


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






def 						a__			(				A__,      A__,      A__,      A__				):
			SCREAMING_SNAKE_CASE_		:     List[Any]					=					sum(a_i[j] for j in range(A__,      len(A__				)				)				)
			SCREAMING_SNAKE_CASE_		:     Tuple					=					sum(a_i[j] * base[j] for j in range(min(len(A__				),      A__				)				)				)

			SCREAMING_SNAKE_CASE_		,      SCREAMING_SNAKE_CASE_		:     Union[str, Any]					=					0, 0
			SCREAMING_SNAKE_CASE_		:     Union[str, Any]					=					n - i

			SCREAMING_SNAKE_CASE_		:     Tuple					=					memo.get(A__				)

			if sub_memo is not None:
						SCREAMING_SNAKE_CASE_		:     str					=					sub_memo.get(A__				)

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

									if max_jump >= 0:
												SCREAMING_SNAKE_CASE_		,      SCREAMING_SNAKE_CASE_		,      SCREAMING_SNAKE_CASE_		:     Dict					=					jumps[max_jump]
												# since the difference between jumps is cached, add c
												SCREAMING_SNAKE_CASE_		:     str					=					diff + c
												for j in range(min(A__,      len(A__				)				)				):
															SCREAMING_SNAKE_CASE_		,      SCREAMING_SNAKE_CASE_		:     Tuple					=					divmod(A__,      1_0				)
												if new_c > 0:
															add(A__,      A__,      A__				)

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

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

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

			SCREAMING_SNAKE_CASE_		:     List[str]					=					sub_memo[c]

			# keep jumps sorted by # of terms skipped
			SCREAMING_SNAKE_CASE_		:     Union[str, Any]					=					0
			while j < len(A__				):
						if jumps[j][1] > dn:
									break
						j += 1

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






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

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

			while i < n:
						i += 1
						SCREAMING_SNAKE_CASE_		:     str					=					ds_c + ds_b
						diff += addend
						SCREAMING_SNAKE_CASE_		:     Optional[int]					=					0
						for j in range(A__				):
									SCREAMING_SNAKE_CASE_		:     List[Any]					=					a_i[j] + addend
									SCREAMING_SNAKE_CASE_		,      SCREAMING_SNAKE_CASE_		:     int					=					divmod(A__,      1_0				)

									ds_c += a_i[j]

						if addend > 0:
									break

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






def 						a__			(				A__,      A__,      A__				):
			for j in range(A__,      len(A__				)				):
						SCREAMING_SNAKE_CASE_		:     Optional[Any]					=					digits[j] + addend
						if s >= 1_0:
									SCREAMING_SNAKE_CASE_		,      SCREAMING_SNAKE_CASE_		:     List[Any]					=					divmod(A__,      1_0				)
									SCREAMING_SNAKE_CASE_		:     Any					=					addend // 1_0 + quotient
						else:
									SCREAMING_SNAKE_CASE_		:     Union[str, Any]					=					s
									SCREAMING_SNAKE_CASE_		:     Tuple					=					addend // 1_0

						if addend == 0:
									break

			while addend > 0:
						SCREAMING_SNAKE_CASE_		,      SCREAMING_SNAKE_CASE_		:     List[Any]					=					divmod(A__,      1_0				)
						digits.append(A__				)






def 						a__			(				A__ = 1_0**1_5				):
			SCREAMING_SNAKE_CASE_		:     int					=					[1]
			SCREAMING_SNAKE_CASE_		:     Tuple					=					1
			SCREAMING_SNAKE_CASE_		:     Dict					=					0
			while True:
						SCREAMING_SNAKE_CASE_		,      SCREAMING_SNAKE_CASE_		:     Optional[Any]					=					next_term(A__,      2_0,      i + dn,      A__				)
						dn += terms_jumped
						if dn == n - i:
									break

