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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 |
---|---|---|---|---|---|---|---|---|---|
#112739 | #6518. Not Another Linear Algebra Problem | gtm1514 | AC ✓ | 2554ms | 277960kb | C++14 | 2.0kb | 2023-06-13 08:44:41 | 2023-06-13 08:44:43 |
Judging History
answer
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
#include <iostream>
using namespace std;
int n,q,mod,ord,jc[10000010],inv[10000010],pw[10000010],cpw[10000010],a[10000010],jcp[10000010],invp[10000010];
int C(int n,int m){
int rn=n%ord,rm=m%ord;
n/=ord;m/=ord;
if(n<m||rn<rm)return 0;
return 1ll*jc[n]*inv[m]%mod*inv[n-m]%mod*jcp[rn]%mod*invp[rm]%mod*invp[rn-rm]%mod;
}
int qpow(int a,int b,int mod){
int ans=1;
while(b){
if(b&1)ans=1ll*ans*a%mod;
a=1ll*a*a%mod;
b>>=1;
}
return ans;
}
struct node{
int sq=1<<16,pw[1<<17],gpw[1<<17];
node(){
pw[0]=gpw[0]=1;
for(int i=1;i<sq;i++){
pw[i]=3ll*pw[i-1]%mod;
}
gpw[1]=3ll*pw[sq-1]%mod;
for(int i=2;i<sq;i++)gpw[i]=1ll*gpw[i-1]*gpw[1]%mod;
}
int get(int n){
return 1ll*gpw[n/sq]*pw[n%sq]%mod;
}
};
int main(){
scanf("%d%d%d",&n,&q,&mod);jc[0]=inv[0]=inv[1]=1;
node P;
for(int i=2;i<=n;i++)inv[i]=1ll*(mod-mod/i)*inv[mod%i]%mod;
for(int i=1;i<=n;i++)jc[i]=1ll*jc[i-1]*i%mod,inv[i]=1ll*inv[i-1]*inv[i]%mod;
pw[0]=cpw[0]=1;pw[1]=q;
for(int i=1;i<=n;i++)pw[i]=1ll*pw[i-1]*pw[1]%mod,cpw[i]=1ll*cpw[i-1]*pw[i-1]%mod;
ord=n+1;
for(int i=1;i<=n;i++)if(pw[i]==1){
ord=i;break;
}
jcp[0]=invp[0]=1;
for(int i=1;i<=n;i++)jcp[i]=1ll*jcp[i-1]*(1-pw[i]+mod)%mod;
invp[n]=qpow(jcp[n],mod-2,mod);
for(int i=n-1;i>=1;i--)invp[i]=1ll*invp[i+1]*(1-pw[i+1]+mod)%mod;
a[0]=1;int invpw=qpow(q,mod-2,mod);
for(int i=1,Inv=1;i<=n;i++){
Inv=1ll*Inv*invpw%mod;
a[i]=1ll*(1ll*((i&1)?(mod-1):1)*cpw[i]+1ll*(pw[i-1]-pw[n]+mod)%mod*(1-pw[i]+mod)%mod*a[i-1])%mod*Inv%mod;
}
for(int i=0;i<=n;i++)a[i]=1ll*a[i]*C(n,i)%mod;
int ans=0,ret=qpow(q,n,mod-1);
if(!ret)ret=mod-1;
for(int i=0,tmp=1;i<=n;i++){
ans=(ans+1ll*P.get(tmp)*a[n-i])%mod;
tmp=1ll*tmp*ret%(mod-1);
}
printf("%d\n",ans);
return 0;
}
詳細信息
Test #1:
score: 100
Accepted
time: 2ms
memory: 16788kb
input:
2 2 1000000007
output:
43046970
result:
ok 1 number(s): "43046970"
Test #2:
score: 0
Accepted
time: 2ms
memory: 17000kb
input:
100 127 998244353
output:
881381862
result:
ok 1 number(s): "881381862"
Test #3:
score: 0
Accepted
time: 3ms
memory: 16792kb
input:
1 2 540053233
output:
9
result:
ok 1 number(s): "9"
Test #4:
score: 0
Accepted
time: 3ms
memory: 16764kb
input:
2 2 156542707
output:
43046970
result:
ok 1 number(s): "43046970"
Test #5:
score: 0
Accepted
time: 1ms
memory: 16824kb
input:
1 2 186225229
output:
9
result:
ok 1 number(s): "9"
Test #6:
score: 0
Accepted
time: 7ms
memory: 16776kb
input:
3 3 109884329
output:
100602209
result:
ok 1 number(s): "100602209"
Test #7:
score: 0
Accepted
time: 3ms
memory: 17004kb
input:
1 2 144802297
output:
9
result:
ok 1 number(s): "9"
Test #8:
score: 0
Accepted
time: 2ms
memory: 16824kb
input:
20 21992843 328859143
output:
110137213
result:
ok 1 number(s): "110137213"
Test #9:
score: 0
Accepted
time: 3ms
memory: 16788kb
input:
22 332524739 654888401
output:
410922781
result:
ok 1 number(s): "410922781"
Test #10:
score: 0
Accepted
time: 7ms
memory: 16972kb
input:
26 302215049 566649113
output:
221720840
result:
ok 1 number(s): "221720840"
Test #11:
score: 0
Accepted
time: 7ms
memory: 16796kb
input:
15 111009527 722130737
output:
648834664
result:
ok 1 number(s): "648834664"
Test #12:
score: 0
Accepted
time: 7ms
memory: 16976kb
input:
82 110032063 394529383
output:
111730592
result:
ok 1 number(s): "111730592"
