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ID题目提交者结果用时内存语言文件大小提交时间测评时间
#62261#5031. 核Appleblue17100 ✓1912ms355032kbC++141.6kb2022-11-17 18:47:032022-11-17 18:47:06

Judging History

你现在查看的是最新测评结果

  • [2023-08-10 23:21:45]
  • System Update: QOJ starts to keep a history of the judgings of all the submissions.
  • [2022-11-17 18:47:06]
  • 评测
  • 测评结果:100
  • 用时:1912ms
  • 内存:355032kb
  • [2022-11-17 18:47:03]
  • 提交

answer

#include<bits/stdc++.h>
using namespace std;
const int N=1e7+5,M=1e5+5;
int n,q,mod,ans,B;
int ksm(int a,int x,int p=mod){
	int tot=1;
	while(x){
		if(x & 1ll) tot=1ll*tot*a%p;
		a=1ll*a*a%p;
		x>>=1ll;
	}
	return tot;
}
int pw[N],ipw[N],PW[N],mul,inv[N];
int pw_nk[N],ipw_knk[N],pw_nnkk[N];
int pow0[M],pow1[M];
void init(int lim){
	int invq=ksm(q,mod-2);
	
	pw[0]=ipw[0]=1;
	for(int i=1;i<=lim;i++) pw[i]=1ll*pw[i-1]*q%mod;
	for(int i=1;i<=lim;i++) ipw[i]=1ll*ipw[i-1]*invq%mod;
	
	int pwn=ksm(q,n,mod-1);
	pw_nk[0]=1;
	for(int i=1;i<=lim;i++) pw_nk[i]=1ll*pw_nk[i-1]*pwn%(mod-1);
	
	ipw_knk[0]=1;
	for(int i=1;i<=lim;i++) ipw_knk[i]=1ll*ipw_knk[i-1]*ipw[n]%mod*pw[i-1]%mod*pw[i-1]%mod;
	
	pw_nnkk[0]=ksm(q,1ll*n*(n-1)/2%(mod-1));
	for(int i=1;i<=lim;i++) pw_nnkk[i]=1ll*pw_nnkk[i-1]*ipw[i-1]%mod;
	
	for(int i=1;i<=lim;i++) PW[i]=1+mod-pw[i];
	
	mul=1;
	inv[0]=1;
	for(int i=1;i<=lim;i++) mul=1ll*mul*PW[i]%mod;
	inv[lim]=ksm(mul,mod-2);
	for(int i=lim-1;i>=1;i--) inv[i]=1ll*inv[i+1]*PW[i+1]%mod;
	
	B=ceil(sqrt(mod));
	pow0[0]=pow1[0]=1;
	for(int i=1;i<=B;i++) pow0[i]=1ll*pow0[i-1]*3%mod;
	for(int i=1;i<=B;i++) pow1[i]=1ll*pow1[i-1]*pow0[B]%mod;
}

int f[N],g[N];

int main(){
	cin>>n>>q>>mod;
	init(n);
	g[0]=1;
	for(int k=1;k<=n;k++){
		g[k]=(1ll*g[k-1]*(1+mod-ipw[n-k+1])+1ll*ipw_knk[k]*inv[k])%mod;
	}
	
	for(int k=0;k<=n;k++){
		if((n-k) & 1) f[k]=mod-1ll*g[n-k]*inv[k]%mod*pw_nnkk[k]%mod;
		else f[k]=1ll*g[n-k]*inv[k]%mod*pw_nnkk[k]%mod;
	}
	for(int i=0;i<=n;i++) ans=(ans+1ll*f[i]*pow0[pw_nk[i]%B]%mod*pow1[pw_nk[i]/B]%mod)%mod;
	cout<<1ll*ans*mul%mod;
}

詳細信息

Subtask #1:

score: 10
Accepted

Test #1:

score: 10
Accepted
time: 2ms
memory: 19688kb

input:

1 2 540053233

output:

9

result:

ok 1 number(s): "9"

Test #2:

score: 0
Accepted
time: 6ms
memory: 19696kb

input:

2 2 156542707

output:

43046970

result:

ok 1 number(s): "43046970"

Test #3:

score: 0
Accepted
time: 5ms
memory: 19748kb

input:

1 2 186225229

output:

9

result:

ok 1 number(s): "9"

Test #4:

score: 0
Accepted
time: 2ms
memory: 21860kb

input:

3 3 109884329

output:

100602209

result:

ok 1 number(s): "100602209"

Test #5:

score: 0
Accepted
time: 2ms
memory: 19616kb

input:

1 2 144802297

output:

9

result:

ok 1 number(s): "9"

Subtask #2:

score: 20
Accepted

Dependency #1:

100%
Accepted

Test #6:

score: 20
Accepted
time: 1ms
memory: 19812kb

input:

20 21992843 328859143

output:

110137213

result:

ok 1 number(s): "110137213"

Test #7:

score: 0
Accepted
time: 0ms
memory: 21812kb

input:

22 332524739 654888401

output:

