



import mpmath  # for roots of unity
import numpy as np






class  SCREAMING_SNAKE_CASE      :





							def __init__( self		:		List[Any]   ,					__lowercase		:		List[str]=None   ,					__lowercase		:		Union[str, Any]=None						):

											'''simple docstring'''
											__a	  =		list(poly_a or [0]						)[:]
											__a	  =		list(poly_b or [0]						)[:]

											# Remove leading zero coefficients
											while self.polyA[-1] == 0:
															self.polyA.pop()
											__a	  =		len(self.polyA						)

											while self.polyB[-1] == 0:
															self.polyB.pop()
											__a	  =		len(self.polyB						)

											# Add 0 to make lengths equal a power of 2
											__a	  =		int(
											    2 ** np.ceil(np.loga(len(self.polyA						) + len(self.polyB						) - 1						)						)						)

											while len(self.polyA						) < self.c_max_length:
															self.polyA.append(0						)
											while len(self.polyB						) < self.c_max_length:
															self.polyB.append(0						)
											# A complex root used for the fourier transform
											__a	  =		complex(mpmath.root(x=1   ,					n=self.c_max_length   ,					k=1						)						)

											# The product
											__a	  =		self.__multiply()





							def     UpperCamelCase_       ( self		:		Optional[int]   ,					__lowercase		:		Optional[int]						):

											'''simple docstring'''
											__a	  =		[[x] for x in self.polyA] if which == """A""" else [[x] for x in self.polyB]
											# Corner case
											if len(__a						) <= 1:
															return dft[0]
											#
											__a	  =		self.c_max_length // 2
											while next_ncol > 0:
															__a	  =		[[] for i in range(__a						)]
															__a	  =		self.root**next_ncol

															# First half of next step
															__a	  =		1
															for j in range(self.c_max_length // (next_ncol * 2)						):
																			for i in range(__a						):
																							new_dft[i].append(dft[i][j] + current_root * dft[i + next_ncol][j]						)
																			current_root *= root
															# Second half of next step
															__a	  =		1
															for j in range(self.c_max_length // (next_ncol * 2)						):
																			for i in range(__a						):
																							new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j]						)
																			current_root *= root
															# Update
															__a	  =		new_dft
															__a	  =		next_ncol // 2
											return dft[0]





							def     UpperCamelCase_       ( self		:		Tuple						):

											'''simple docstring'''
											__a	  =		self.__dft("""A"""						)
											__a	  =		self.__dft("""B"""						)
											__a	  =		[[dft_a[i] * dft_b[i] for i in range(self.c_max_length						)]]
											del dft_a
											del dft_b

											# Corner Case
											if len(inverce_c[0]						) <= 1:
															return inverce_c[0]
											# Inverse DFT
											__a	  =		2
											while next_ncol <= self.c_max_length:
															__a	  =		[[] for i in range(__a						)]
															__a	  =		self.root ** (next_ncol // 2)
															__a	  =		1
															# First half of next step
															for j in range(self.c_max_length // next_ncol						):
																			for i in range(next_ncol // 2						):
																							# Even positions
																							new_inverse_c[i].append(
																							    (
																							        inverce_c[i][j]
																							        + inverce_c[i][j + self.c_max_length // next_ncol]
																							    )
																							    / 2						)
																							# Odd positions
																							new_inverse_c[i + next_ncol // 2].append(
																							    (
																							        inverce_c[i][j]
																							        - inverce_c[i][j + self.c_max_length // next_ncol]
																							    )
																							    / (2 * current_root)						)
																			current_root *= root
															# Update
															__a	  =		new_inverse_c
															next_ncol *= 2
											# Unpack
											__a	  =		[round(x[0].real   ,					8						) + round(x[0].imag   ,					8						) * 1j for x in inverce_c]

											# Remove leading 0's
											while inverce_c[-1] == 0:
															inverce_c.pop()
											return inverce_c







							def __str__( self		:		Union[str, Any]						):

											'''simple docstring'''
											__a	  =		"""A = """ + """ + """.join(
											    F"{coef}*x^{i}" for coef, i in enumerate(self.polyA[: self.len_A]						)						)
											__a	  =		"""B = """ + """ + """.join(
											    F"{coef}*x^{i}" for coef, i in enumerate(self.polyB[: self.len_B]						)						)
											__a	  =		"""A*B = """ + """ + """.join(
											    F"{coef}*x^{i}" for coef, i in enumerate(self.product						)						)

											return F"{a}\n{b}\n{c}"


# Unit tests
if __name__ == "__main__":
						import doctest

						doctest.testmod()





a_    :  Dict						  =		8.314462  # Unit - J mol-1 K-1

def      __lowercase(						UpperCAmelCase__ , UpperCAmelCase__ , UpperCAmelCase__			):


      """simple docstring"""



      if moles < 0 or kelvin < 0 or volume < 0:
            raise ValueError("Invalid inputs. Enter positive value."			)
      return moles * kelvin * UNIVERSAL_GAS_CONSTANT / volume

def      __lowercase(						UpperCAmelCase__ , UpperCAmelCase__ , UpperCAmelCase__			):


      """simple docstring"""



      if moles < 0 or kelvin < 0 or pressure < 0:
            raise ValueError("Invalid inputs. Enter positive value."			)
      return moles * kelvin * UNIVERSAL_GAS_CONSTANT / pressure


if __name__ == "__main__":
     from doctest import testmod

     testmod()