結果
| 問題 | No.2747 Permutation Adjacent Sum |
| ユーザー |
 tassei903
|
| 提出日時 | 2024-04-12 00:00:27 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 1,708 ms / 3,000 ms |
| コード長 | 13,833 bytes |
| コンパイル時間 | 286 ms |
| コンパイル使用メモリ | 82,304 KB |
| 実行使用メモリ | 255,180 KB |
| 最終ジャッジ日時 | 2024-04-12 00:03:24 |
| 合計ジャッジ時間 | 34,384 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge2 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 674 ms
150,356 KB |
| testcase_01 | AC | 109 ms
80,416 KB |
| testcase_02 | AC | 440 ms
125,760 KB |
| testcase_03 | AC | 107 ms
80,612 KB |
| testcase_04 | AC | 725 ms
142,872 KB |
| testcase_05 | AC | 1,708 ms
247,748 KB |
| testcase_06 | AC | 771 ms
168,276 KB |
| testcase_07 | AC | 655 ms
148,696 KB |
| testcase_08 | AC | 988 ms
173,048 KB |
| testcase_09 | AC | 1,479 ms
233,780 KB |
| testcase_10 | AC | 226 ms
94,592 KB |
| testcase_11 | AC | 681 ms
149,260 KB |
| testcase_12 | AC | 64 ms
68,696 KB |
| testcase_13 | AC | 339 ms
107,104 KB |
| testcase_14 | AC | 1,024 ms
192,172 KB |
| testcase_15 | AC | 1,495 ms
252,052 KB |
| testcase_16 | AC | 750 ms
157,008 KB |
| testcase_17 | AC | 1,345 ms
247,636 KB |
| testcase_18 | AC | 1,356 ms
185,692 KB |
| testcase_19 | AC | 161 ms
86,824 KB |
| testcase_20 | AC | 690 ms
142,960 KB |
| testcase_21 | AC | 1,083 ms
173,256 KB |
| testcase_22 | AC | 1,167 ms
210,512 KB |
| testcase_23 | AC | 574 ms
128,052 KB |
| testcase_24 | AC | 561 ms
128,248 KB |
| testcase_25 | AC | 424 ms
120,068 KB |
| testcase_26 | AC | 909 ms
166,700 KB |
| testcase_27 | AC | 1,123 ms
173,448 KB |
| testcase_28 | AC | 1,033 ms
177,684 KB |
| testcase_29 | AC | 715 ms
142,884 KB |
| testcase_30 | AC | 1,697 ms
254,920 KB |
| testcase_31 | AC | 1,692 ms
247,988 KB |
| testcase_32 | AC | 1,534 ms
248,096 KB |
| testcase_33 | AC | 1,696 ms
247,800 KB |
| testcase_34 | AC | 1,696 ms
255,180 KB |
| testcase_35 | AC | 41 ms
56,204 KB |
| testcase_36 | AC | 40 ms
55,216 KB |
| testcase_37 | AC | 41 ms
56,348 KB |
| testcase_38 | AC | 41 ms
56,916 KB |
| testcase_39 | AC | 41 ms
56,488 KB |
| testcase_40 | AC | 40 ms
55,640 KB |
| testcase_41 | AC | 40 ms
56,656 KB |
ソースコード
def Smallest_Prime_Factor(N):
"""0,1,2,...,Nの最小の素因数のリスト(0,1については1にしている)
"""
if N==0:
return [1]
N=abs(N)
L=list(range(N+1))
L[0]=L[1]=1
for x in range(4,N+1,2): L[x]=2
for x in range(9,N+1,6):
if L[x]==x: L[x]=3
x=5
Flag=0
while x*x<=N:
if L[x]==x:
y=x*x
while y<=N:
if L[y]==y:
L[y]=x
y+=x<<1
x+=2+2*Flag
Flag^=1
return L
# K乗-リスト
def Power_List(N,K,Mod):
""" i=0,1,...,N における i^K (mod Mod) のリストを求める.
