



a_						:     Tuple	     =		range(2, 2_0 + 1)
a_						:     Dict	     =		[1_0**k for k in range(ks[-1] + 1)]
a_						:     dict[int, dict[int, list[list[int]]]]	     =		{}

def     __lowercase(	UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__ ):


      """simple docstring"""



      lowerCamelCase								=		sum(a_i[j] for j in range(_UpperCAmelCase   ,   len(_UpperCAmelCase ) ) )
      lowerCamelCase								=		sum(a_i[j] * base[j] for j in range(min(len(_UpperCAmelCase )   ,   _UpperCAmelCase ) ) )

      lowerCamelCase			,							lowerCamelCase								=		0, 0
      lowerCamelCase								=		n - i

      lowerCamelCase								=		memo.get(_UpperCAmelCase )

      if sub_memo is not None:
            lowerCamelCase								=		sub_memo.get(_UpperCAmelCase )

            if jumps is not None and len(_UpperCAmelCase ) > 0:
                  # find and make the largest jump without going over
                  lowerCamelCase								=		-1
                  for _k in range(len(_UpperCAmelCase ) - 1   ,   -1   ,   -1 ):
                        if jumps[_k][2] <= k and jumps[_k][1] <= max_dn:
                              lowerCamelCase								=		_k
                              break

                  if max_jump >= 0:
                        lowerCamelCase			,							lowerCamelCase			,							lowerCamelCase								=		jumps[max_jump]
                        # since the difference between jumps is cached, add c
                        lowerCamelCase								=		diff + c
                        for j in range(min(_UpperCAmelCase   ,   len(_UpperCAmelCase ) ) ):
                              lowerCamelCase			,							lowerCamelCase								=		divmod(_UpperCAmelCase   ,   10 )
                        if new_c > 0:
                              add(_UpperCAmelCase   ,   _UpperCAmelCase   ,   _UpperCAmelCase )

            else:
                  lowerCamelCase								=		[]
      else:
            lowerCamelCase								=		{c: []}
            lowerCamelCase								=		sub_memo

      if dn >= max_dn or c + diff >= base[k]:
            return diff, dn

      if k > ks[0]:
            while True:
                  # keep doing smaller jumps
                  lowerCamelCase			,							lowerCamelCase								=		next_term(_UpperCAmelCase   ,   k - 1   ,   i + dn   ,   _UpperCAmelCase )
                  diff += _diff
                  dn += terms_jumped

                  if dn >= max_dn or c + diff >= base[k]:
                        break
      else:
            # would be too small a jump, just compute sequential terms instead
            lowerCamelCase			,							lowerCamelCase								=		compute(_UpperCAmelCase   ,   _UpperCAmelCase   ,   i + dn   ,   _UpperCAmelCase )
            diff += _diff
            dn += terms_jumped

      lowerCamelCase								=		sub_memo[c]

      # keep jumps sorted by # of terms skipped
      lowerCamelCase								=		0
      while j < len(_UpperCAmelCase ):
            if jumps[j][1] > dn:
                  break
            j += 1

      # cache the jump for this value digitsum(b) and c
      sub_memo[c].insert(_UpperCAmelCase   ,   (diff, dn, k) )
      return (diff, dn)

def     __lowercase(	UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__ ):


      """simple docstring"""



      if i >= n:
            return 0, i
      if k > len(_UpperCAmelCase ):
            a_i.extend([0 for _ in range(k - len(_UpperCAmelCase ) )] )

      # note: a_i -> b * 10^k + c
      # ds_b -> digitsum(b)
      # ds_c -> digitsum(c)
      lowerCamelCase								=		i
      lowerCamelCase			,							lowerCamelCase			,							lowerCamelCase								=		0, 0, 0
      for j in range(len(_UpperCAmelCase ) ):
            if j >= k:
                  ds_b += a_i[j]
            else:
                  ds_c += a_i[j]

      while i < n:
            i += 1
            lowerCamelCase								=		ds_c + ds_b
            diff += addend
            lowerCamelCase								=		0
            for j in range(_UpperCAmelCase ):
                  lowerCamelCase								=		a_i[j] + addend
                  lowerCamelCase			,							lowerCamelCase								=		divmod(_UpperCAmelCase   ,   10 )

                  ds_c += a_i[j]

            if addend > 0:
                  break

      if addend > 0:
            add(_UpperCAmelCase   ,   _UpperCAmelCase   ,   _UpperCAmelCase )
      return diff, i - start_i

def     __lowercase(	UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__ ):