410922781

result:

ok 1 number(s): "410922781"

Test #8:

score: 0
Accepted
time: 2ms
memory: 19744kb

input:

26 302215049 566649113

output:

221720840

result:

ok 1 number(s): "221720840"

Test #9:

score: 0
Accepted
time: 2ms
memory: 19692kb

input:

15 111009527 722130737

output:

648834664

result:

ok 1 number(s): "648834664"

Test #10:

score: 0
Accepted
time: 2ms
memory: 21796kb

input:

82 110032063 394529383

output:

111730592

result:

ok 1 number(s): "111730592"

Test #11:

score: 0
Accepted
time: 2ms
memory: 19764kb

input:

9 11172911 259650437

output:

68381774

result:

ok 1 number(s): "68381774"

Test #12:

score: 0
Accepted
time: 2ms
memory: 19744kb

input:

86 12016027 354886243

output:

263687778

result:

ok 1 number(s): "263687778"

Test #13:

score: 0
Accepted
time: 0ms
memory: 21676kb

input:

91 273689959 454097881

output:

114436127

result:

ok 1 number(s): "114436127"

Test #14:

score: 0
Accepted
time: 6ms
memory: 19856kb

input:

73 148878967 694206977

output:

176215101

result:

ok 1 number(s): "176215101"

Test #15:

score: 0
Accepted
time: 1ms
memory: 21896kb

input:

45 205982233 227598247

output:

156769598

result:

ok 1 number(s): "156769598"

Subtask #3:

score: 10
Accepted

Dependency #2:

100%
Accepted

Test #16:

score: 10
Accepted
time: 2ms
memory: 21744kb

input:

2778 122825869 147297463

output:

43419574

result:

ok 1 number(s): "43419574"

Test #17:

score: 0
Accepted
time: 0ms
memory: 19696kb

input:

289 7729669 589652893

output:

552952137

result:

ok 1 number(s): "552952137"

Test #18:

score: 0
Accepted
time: 3ms
memory: 19772kb

input:

2281 35651417 203950963

output:

21659018

result:

ok 1 number(s): "21659018"

Test #19:

score: 0
Accepted
time: 2ms
memory: 19632kb

input:

1684 258745639 373223677

output:

355596229

result:

ok 1 number(s): "355596229"

Test #20:

score: 0
Accepted
time: 7ms
memory: 19640kb

input:

2107 86850989 455823859

output:

245960059

result:

ok 1 number(s): "245960059"

Test #21:

score: 0
Accepted
time: 2ms
memory: 21740kb

input:

1323 43290799 791120419

output:

509649562

result:

ok 1 number(s): "509649562"

Test #22:

score: 0
Accepted
time: 1ms
memory: 19708kb

input:

2401 34064903 185314627

output:

70571452

result:

ok 1 number(s): "70571452"

Test #23:

score: 0
Accepted
time: 2ms
memory: 21744kb

input:

1073 82288187 564447959

output:

168200843

result:

ok 1 number(s): "168200843"

Test #24:

score: 0
Accepted
time: 3ms
memory: 21820kb

input:

1926 29995039 129122281

output:

60921463

result:

ok 1 number(s): "60921463"

Test #25:

score: 0
Accepted
time: 2ms
memory: 19776kb

input:

3000 66915659 765705179

output:

222619979

result:

ok 1 number(s): "222619979"

Subtask #4:

score: 20
Accepted

Test #26:

score: 20
Accepted
time: 195ms
memory: 55692kb

input:

998818 198334853 998244353

output:

153251445

result:

ok 1 number(s): "153251445"

Test #27:

score: 0
Accepted
time: 185ms
memory: 57268kb

input:

914379 128814383 998244353

output:

477606145

result:

ok 1 number(s): "477606145"

Test #28:

score: 0
Accepted
time: 177ms
memory: 54552kb

input:

944474 478445339 998244353

output:

174204073

result:

ok 1 number(s): "174204073"

Test #29:

score: 0
Accepted
time: 180ms
memory: 55432kb

input:

948637 711592127 998244353

output:

178256114

result:

ok 1 number(s): "178256114"

Test #30:

score: 0
Accepted
time: 175ms
memory: 54552kb

input:

927564 14465663 998244353

output:

315244613

result:

ok 1 number(s): "315244613"

Test #31:

score: 0
Accepted
time: 177ms
memory: 53436kb

input:

934615 392799073 998244353

output:

892700270

result:

ok 1 number(s): "892700270"

Test #32:

score: 0
Accepted
time: 160ms
memory: 55412kb

input:

917196 124972031 998244353

output:

782017412

result:

ok 1 number(s): "782017412"

Test #33:

score: 0
Accepted
time: 176ms
memory: 59072kb

input:

957149 392606173 998244353

output:

159348443

result:

ok 1 number(s): "159348443"

Test #34:

score: 0
Accepted
time: 199ms
memory: 59196kb

input:

997042 184649453 998244353

output:

464643024

result:

ok 1 number(s): "464643024"