[計算量] O(N log log N+pi(N) log K)
N,K,Mod: int
"""
S=Smallest_Prime_Factor(N)
A=[0]*(N+1); A[1]=pow(1,K,Mod)
for i in range(2,N+1):
if S[i]<i:
A[i]=A[S[i]]*A[i//S[i]]%Mod
else:
A[i]=pow(i,K,Mod)
return A
def Lagrange_Interpolation_Point_Arithmetic(L,a,b,X,P):
""" 法が P の下でのLagrange 補間を行い, x=X での値を返す. ただし, x_i=ai+b
[Input]
L: [y_0, ..., y_n]: F(x_i)=y_i (mod P)
X: F(X) を返す.
P: 法
[Output]
F(X)
[Complexity]
O(N+log P)
"""
d=len(L)-1
X%=P
Left=[1]*(d+1)
for i in range(d+1):
if i:
Left[i]=(Left[i-1]*(X-(a*i+b)))%P
else:
Left[i]=(X-(a*i+b))%P
Right=[1]*(d+1)
for i in range(d,-1,-1):
if i<d:
Right[i]=(Right[i+1]*(X-(a*i+b)))%P
else:
Right[i]=(X-(a*i+b))%P
fact=1
for i in range(1,d+1): fact=(fact*i)%P
Fact_inv=[1]*(d+1); Fact_inv[-1]=pow(fact,P-2,P)
for i in range(d-1,-1,-1):
Fact_inv[i]=(Fact_inv[i+1]*(i+1))%P
Y=0
coef=pow(-a,d*(P-2),P)
for i in range(d+1):
V_inv=(Fact_inv[i]*Fact_inv[d-i])%P
if i==0:
S=(Right[i+1]*V_inv)%P
elif i==d:
S=(Left[i-1]*V_inv)%P
else:
u=(Left[i-1]*Right[i+1])%P
S=(u*V_inv)%P
Y=(Y+coef*L[i]*S)%P
coef=-coef
return Y
#==================================================
# N,M,K=map(int,input().split())
# d=M+K
# Mod=10**9+7
# A=Power_List(d,K,Mod)
# for _ in range(M):
# for i in range(1,d+1):
# A[i]=(A[i]+A[i-1])%Mod
# print(Lagrange_Interpolation_Point_Arithmetic(A,1,0,N,Mod))
Mod = 998244353
b = 10**6
p = [1, 373341033, 45596018, 834980587, 623627864, 428937595, 442819817, 499710224, 833655840, 83857087, 295201906, 788488293, 671639287, 849315549, 597398273, 813259672, 732727656, 244038325, 122642896, 310517972, 160030060, 483239722, 683879839, 712910418, 384710263, 433880730, 844360005, 513089677, 101492974, 959253371, 957629942, 678615452, 34035221, 56734233, 524027922, 31729117, 102311167, 330331487, 8332991, 832392662, 545208507, 594075875, 318497156, 859275605, 300738984, 767818091, 864118508, 878131539, 316588744, 812496962, 213689172, 584871249, 980836133, 54096741, 417876813, 363266670, 335481797, 730839588, 393495668, 435793297, 760025067, 811438469, 720976283, 650770098, 586537547, 117371703, 566486504, 749562308, 708205284, 932912293, 939830261, 983699513, 206579820, 301188781, 593164676, 770845925, 247687458, 41047791, 266419267, 937835947, 506268060, 6177705, 936268003, 166873118, 443834893, 328979964, 470135404, 954410105, 117565665, 832761782, 39806322, 478922755, 394880724, 821825588, 468705875, 512554988, 232240472, 876497899, 356048018, 895187265, 808258749, 575505950, 68190615, 939065335, 552199946, 694814243, 385460530, 529769387, 640377761, 916128300, 440133909, 362216114, 826373774, 502324157, 457648395, 385510728, 904737188, 78988746, 454565719, 623828097, 686156489, 713476044, 63602402, 570334625, 681055904, 222059821, 477211096, 343363294, 833792655, 461853093, 741797144, 74731896, 930484262, 268372735, 941222802, 677432735, 474842829, 700451655, 400176109, 697644778, 390377694, 790010794, 360642718, 505712943, 946647976, 339045014, 715797300, 251680896, 70091750, 40517433, 12629586, 850635539, 110877109, 571935891, 695965747, 634938288, 69072133, 155093216, 749696762, 963086402, 544711799, 724471925, 334646013, 574791029, 722417626, 377929821, 743946412, 988034679, 405207112, 