      """simple docstring"""



      for j in range(_UpperCAmelCase   ,   len(_UpperCAmelCase ) ):
            lowerCamelCase								=		digits[j] + addend
            if s >= 10:
                  lowerCamelCase			,							lowerCamelCase								=		divmod(_UpperCAmelCase   ,   10 )
                  lowerCamelCase								=		addend // 10 + quotient
            else:
                  lowerCamelCase								=		s
                  lowerCamelCase								=		addend // 10

            if addend == 0:
                  break

      while addend > 0:
            lowerCamelCase			,							lowerCamelCase								=		divmod(_UpperCAmelCase   ,   10 )
            digits.append(_UpperCAmelCase )

def     __lowercase(	UpperCAmelCase__ = 10**15 ):


      """simple docstring"""



      lowerCamelCase								=		[1]
      lowerCamelCase								=		1
      lowerCamelCase								=		0
      while True:
            lowerCamelCase			,							lowerCamelCase								=		next_term(_UpperCAmelCase   ,   20   ,   i + dn   ,   _UpperCAmelCase )
            dn += terms_jumped
            if dn == n - i:
                  break

      lowerCamelCase								=		0
      for j in range(len(_UpperCAmelCase ) ):
            a_n += digits[j] * 10**j
      return a_n


if __name__ == "__main__":
     print(f"""{solution() = }""")











import os
import unicodedata
from shutil import copyfile
from typing import Any, Dict, List, Optional, Tuple

import sentencepiece as spm

from ...tokenization_utils import AddedToken, PreTrainedTokenizer
from ...utils import SPIECE_UNDERLINE, logging


a_						:     int	     =		logging.get_logger(__name__)

a_						:     List[str]	     =		{'vocab_file': 'spiece.model'}

a_						:     Optional[Any]	     =		{
    'vocab_file': {
        'TsinghuaAI/CPM-Generate': 'https://huggingface.co/TsinghuaAI/CPM-Generate/resolve/main/spiece.model',
    }
}





class    lowerCamelCase__  (						UpperCAmelCase_):
     """simple docstring"""



     def __init__(self				,			__a				,			__a=False				,			__a=True				,			__a=False				,			__a="<s>"				,			__a="</s>"				,			__a="<unk>"				,			__a="<sep>"				,			__a="<pad>"				,			__a="<cls>"				,			__a="<mask>"				,			__a=["<eop>", "<eod>"]				,			__a = None				,			**__a				,			):






           '''simple docstring'''



           lowerCamelCase								=		AddedToken(__a				,			lstrip=__a				,			rstrip=__a    ) if isinstance(__a				,			__a    ) else mask_token

           lowerCamelCase								=		{} if sp_model_kwargs is None else sp_model_kwargs

           super().__init__(
               do_lower_case=__a				,			remove_space=__a				,			keep_accents=__a				,			bos_token=__a				,			eos_token=__a				,			unk_token=__a				,			sep_token=__a				,			pad_token=__a				,			cls_token=__a				,			mask_token=__a				,			additional_special_tokens=__a				,			sp_model_kwargs=self.sp_model_kwargs				,			**__a				,			)

           lowerCamelCase								=		3

           lowerCamelCase								=		do_lower_case
           lowerCamelCase								=		remove_space
           lowerCamelCase								=		keep_accents
           lowerCamelCase								=		vocab_file

           lowerCamelCase								=		spm.SentencePieceProcessor(**self.sp_model_kwargs    )
           self.sp_model.Load(__a    )

           try:
                 import jieba
           except ModuleNotFoundError as error:
                 raise error.__class__(
                     "You need to install jieba to use CpmTokenizer or CpmTokenizerFast. "
                     "See https://pypi.org/project/jieba/ for installation."    )
           lowerCamelCase								=		jieba
           lowerCamelCase								=		str.maketrans(" \n"				,			"\u2582\u2583"    )







     @property
     # Copied from transformers.models.xlnet.tokenization_xlnet.XLNetTokenizer.vocab_size
     def 						_a      (self    ):






           '''simple docstring'''



           return len(self.sp_model    )







     def 						_a      (self    ):






           '''simple docstring'''



           lowerCamelCase								=		{self.convert_ids_to_tokens(__a    ): i for i in range(self.vocab_size    )}
           vocab.update(self.added_tokens_encoder    )
           return vocab







     def __getstate__(self    ):






           '''simple docstring'''



           lowerCamelCase								=		self.__dict__.copy()
           lowerCamelCase								=		None
           return state







     def __setstate__(self				,			__a    ):






           '''simple docstring'''



           lowerCamelCase								=		d

           # for backward compatibility
           if not hasattr(self				,			"sp_model_kwargs"    ):
                 lowerCamelCase								=		{}

           lowerCamelCase								=		spm.SentencePieceProcessor(**self.sp_model_kwargs    )
           self.sp_model.Load(self.vocab_file    )







     def 						_a      (self				,			__a    ):