Test #35:

score: 0
Accepted
time: 183ms
memory: 57440kb

input:

953353 14071961 998244353

output:

391688875

result:

ok 1 number(s): "391688875"

Subtask #5:

score: 10
Accepted

Test #36:

score: 10
Accepted
time: 1860ms
memory: 352812kb

input:

9909956 720431399 720431401

output:

86883659

result:

ok 1 number(s): "86883659"

Test #37:

score: 0
Accepted
time: 1869ms
memory: 352888kb

input:

9924163 267052829 267052831

output:

75754681

result:

ok 1 number(s): "75754681"

Test #38:

score: 0
Accepted
time: 1869ms
memory: 353976kb

input:

9967885 197873129 197873131

output:

16653739

result:

ok 1 number(s): "16653739"

Test #39:

score: 0
Accepted
time: 1832ms
memory: 353568kb

input:

9952642 101872151 101872153

output:

0

result:

ok 1 number(s): "0"

Test #40:

score: 0
Accepted
time: 1886ms
memory: 354048kb

input:

9955909 167874431 167874433

output:

130012020

result:

ok 1 number(s): "130012020"

Test #41:

score: 0
Accepted
time: 1912ms
memory: 355032kb

input:

9994785 399509567 399509569

output:

153324498

result:

ok 1 number(s): "153324498"

Test #42:

score: 0
Accepted
time: 1873ms
memory: 353804kb

input:

9954011 108819131 108819133

output:

101671540

result:

ok 1 number(s): "101671540"

Test #43:

score: 0
Accepted
time: 1903ms
memory: 354944kb

input:

9997570 213315827 213315829

output:

57441081

result:

ok 1 number(s): "57441081"

Test #44:

score: 0
Accepted
time: 1855ms
memory: 354872kb

input:

9995867 113028299 113028301

output:

67837072

result:

ok 1 number(s): "67837072"

Test #45:

score: 0
Accepted
time: 1843ms
memory: 352612kb

input:

9909335 247275617 247275619

output:

202966817

result:

ok 1 number(s): "202966817"

Subtask #6:

score: 30
Accepted

Dependency #1:

100%
Accepted

Dependency #2:

100%
Accepted

Dependency #3:

100%
Accepted

Dependency #4:

100%
Accepted

Dependency #5:

100%
Accepted

Test #46:

score: 30
Accepted
time: 1882ms
memory: 353276kb

input:

9921815 38466881 725310841

output:

601117286

result:

ok 1 number(s): "601117286"

Test #47:

score: 0
Accepted
time: 1891ms
memory: 353064kb

input:

9919464 4830599 747345523

output:

168521454

result:

ok 1 number(s): "168521454"

Test #48:

score: 0
Accepted
time: 1889ms
memory: 354560kb

input:

9981374 3616373 154722097

output:

2696288

result:

ok 1 number(s): "2696288"

Test #49:

score: 0
Accepted
time: 1880ms
memory: 352980kb

input:

9906664 12433457 558159149

output:

538699014

result:

ok 1 number(s): "538699014"

Test #50:

score: 0
Accepted
time: 1894ms
memory: 354796kb

input:

9985736 46853 410275823

output:

258567756

result:

ok 1 number(s): "258567756"

Test #51:

score: 0
Accepted
time: 1909ms
memory: 354216kb

input:

9962926 33790087 203505083

output:

40932778

result:

ok 1 number(s): "40932778"

Test #52:

score: 0
Accepted
time: 1850ms
memory: 352360kb

input:

9903735 146658401 157137433

output:

154493145

result:

ok 1 number(s): "154493145"

Test #53:

score: 0
Accepted
time: 1855ms
memory: 352296kb

input:

9913516 105010771 110717611

output:

67979325

result:

ok 1 number(s): "67979325"

Test #54:

score: 0
Accepted
time: 1827ms
memory: 353868kb

input:

9953517 268142489 675913921

output:

523115756

result:

ok 1 number(s): "523115756"

Test #55:

score: 0
Accepted
time: 1875ms
memory: 354372kb

input:

9981005 11993207 114120883

output:

7261617

result:

ok 1 number(s): "7261617"

Test #56:

score: 0
Accepted
time: 1879ms
memory: 353520kb

input:

9945956 36522077 168104303

output:

82398556

result:

ok 1 number(s): "82398556"

Test #57:

score: 0
Accepted
time: 1867ms
memory: 354088kb

input:

9967933 15301477 352827883

output:

242773007

result:

ok 1 number(s): "242773007"

Test #58:

score: 0
Accepted
time: 1873ms
memory: 352716kb

input:

9911781 83845891 360130933

output:

158254305

result:

ok 1 number(s): "158254305"

Test #59:

score: 0
Accepted
time: 1898ms
memory: 352684kb

input:

9916390 100404191 108138473

output:

103346432

result:

ok 1 number(s): "103346432"

Test #60:

score: 0
Accepted
time: 1877ms
memory: 354536kb

input:

9974438 7828049 430399297

output:

76675277

result:

ok 1 number(s): "76675277"