18063742, 104121967, 638607426, 607304611, 751377777, 35834555, 313632531, 18058363, 656121134, 40763559, 562910912, 495867250, 48767038, 210864657, 659137294, 715390025, 865854329, 324322857, 388911184, 286059202, 636456178, 421290700, 832276048, 726437551, 526417714, 252522639, 386147469, 674313019, 274769381, 226519400, 272047186, 117153405, 712896591, 486826649, 119444874, 338909703, 18536028, 41814114, 245606459, 140617938, 250512392, 57084755, 157807456, 261113192, 40258068, 194807105, 325341339, 884328111, 896332013, 880836012, 737358206, 202713771, 785454372, 399586250, 485457499, 640827004, 546969497, 749602473, 159788463, 159111724, 218592929, 675932866, 314795475, 811539323, 246883213, 696818315, 759880589, 4302336, 353070689, 477909706, 559289160, 79781699, 878094972, 840903973, 367416824, 973366814, 848259019, 462421750, 667227759, 897917455, 81800722, 956276337, 942686845, 420541799, 417005912, 272641764, 941778993, 217214373, 192220616, 267901132, 50530621, 652678397, 354880856, 164289049, 781023184, 105376215, 315094878, 607856504, 733905911, 457743498, 992735713, 35212756, 231822660, 276036750, 734558079, 424180850, 433186147, 308380947, 18333316, 12935086, 351491725, 655645460, 535812389, 521902115, 67016984, 48682076, 64748124, 489360447, 361275315, 786336279, 805161272, 468129309, 645091350, 887284732, 913004502, 358814684, 281295633, 328970139, 395955130, 164840186, 820902807, 761699708, 246274415, 592331769, 913846362, 866682684, 600130702, 903837674, 529462989, 90612675, 526540127, 533047427, 110008879, 674279751, 801920753, 645226926, 676886948, 752481486, 474034007, 457790341, 166813684, 287671032, 188118664, 244731384, 404032157, 269766986, 423996017, 182948540, 356801634, 737863144, 652014069, 206068022, 504569410, 919894484, 593398649, 963768176, 882517476, 702523597, 949028249, 128957299, 171997372, 50865043, 20937461, 690959202, 581356488, 369182214, 993580422, 193500140, 540665426, 365786018, 743731625, 144980423, 979536721, 773259009, 617053935, 247670131, 843705280, 30419459, 985463402, 261585206, 237885042, 111276893, 488166208, 137660292, 720784236, 244467770, 26368504, 792857103, 666885724, 670313309, 905683034, 259415897, 512017253, 826265493, 111960112, 633652060, 918048438, 516432938, 386972415, 996212724, 610073831, 444094191, 72480267, 665038087, 11584804, 301029012, 723617861, 113763819, 778259899, 937766095, 535448641, 593907889, 783573565, 673298635, 599533244, 655712590, 173350007, 868198597, 169013813, 585161712, 697502214, 573994984, 285943986, 675831407, 3134056, 965907646, 401920943, 665949756, 236277883, 612745912, 813282113, 892454686, 901222267, 624900982, 927122298, 686321335, 84924870, 927606072, 506664166, 353631992, 165913238, 566073550, 816674343, 864877926, 171259407, 908752311, 874007723, 803597299, 613676466, 880336545, 282280109, 128761001, 58852065, 474075900, 434816091, 364856903, 149123648, 388854780, 314693916, 423183826, 419733481, 888483202, 238933227, 336564048, 757103493, 100189123, 855479832, 51370348, 403061033, 496971759, 831753030, 251718753, 272779384, 683379259, 488844621, 881783783, 659478190, 445719559, 740782647, 546525906, 985524427, 548033568, 