Test #13:
score: 0
Accepted
time: 2ms
memory: 16864kb
input:
9 11172911 259650437
output:
68381774
result:
ok 1 number(s): "68381774"
Test #14:
score: 0
Accepted
time: 2ms
memory: 16864kb
input:
86 12016027 354886243
output:
263687778
result:
ok 1 number(s): "263687778"
Test #15:
score: 0
Accepted
time: 5ms
memory: 16736kb
input:
91 273689959 454097881
output:
114436127
result:
ok 1 number(s): "114436127"
Test #16:
score: 0
Accepted
time: 3ms
memory: 17000kb
input:
73 148878967 694206977
output:
176215101
result:
ok 1 number(s): "176215101"
Test #17:
score: 0
Accepted
time: 3ms
memory: 16976kb
input:
45 205982233 227598247
output:
156769598
result:
ok 1 number(s): "156769598"
Test #18:
score: 0
Accepted
time: 2ms
memory: 16980kb
input:
2778 122825869 147297463
output:
43419574
result:
ok 1 number(s): "43419574"
Test #19:
score: 0
Accepted
time: 2ms
memory: 16824kb
input:
289 7729669 589652893
output:
552952137
result:
ok 1 number(s): "552952137"
Test #20:
score: 0
Accepted
time: 2ms
memory: 16784kb
input:
2281 35651417 203950963
output:
21659018
result:
ok 1 number(s): "21659018"
Test #21:
score: 0
Accepted
time: 2ms
memory: 16720kb
input:
1684 258745639 373223677
output:
355596229
result:
ok 1 number(s): "355596229"
Test #22:
score: 0
Accepted
time: 3ms
memory: 16724kb
input:
2107 86850989 455823859
output:
245960059
result:
ok 1 number(s): "245960059"
Test #23:
score: 0
Accepted
time: 2ms
memory: 16784kb
input:
1323 43290799 791120419
output:
509649562
result:
ok 1 number(s): "509649562"
Test #24:
score: 0
Accepted
time: 2ms
memory: 16744kb
input:
2401 34064903 185314627
output:
70571452
result:
ok 1 number(s): "70571452"
Test #25:
score: 0
Accepted
time: 7ms
memory: 16764kb
input:
1073 82288187 564447959
output:
168200843
result:
ok 1 number(s): "168200843"
Test #26:
score: 0
Accepted
time: 0ms
memory: 16828kb
input:
1926 29995039 129122281
output:
60921463
result:
ok 1 number(s): "60921463"
Test #27:
score: 0
Accepted
time: 0ms
memory: 17008kb
input:
3000 66915659 765705179
output:
222619979
result:
ok 1 number(s): "222619979"
Test #28:
score: 0
Accepted
time: 246ms
memory: 42056kb
input:
998818 198334853 998244353
output:
153251445
result:
ok 1 number(s): "153251445"
Test #29:
score: 0
Accepted
time: 226ms
memory: 46364kb
input:
914379 128814383 998244353
output:
477606145
result:
ok 1 number(s): "477606145"
Test #30:
score: 0
Accepted
time: 235ms
memory: 42016kb
input:
944474 478445339 998244353
output:
174204073
result:
ok 1 number(s): "174204073"
Test #31:
score: 0
Accepted
time: 244ms
memory: 43284kb
input:
948637 711592127 998244353
output:
178256114
result:
ok 1 number(s): "178256114"
Test #32:
score: 0
Accepted
time: 242ms
memory: 42056kb
input:
927564 14465663 998244353
output:
315244613
result:
ok 1 number(s): "315244613"
Test #33:
score: 0
Accepted
time: 239ms
memory: 39612kb
input:
934615 392799073 998244353
output:
892700270
result:
ok 1 number(s): "892700270"
Test #34:
score: 0
Accepted
time: 235ms
memory: 39800kb
input:
917196 124972031 998244353
output:
782017412
result:
ok 1 number(s): "782017412"
Test #35:
score: 0
Accepted
time: 245ms
memory: 43316kb
input:
957149 392606173 998244353
output:
159348443
result:
ok 1 number(s): "159348443"
Test #36:
score: 0
Accepted
time: 241ms
memory: 46756kb
input:
997042 184649453 998244353
output:
464643024
result:
ok 1 number(s): "464643024"
Test #37:
score: 0
Accepted
time: 233ms
memory: 46536kb
input:
953353 14071961 998244353
output:
391688875
result:
ok 1 number(s): "391688875"
Test #38:
score: 0
Accepted
time: 2553ms
memory: 277400kb
input:
