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QOJ
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 | Appleblue17 | 100 ✓ | 1912ms | 355032kb | C++14 | 1.6kb | 2022-11-17 18:47:03 | 2022-11-17 18:47:06 |
Judging History
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"