 1							):
   lowerCamelCase__	:     Any								=		pow(_lowerCamelCase     ,  _lowerCamelCase     ,  _lowerCamelCase							)
   if val in li:
    break
   li.append(_lowerCamelCase							)
  else:
   return r
 return None


if __name__ == "__main__":
      A_     :					Any							=     int(input("Enter a prime number q: "))
      A_     :					List[str]							=     find_primitive(q)
      if a is None:
            print(f"Cannot find the primitive for the value: {a!r}")
      else:
            A_     :					str							=     int(input("Enter private key of A: "))
            A_     :					List[Any]							=     pow(a, a_private, q)
            A_     :					List[str]							=     int(input("Enter private key of B: "))
            A_     :					Any							=     pow(a, b_private, q)

            A_     :					Union[str, Any]							=     pow(b_public, a_private, q)
            A_     :					Tuple							=     pow(a_public, b_private, q)

            print("The key value generated by A is: ", a_secret)
            print("The key value generated by B is: ", b_secret)


"""simple docstring"""






import numpy as np



def     a_		(   lowerCamelCase   ,     lowerCamelCase="utf-8"   ,     lowerCamelCase="surrogatepass"			):
				UpperCAmelCase__			 =				bin(int.from_bytes(text.encode(lowerCamelCase   ,     lowerCamelCase			)   ,     'big'			)			)[2:]
				return bits.zfill(8 * ((len(lowerCamelCase			) + 7) // 8)			)



def     a_		(   lowerCamelCase   ,     lowerCamelCase="utf-8"   ,     lowerCamelCase="surrogatepass"			):
				UpperCAmelCase__			 =				int(lowerCamelCase   ,     2			)
				return n.to_bytes((n.bit_length() + 7) // 8   ,     'big'			).decode(lowerCamelCase   ,     lowerCamelCase			) or "\0"



def     a_		(   lowerCamelCase   ,     lowerCamelCase			):
				if size_par + len(lowerCamelCase			) <= 2**size_par - (len(lowerCamelCase			) - 1):
								raise ValueError('size of parity don\'t match with size of data'			)

				UpperCAmelCase__			 =				[]
				UpperCAmelCase__			 =				[]
				UpperCAmelCase__			 =				[bin(lowerCamelCase			)[2:] for x in range(1   ,     size_par + len(lowerCamelCase			) + 1			)]

				# sorted information data for the size of the output data
				UpperCAmelCase__			 =				[]
				# data position template + parity
				UpperCAmelCase__			 =				[]
				# parity bit counter
				UpperCAmelCase__			 =				0
				# counter position of data bits
				UpperCAmelCase__			 =				0

				for x in range(1   ,     size_par + len(lowerCamelCase			) + 1			):
								# Performs a template of bit positions - who should be given,
								# and who should be parity
								if qtd_bp < size_par:
												if (np.log(lowerCamelCase			) / np.log(2			)).is_integer():
																data_out_gab.append('P'			)
																UpperCAmelCase__			 =				qtd_bp + 1
												else:
																data_out_gab.append('D'			)
								else:
												data_out_gab.append('D'			)

								# Sorts the data to the new output size
								if data_out_gab[-1] == "D":
												data_ord.append(data[cont_data]			)
												cont_data += 1
								else:
												data_ord.append(lowerCamelCase			)

    # Calculates parity
				UpperCAmelCase__			 =				0  # parity bit counter
				for bp in range(1   ,     size_par + 1			):
								# Bit counter one for a given parity
								UpperCAmelCase__			 =				0
								# counter to control the loop reading
								UpperCAmelCase__			 =				0
								for x in data_ord:
												if x is not None:
																try:
																				UpperCAmelCase__			 =				(bin_pos[cont_loop])[-1 * (bp)]
																except IndexError:
																				UpperCAmelCase__			 =				'0'
																if aux == "1" and x == "1":
																				cont_bo += 1
												cont_loop += 1
								parity.append(cont_bo % 2			)

								qtd_bp += 1

				# Mount the message
				UpperCAmelCase__			 =				0  # parity bit counter
				for x in range(0   ,     size_par + len(lowerCamelCase			)			):
								if data_ord[x] is None:
												data_out.append(str(parity[cont_bp]			)			)
												cont_bp += 1
								else:
												data_out.append(data_ord[x]			)

				return data_out



def     a_		(   lowerCamelCase   ,     lowerCamelCase			):
				UpperCAmelCase__			 =				[]
				# Parity bit counter
				UpperCAmelCase__			 =				0
				# Counter p data bit reading
				UpperCAmelCase__			 =				0
				# list of parity received
				UpperCAmelCase__			 =				[]
				UpperCAmelCase__			 =				[]

				for x in range(1   ,     len(lowerCamelCase			) + 1			):
								# Performs a template of bit positions - who should be given,
								#  and who should be parity
								if qtd_bp < size_par and (np.log(lowerCamelCase			) / np.log(2			)).is_integer():
												data_out_gab.append('P'			)
												UpperCAmelCase__			 =				qtd_bp + 1
								else:
												data_out_gab.append('D'			)

								# Sorts the data to the new output size
								if data_out_gab[-1] == "D":
												data_output.append(data[cont_data]			)
								else:
												parity_received.append(data[cont_data]			)
								cont_data += 1

				# -----------calculates the parity with the data
				UpperCAmelCase__			 =				[]
				UpperCAmelCase__			 =				[]
				UpperCAmelCase__			 =				[bin(lowerCamelCase			)[2:] for x in range(1   ,     size_par + len(lowerCamelCase			) + 1			)]

				#  sorted information data for the size of the output data
				UpperCAmelCase__			 =				[]
				# Data position feedback + parity
				UpperCAmelCase__			 =				[]
				# Parity bit counter
				UpperCAmelCase__			 =				0
				# Counter p data bit reading
				UpperCAmelCase__			 =				0

				for x in range(1   ,     size_par + len(lowerCamelCase			) + 1			):
								# Performs a template position of bits - who should be given,
								# and who should be parity
								if qtd_bp < size_par and (np.log(lowerCamelCase			) / np.log(2			)).is_integer():
												data_out_gab.append('P'			)
												UpperCAmelCase__			 =				qtd_bp + 1
								else:
												data_out_gab.append('D'			)

								# Sorts the data to the new output size
								if data_out_gab[-1] == "D":
												data_ord.append(data_output[cont_data]			)
												cont_data += 1
								else:
												data_ord.append(lowerCamelCase			)

    # Calculates parity
				UpperCAmelCase__			 =				0  # parity bit counter
				for bp in range(1   ,     size_par + 1			):
								# Bit counter one for a certain parity
								UpperCAmelCase__			 =				0
								# Counter to control loop reading
								UpperCAmelCase__			 =				0
								for x in data_ord:
												if x is not None:
																try:
																				UpperCAmelCase__			 =				(bin_pos[cont_loop])[-1 * (bp)]
																except IndexError:
																				UpperCAmelCase__			 =				'0'
																if aux == "1" and x == "1":
																				cont_bo += 1
												cont_loop += 1
								parity.append(str(cont_bo % 2			)			)

								qtd_bp += 1

				# Mount the message
				UpperCAmelCase__			 =				0  # Parity bit counter
				for x in range(0   ,     size_par + len(lowerCamelCase			)			):
								if data_ord[x] is None:
												data_out.append(str(parity[cont_bp]			)			)
												cont_bp += 1
								else:
												data_out.append(data_ord[x]			)

				UpperCAmelCase__			 =				parity_received == parity
				return data_output, ack