333772553, 331916427, 752533273, 730387628, 93829695, 655989476, 930661318, 334885743, 466041862, 428105027, 888238707, 232218076, 769865249, 730641039, 616996159, 231721356, 326973501, 426068899, 722403656, 742756734, 663270261, 364187931, 350431704, 671823672, 633125919, 226166717, 386814657, 237594135, 451479365, 546182474, 119366536, 465211069, 605313606, 728508871, 249619035, 663053607, 900453742, 48293872, 229958401, 62402409, 69570431, 71921532, 960467929, 537087913, 514588945, 513856225, 415497414, 286592050, 645469437, 102052166, 163298189, 873938719, 617583886, 986843080, 962390239, 580971332, 665147020, 88900164, 89866970, 826426395, 616059995, 443012312, 659160562, 229855967, 687413213, 59809521, 398599610, 325666688, 154765991, 159186619, 210830877, 386454418, 84493735, 974220646, 820097297, 2191828, 481459931, 729073424, 551556379, 926316039, 151357011, 808637654, 218058015, 786112034, 850407126, 84202800, 94214098, 30019651, 121701603, 176055335, 865461951, 553631971, 286620803, 984061713, 888573766, 302767023, 977070668, 110954576, 83922475, 51568171, 60949367, 19533020, 510592752, 615419476, 341370469, 912573425, 286207526, 206707897, 384156962, 414163604, 193301813, 749570167, 366933789, 11470970, 600191572, 391667731, 328736286, 30645366, 215162519, 604947226, 236199953, 718439098, 411423177, 803407599, 632441623, 766760224, 263006576, 757681534, 61082578, 681666415, 947466395, 12206799, 659767098, 933746852, 978860867, 59215985, 161179205, 439197472, 259779111, 511621808, 145770512, 882749888, 943124465, 872053396, 631078482, 166861622, 743415395, 772287179, 602427948, 924112080, 385643091, 794973480, 883782693, 869723371, 805963889, 313106351, 262132854, 400034567, 488248149, 265769800, 791715397, 408753255, 468381897, 415812467, 172922144, 64404368, 281500398, 512318142, 288791777, 955559118, 242484726, 536413695, 205340854, 707803527, 576699812, 218525078, 875554190, 46283078, 833841915, 763148293, 807722138, 788080170, 556901372, 150896699, 253151120, 97856807, 918256774, 771557187, 582547026, 472709375, 911615063, 743371401, 641382840, 446540967, 184639537, 157247760, 775930891, 939702814, 499082462, 19536133, 548753627, 593243221, 563850263, 185475971, 687419227, 396799323, 657976136, 864535682, 433009242, 860830935, 33107339, 517661450, 467651311, 812398757, 202133852, 431839017, 709549400, 99643620, 773282878, 290471030, 61134552, 129206504, 929147251, 837008968, 422332597, 353775281, 469563025, 62265336, 835064501, 851685235, 21197005, 264793769, 326416680, 118842991, 84257200, 763248924, 687559609, 150907932, 401832452, 242726978, 766752066, 959173604, 390269102, 992293822, 744816299, 476631694, 177284763, 702429415, 374065901, 169855231, 629007616, 719169602, 564737074, 475119050, 714502830, 40993711, 820235888, 749063595, 239329111, 612759169, 18591377, 419142436, 442202439, 941600951, 158013406, 637073231, 471564060, 447222237, 701248503, 599797734, 577221870, 69656699, 51052704, 6544303, 10958310, 554955500, 943192237, 192526269, 897983911, 961628039, 240232720, 627280533, 710239542, 70255649, 261743865, 228474833, 776408079, 304180483, 63607040, 953297493, 758058902, 395529997, 