9909956 720431399 720431401
output:
86883659
result:
ok 1 number(s): "86883659"
Test #39:
score: 0
Accepted
time: 2455ms
memory: 277268kb
input:
9924163 267052829 267052831
output:
75754681
result:
ok 1 number(s): "75754681"
Test #40:
score: 0
Accepted
time: 2424ms
memory: 277600kb
input:
9967885 197873129 197873131
output:
16653739
result:
ok 1 number(s): "16653739"
Test #41:
score: 0
Accepted
time: 2104ms
memory: 277688kb
input:
9952642 101872151 101872153
output:
0
result:
ok 1 number(s): "0"
Test #42:
score: 0
Accepted
time: 2448ms
memory: 277644kb
input:
9955909 167874431 167874433
output:
130012020
result:
ok 1 number(s): "130012020"
Test #43:
score: 0
Accepted
time: 2467ms
memory: 277880kb
input:
9994785 399509567 399509569
output:
153324498
result:
ok 1 number(s): "153324498"
Test #44:
score: 0
Accepted
time: 2417ms
memory: 277432kb
input:
9954011 108819131 108819133
output:
101671540
result:
ok 1 number(s): "101671540"
Test #45:
score: 0
Accepted
time: 2464ms
memory: 277924kb
input:
9997570 213315827 213315829
output:
57441081
result:
ok 1 number(s): "57441081"
Test #46:
score: 0
Accepted
time: 2481ms
memory: 277864kb
input:
9995867 113028299 113028301
output:
67837072
result:
ok 1 number(s): "67837072"
Test #47:
score: 0
Accepted
time: 2426ms
memory: 277092kb
input:
9909335 247275617 247275619
output:
202966817
result:
ok 1 number(s): "202966817"
Test #48:
score: 0
Accepted
time: 2542ms
memory: 276716kb
input:
9921815 38466881 725310841
output:
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result:
ok 1 number(s): "601117286"
Test #49:
score: 0
Accepted
time: 2509ms
memory: 276744kb
input:
9919464 4830599 747345523
output:
168521454
result:
ok 1 number(s): "168521454"
Test #50:
score: 0
Accepted
time: 2484ms
memory: 277892kb
input:
9981374 3616373 154722097
output:
2696288
result:
ok 1 number(s): "2696288"
Test #51:
score: 0
Accepted
time: 2537ms
memory: 277068kb
input:
9906664 12433457 558159149
output:
538699014
result:
ok 1 number(s): "538699014"
Test #52:
score: 0
Accepted
time: 2485ms
memory: 277960kb
input:
9985736 46853 410275823
output:
258567756
result:
ok 1 number(s): "258567756"
Test #53:
score: 0
Accepted
time: 2462ms
memory: 277484kb
input:
9962926 33790087 203505083
output:
40932778
result:
ok 1 number(s): "40932778"
Test #54:
score: 0
Accepted
time: 2433ms
memory: 276852kb
input:
9903735 146658401 157137433
output:
154493145
result:
ok 1 number(s): "154493145"
Test #55:
score: 0
Accepted
time: 2434ms
memory: 276904kb
input:
9913516 105010771 110717611
output:
67979325
result:
ok 1 number(s): "67979325"
Test #56:
score: 0
Accepted
time: 2514ms
memory: 277616kb
input:
9953517 268142489 675913921
output:
523115756
result:
ok 1 number(s): "523115756"
Test #57:
score: 0
Accepted
time: 2413ms
memory: 277664kb
input:
9981005 11993207 114120883
output:
7261617
result:
ok 1 number(s): "7261617"
Test #58:
score: 0
Accepted
time: 2493ms
memory: 277520kb
input:
9945956 36522077 168104303
output:
82398556
result:
ok 1 number(s): "82398556"
Test #59:
score: 0
Accepted
time: 2554ms
memory: 277548kb
input:
9967933 15301477 352827883
output:
242773007
result:
ok 1 number(s): "242773007"
Test #60:
score: 0
Accepted
time: 2449ms
memory: 277312kb
input:
9911781 83845891 360130933
output:
158254305
result:
ok 1 number(s): "158254305"
Test #61:
score: 0
Accepted
time: 2421ms
memory: 276964kb
input:
9916390 100404191 108138473
output:
103346432
result:
ok 1 number(s): "103346432"
Test #62:
score: 0
Accepted
time: 2497ms
memory: 277568kb
input:
9974438 7828049 430399297
output:
76675277
result:
ok 1 number(s): "76675277"