           '''simple docstring'''



           if self.remove_space:
                 lowerCamelCase								=		" ".join(inputs.strip().split()    )
           else:
                 lowerCamelCase								=		inputs
           lowerCamelCase								=		outputs.replace("``"				,			"\""    ).replace("''"				,			"\""    )

           if not self.keep_accents:
                 lowerCamelCase								=		unicodedata.normalize("NFKD"				,			__a    )
                 lowerCamelCase								=		"".join([c for c in outputs if not unicodedata.combining(__a    )]    )
           if self.do_lower_case:
                 lowerCamelCase								=		outputs.lower()

           return outputs







     def 						_a      (self				,			__a    ):






           '''simple docstring'''



           lowerCamelCase								=		self.preprocess_text(__a    )
           lowerCamelCase								=		self.sp_model.encode(__a				,			out_type=__a    )
           lowerCamelCase								=		[]
           for piece in pieces:
                 if len(__a    ) > 1 and piece[-1] == str(","    ) and piece[-2].isdigit():
                       lowerCamelCase								=		self.sp_model.EncodeAsPieces(piece[:-1].replace(__a				,			""    )    )
                       if piece[0] != SPIECE_UNDERLINE and cur_pieces[0][0] == SPIECE_UNDERLINE:
                             if len(cur_pieces[0]    ) == 1:
                                   lowerCamelCase								=		cur_pieces[1:]
                             else:
                                   lowerCamelCase								=		cur_pieces[0][1:]
                       cur_pieces.append(piece[-1]    )
                       new_pieces.extend(__a    )
                 else:
                       new_pieces.append(__a    )

           return new_pieces







     def 						_a      (self				,			__a    ):






           '''simple docstring'''



           return self.sp_model.PieceToId(__a    )







     def 						_a      (self				,			__a    ):






           '''simple docstring'''



           return self.sp_model.IdToPiece(__a    )







     def 						_a      (self				,			__a    ):






           '''simple docstring'''



           lowerCamelCase								=		"".join(__a    ).replace(__a				,			" "    ).strip()
           return out_string







     def 						_a      (self				,			__a				,			__a = None    ):






           '''simple docstring'''



           lowerCamelCase								=		[self.sep_token_id]
           lowerCamelCase								=		[self.cls_token_id]
           if token_ids_a is None:
                 return token_ids_a + sep + cls
           return token_ids_a + sep + token_ids_a + sep + cls







     def 						_a      (self				,			__a				,			__a = None				,			__a = False    ):






           '''simple docstring'''



           if already_has_special_tokens:
                 return super().get_special_tokens_mask(
                     token_ids_a=__a				,			token_ids_a=__a				,			already_has_special_tokens=__a    )

           if token_ids_a is not None:
                 return ([0] * len(__a    )) + [1] + ([0] * len(__a    )) + [1, 1]
           return ([0] * len(__a    )) + [1, 1]







     def 						_a      (self				,			__a				,			__a = None    ):






           '''simple docstring'''



           lowerCamelCase								=		[self.sep_token_id]
           lowerCamelCase								=		[2]

           if token_ids_a is None:
                 return len(token_ids_a + sep    ) * [0] + cls_segment_id
           return len(token_ids_a + sep    ) * [0] + len(token_ids_a + sep    ) * [1] + cls_segment_id







     def 						_a      (self				,			__a				,			__a = None    ):






           '''simple docstring'''



           if not os.path.isdir(__a    ):
                 logger.error(F"""Vocabulary path ({save_directory}) should be a directory"""    )
                 return
           lowerCamelCase								=		os.path.join(
               __a				,			(filename_prefix + "-" if filename_prefix else "") + VOCAB_FILES_NAMES["vocab_file"]    )

           if os.path.abspath(self.vocab_file    ) != os.path.abspath(__a    ) and os.path.isfile(self.vocab_file    ):
                 copyfile(self.vocab_file				,			__a    )
           elif not os.path.isfile(self.vocab_file    ):
                 with open(__a				,			"wb"    ) as fi:
                       lowerCamelCase								=		self.sp_model.serialized_model_proto()
                       fi.write(__a    )

           return (out_vocab_file,)







     def 						_a      (self				,			*__a				,			**__a    ):






           '''simple docstring'''



           lowerCamelCase								=		super()._decode(*__a				,			**__a    )
           lowerCamelCase								=		text.replace(" "				,			""    ).replace("\u2582"				,			" "    ).replace("\u2583"				,			"\n"    )
           return text