156010331, 825833840, 539880795, 234683685, 52626619, 751843490, 116909119, 62806842, 574857555, 353417551, 40061330, 822203768, 681051568, 490913702, 9322961, 766631257, 124794668, 37844313, 163524507, 729108319, 490867505, 47035168, 682765157, 53842115, 817965276, 757179922, 339238384, 909741023, 150530547, 158444563, 140949492, 993302799, 551621442, 137578883, 475122706, 443869843, 605400098, 689361523, 769596520, 801661499, 474900284, 586624857, 349960501, 134084537, 650564083, 877097974, 379857427, 887890124, 159436401, 133274277, 986182139, 729720334, 568925901, 459461496, 499309445, 493171177, 460958750, 380694152, 168836226, 840160881, 141116880, 225064950, 109618190, 842341383, 85305729, 759273275, 97369807, 669317759, 766247510, 829017039, 550323884, 261274540, 918239352, 29606025, 870793828, 293683814, 378510746, 367270918, 481292028, 813097823, 798448487, 230791733, 899305835, 504040630, 162510533, 479367951, 275282274, 806951470, 462774647, 56473153, 184659008, 905122161, 664034750, 109726629, 59372704, 325795100, 486860143, 843736533, 924723613, 880348000, 801252478, 616515290, 776142608, 284803450, 583439582, 274826676, 6018349, 377403437, 244041569, 527081707, 544763288, 708818585, 354033051, 904309832, 589922898, 673933870, 682858433, 945260111, 899893421, 515264973, 911685911, 9527148, 239480646, 524126897, 48259065, 578214879, 118677219, 786127243, 869205770, 923276513, 937928886, 802186160, 12198440, 638784295, 34200904, 758925811, 185027790, 80918046, 120604699, 610456697, 573601211, 208296321, 49743354, 653691911, 490750754, 674335312, 887877110, 875880304, 308360096, 414636410, 886100267, 8525751, 636257427, 558338775, 500159951, 696213291, 97268896, 364983542, 937928436, 641582714, 586211304, 345265657, 994704486, 443549763, 207259440, 302122082, 166055224, 623250998, 239642551, 476337075, 283167364, 211328914, 68064804, 950202136, 187552679, 18938709, 646784245, 598764068, 538505481, 610424991, 864445053, 390248689, 278395191, 686098470, 935957187, 868529577, 329970687, 804930040, 84992079, 474569269, 810762228, 573258936, 756464212, 155080225, 286966169, 283614605, 19283401, 24257676, 871831819, 612689791, 846988741, 617120754, 971716517, 979541482, 297910784, 991087897, 783825907, 214821357, 689498189, 405026419, 946731704, 609346370, 707669156, 457703127, 957341187, 980735523, 649367684, 791011898, 82098966, 234729712, 105002711, 130614285, 291032164, 193188049, 363211260, 58108651, 100756444, 954947696, 346032213, 863300806, 36876722, 622610957, 289232396, 667938985, 734886266, 395881057, 417188702, 183092975, 887586469, 83334648, 797819763, 100176902, 781587414, 841864935, 371674670, 18247584, 0, 0, 0, 0, 0, 0, 0]
def fact(n):
N = n//b
res = p[N]
for i in range(N*b+1,n+1):
res *= i
res %= Mod
return res
N, K = list(map(int, input().split()))
A = []
for i in range(K+3):
A.append(pow(i, K, Mod))
from itertools import accumulate
A = list(accumulate(A))
R1 = Lagrange_Interpolation_Point_Arithmetic(A, 1, 0, N, Mod)
B = []
for i in range(K+3):
B.append(pow(i, K+1, Mod))
B = list(accumulate(B))
R2 = Lagrange_Interpolation_Point_Arithmetic(B, 1, 0, N, Mod)
print(2 * (R1*N%Mod - R2) * fact(N-1) % Mod)