






__lowerCamelCase      :    int   		=   range(2, 20 + 1)
__lowerCamelCase      :    int   		=   [10**k for k in range(ks[-1] + 1)]
__lowerCamelCase      :    dict[int, dict[int, list[list[int]]]]   		=   {}







def   SCREAMING_SNAKE_CASE       (				snake_case_      :							List[Any]  ,						snake_case_      :							Optional[int]  ,						snake_case_      :							int  ,						snake_case_      :							Optional[int]     ):
	snake_case__				:   Optional[int]     =						sum(a_i[j] for j in range(snake_case_  ,						len(snake_case_     )     )     )
	snake_case__				:   Optional[Any]     =						sum(a_i[j] * base[j] for j in range(min(len(snake_case_     )  ,						snake_case_     )     )     )

	snake_case__,		snake_case__				:   Tuple     =						0, 0
	snake_case__				:   Tuple     =						n - i

	snake_case__				:   int     =						memo.get(snake_case_     )

	if sub_memo is not None:
		snake_case__				:   Tuple     =						sub_memo.get(snake_case_     )

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

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

		else:
			snake_case__				:   List[Any]     =						[]
	else:
		snake_case__				:   str     =						{c: []}
		snake_case__				:   str     =						sub_memo

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

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

	snake_case__				:   Optional[Any]     =						sub_memo[c]

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

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







def   SCREAMING_SNAKE_CASE       (				snake_case_      :							int  ,						snake_case_      :							Any  ,						snake_case_      :							str  ,						snake_case_      :							Optional[int]     ):
	if i >= n:
		return 0, i
	if k > len(snake_case_     ):
		a_i.extend([0 for _ in range(k - len(snake_case_     )     )]     )

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

	while i < n:
		i += 1
		snake_case__				:   str     =						ds_c + ds_b
		diff += addend
		snake_case__				:   Any     =						0
		for j in range(snake_case_     ):
			snake_case__				:   Optional[int]     =						a_i[j] + addend
			snake_case__,		snake_case__				:   str     =						divmod(snake_case_  ,						10     )

			ds_c += a_i[j]

		if addend > 0:
			break

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







def   SCREAMING_SNAKE_CASE       (				snake_case_      :							Optional[int]  ,						snake_case_      :							List[str]  ,						snake_case_      :							List[str]     ):
	for j in range(snake_case_  ,						len(snake_case_     )     ):
		snake_case__				:   int     =						digits[j] + addend
		if s >= 10:
			snake_case__,		snake_case__				:   List[Any]     =						divmod(snake_case_  ,						10     )
			snake_case__				:   Optional[int]     =						addend // 10 + quotient
		else:
			snake_case__				:   Optional[Any]     =						s
			snake_case__				:   Optional[Any]     =						addend // 10

		if addend == 0:
			break

	while addend > 0:
		snake_case__,		snake_case__				:   List[str]     =						divmod(snake_case_  ,						10     )
		digits.append(snake_case_     )







def   SCREAMING_SNAKE_CASE       (				snake_case_      :							int = 10**15     ):
	snake_case__				:   List[Any]     =						[1]
	snake_case__				:   int     =						1
	snake_case__				:   List[Any]     =						0
	while True:
		snake_case__,		snake_case__				:   Optional[Any]     =						next_term(snake_case_  ,						20  ,						i + dn  ,						snake_case_     )
		dn += terms_jumped
		if dn == n - i:
			break

	snake_case__				:   Union[str, Any]     =						0
	for j in range(len(snake_case_     )     ):
		a_n += digits[j] * 10**j
	return a_n


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











from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_tf_available,
    is_torch_available,
)