			SCREAMING_SNAKE_CASE_		:     Any					=					0
			for j in range(len(A__				)				):
						a_n += digits[j] * 1_0**j
			return a_n


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









from . import (
    albert,
    align,
    altclip,
    audio_spectrogram_transformer,
    auto,
    autoformer,
    bark,
    bart,
    barthez,
    bartpho,
    beit,
    bert,
    bert_generation,
    bert_japanese,
    bertweet,
    big_bird,
    bigbird_pegasus,
    biogpt,
    bit,
    blenderbot,
    blenderbot_small,
    blip,
    blip_a,
    bloom,
    bridgetower,
    byta,
    camembert,
    canine,
    chinese_clip,
    clap,
    clip,
    clipseg,
    codegen,
    conditional_detr,
    convbert,
    convnext,
    convnextva,
    cpm,
    cpmant,
    ctrl,
    cvt,
    dataavec,
    deberta,
    deberta_va,
    decision_transformer,
    deformable_detr,
    deit,
    deprecated,
    deta,
    detr,
    dialogpt,
    dinat,
    distilbert,
    dit,
    donut,
    dpr,
    dpt,
    efficientformer,
    efficientnet,
    electra,
    encodec,
    encoder_decoder,
    ernie,
    ernie_m,
    esm,
    falcon,
    flaubert,
    flava,
    fnet,
    focalnet,
    fsmt,
    funnel,
    git,
    glpn,
    gpta,
    gpt_bigcode,
    gpt_neo,
    gpt_neox,
    gpt_neox_japanese,
    gpt_swa,
    gptj,
    gptsan_japanese,
    graphormer,
    groupvit,
    herbert,
    hubert,
    ibert,
    imagegpt,
    informer,
    instructblip,
    jukebox,
    layoutlm,
    layoutlmva,
    layoutlmva,
    layoutxlm,
    led,
    levit,
    lilt,
    llama,
    longformer,
    longta,
    luke,
    lxmert,
    mam_aaa,
    marian,
    markuplm,
    maskaformer,
    maskformer,
    mbart,
    mbartaa,
    mega,
    megatron_bert,
    megatron_gpta,
    mgp_str,
    mluke,
    mobilebert,
    mobilenet_va,
    mobilenet_va,
    mobilevit,
    mobilevitva,
    mpnet,
    mra,
    mta,
    musicgen,
    mvp,
    nat,
    nezha,
    nllb,
    nllb_moe,
    nystromformer,
    oneformer,
    open_llama,
    openai,
    opt,
    owlvit,
    pegasus,
    pegasus_x,
    perceiver,
    phobert,
    pixastruct,
    plbart,
    poolformer,
    prophetnet,
    qdqbert,
    rag,
    realm,
    reformer,
    regnet,
    rembert,
    resnet,
    roberta,
    roberta_prelayernorm,
    roc_bert,
    roformer,
    rwkv,
    sam,
    segformer,
    sew,
    sew_d,
    speech_encoder_decoder,
    speech_to_text,
    speech_to_text_a,
    speechta,
    splinter,
    squeezebert,
    swiftformer,
    swin,
    swinasr,
    swinva,
    switch_transformers,
    ta,
    table_transformer,
    tapas,
    time_series_transformer,
    timesformer,
    timm_backbone,
    transfo_xl,
    trocr,
    tvlt,
    umta,
    unispeech,
    unispeech_sat,
    upernet,
    videomae,
    vilt,
    vision_encoder_decoder,
    vision_text_dual_encoder,
    visual_bert,
    vit,
    vit_hybrid,
    vit_mae,
    vit_msn,
    vivit,
    wavaveca,
    wavaveca_conformer,
    wavaveca_phoneme,
    wavaveca_with_lm,
    wavlm,
    whisper,
    x_clip,
    xglm,
    xlm,
    xlm_prophetnet,
    xlm_roberta,
    xlm_roberta_xl,
    xlnet,
    xmod,
    yolos,
    yoso,
)