__lowerCamelCase      :    Tuple   		=   {
    """configuration_roberta_prelayernorm""": [
        """ROBERTA_PRELAYERNORM_PRETRAINED_CONFIG_ARCHIVE_MAP""",
        """RobertaPreLayerNormConfig""",
        """RobertaPreLayerNormOnnxConfig""",
    ],
}

try:
	if not is_torch_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	__lowerCamelCase      :    Tuple   		=   [
	    """ROBERTA_PRELAYERNORM_PRETRAINED_MODEL_ARCHIVE_LIST""",
	    """RobertaPreLayerNormForCausalLM""",
	    """RobertaPreLayerNormForMaskedLM""",
	    """RobertaPreLayerNormForMultipleChoice""",
	    """RobertaPreLayerNormForQuestionAnswering""",
	    """RobertaPreLayerNormForSequenceClassification""",
	    """RobertaPreLayerNormForTokenClassification""",
	    """RobertaPreLayerNormModel""",
	    """RobertaPreLayerNormPreTrainedModel""",
	]

try:
	if not is_tf_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	__lowerCamelCase      :    Union[str, Any]   		=   [
	    """TF_ROBERTA_PRELAYERNORM_PRETRAINED_MODEL_ARCHIVE_LIST""",
	    """TFRobertaPreLayerNormForCausalLM""",
	    """TFRobertaPreLayerNormForMaskedLM""",
	    """TFRobertaPreLayerNormForMultipleChoice""",
	    """TFRobertaPreLayerNormForQuestionAnswering""",
	    """TFRobertaPreLayerNormForSequenceClassification""",
	    """TFRobertaPreLayerNormForTokenClassification""",
	    """TFRobertaPreLayerNormMainLayer""",
	    """TFRobertaPreLayerNormModel""",
	    """TFRobertaPreLayerNormPreTrainedModel""",
	]

try:
	if not is_flax_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	__lowerCamelCase      :    List[Any]   		=   [
	    """FlaxRobertaPreLayerNormForCausalLM""",
	    """FlaxRobertaPreLayerNormForMaskedLM""",
	    """FlaxRobertaPreLayerNormForMultipleChoice""",
	    """FlaxRobertaPreLayerNormForQuestionAnswering""",
	    """FlaxRobertaPreLayerNormForSequenceClassification""",
	    """FlaxRobertaPreLayerNormForTokenClassification""",
	    """FlaxRobertaPreLayerNormModel""",
	    """FlaxRobertaPreLayerNormPreTrainedModel""",
	]


if TYPE_CHECKING:
	from .configuration_roberta_prelayernorm import (
	    ROBERTA_PRELAYERNORM_PRETRAINED_CONFIG_ARCHIVE_MAP,
	    RobertaPreLayerNormConfig,
	    RobertaPreLayerNormOnnxConfig,
	)

	try:
		if not is_torch_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_roberta_prelayernorm import (
		    ROBERTA_PRELAYERNORM_PRETRAINED_MODEL_ARCHIVE_LIST,
		    RobertaPreLayerNormForCausalLM,
		    RobertaPreLayerNormForMaskedLM,
		    RobertaPreLayerNormForMultipleChoice,
		    RobertaPreLayerNormForQuestionAnswering,
		    RobertaPreLayerNormForSequenceClassification,
		    RobertaPreLayerNormForTokenClassification,
		    RobertaPreLayerNormModel,
		    RobertaPreLayerNormPreTrainedModel,
		)

	try:
		if not is_tf_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_tf_roberta_prelayernorm import (
		    TF_ROBERTA_PRELAYERNORM_PRETRAINED_MODEL_ARCHIVE_LIST,
		    TFRobertaPreLayerNormForCausalLM,
		    TFRobertaPreLayerNormForMaskedLM,
		    TFRobertaPreLayerNormForMultipleChoice,
		    TFRobertaPreLayerNormForQuestionAnswering,
		    TFRobertaPreLayerNormForSequenceClassification,
		    TFRobertaPreLayerNormForTokenClassification,
		    TFRobertaPreLayerNormMainLayer,
		    TFRobertaPreLayerNormModel,
		    TFRobertaPreLayerNormPreTrainedModel,
		)

	try:
		if not is_flax_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_flax_roberta_prelayernorm import (
		    FlaxRobertaPreLayerNormForCausalLM,
		    FlaxRobertaPreLayerNormForMaskedLM,
		    FlaxRobertaPreLayerNormForMultipleChoice,
		    FlaxRobertaPreLayerNormForQuestionAnswering,
		    FlaxRobertaPreLayerNormForSequenceClassification,
		    FlaxRobertaPreLayerNormForTokenClassification,
		    FlaxRobertaPreLayerNormModel,
		    FlaxRobertaPreLayerNormPreTrainedModel,
		)

else:
	import sys

	__lowerCamelCase      :    Dict   		=   _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)



