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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 |
---|---|---|---|---|---|---|---|---|---|
#69651 | #5031. 核 | zhouhuanyi | 60 | 1983ms | 354784kb | C++11 | 2.5kb | 2022-12-29 14:14:44 | 2022-12-29 14:14:47 |
Judging History
answer
#include<iostream>
#include<cstdio>
#define N 10000001
#define Base 100000
using namespace std;
int read()
{
char c=0;
int sum=0;
while (c<'0'||c>'9') c=getchar();
while ('0'<=c&&c<='9') sum=sum*10+c-'0',c=getchar();
return sum;
}
int n,q,invq,mod,pwa[N+1],pwb[N+1],pw[N+1],s1[N+1],s2[N+1],invs[N+1],invpw[N+1],qnum[N+1],qfac[N+1],invqfac[N+1],dp[N+1],ans;
void Adder(int &x,int d)
{
x+=d;
if (x>=mod) x-=mod;
return;
}
void Adder2(int &x,int d)
{
x+=d;
if (x<0) x+=mod;
return;
}
int MD(int x)
{
return (x>=mod)?x-mod:x;
}
int MD2(int x)
{
return (x<0)?x+mod:x;
}
int fast_pow(int a,int b)
{
int res=1,mul=a;
while (b)
{
if (b&1) res=1ll*res*mul%mod;
mul=1ll*mul*mul%mod,b>>=1;
}
return res;
}
int qC(int x,int y)
{
if (x<y) return 0;
return 1ll*qfac[x]*invqfac[y]%mod*invqfac[x-y]%mod;
}
int get_fast_pow(int x)
{
return 1ll*pwa[x%Base]*pwb[x/Base]%mod;
}
int main()
{
int cst,rst,kst,dst=1,rest,delta,ds,d1,d2;
n=read(),q=read(),mod=read(),qfac[0]=pw[0]=invpw[0]=pwa[0]=pwb[0]=s1[0]=s2[n+2]=1,cst=MD2(q-1),rst=fast_pow(cst,mod-2),invq=fast_pow(q,mod-2),rest=1ll*cst*invq%mod;
for (int i=1;i<=Base;++i) pwa[i]=3ll*pwa[i-1]%mod;
for (int i=1;i<=Base;++i) pwb[i]=1ll*pwb[i-1]*pwa[Base]%mod;
for (int i=1;i<=n+1;++i) pw[i]=1ll*pw[i-1]*q%mod,invpw[i]=1ll*invpw[i-1]*invq%mod;
delta=1ll*MD2(pw[n+1]-pw[n])*rest%mod,ds=MD(MD2(pw[n+1]-pw[n])+rest);
for (int i=1;i<=n+1;++i) s1[i]=1ll*s1[i-1]*MD2(1-pw[i])%mod;
for (int i=n+1;i>=1;--i) s2[i]=1ll*s2[i+1]*MD2(1-pw[i])%mod;
kst=fast_pow(s1[n+1],mod-2);
for (int i=1;i<=n+1;++i) invs[i]=1ll*s1[i-1]*s2[i+1]%mod*kst%mod;
for (int i=1;i<=n+1;++i) qnum[i]=1ll*MD2(pw[i]-1)*rst%mod;
for (int i=1;i<=n+1;++i) qfac[i]=1ll*qfac[i-1]*qnum[i]%mod;
invqfac[n+1]=fast_pow(qfac[n+1],mod-2);
for (int i=n;i>=0;--i) invqfac[i]=1ll*invqfac[i+1]*qnum[i+1]%mod;
dp[0]=1,dp[1]=MD2(MD2(pw[n]-pw[n-1])-1);
for (int i=2;i<=n;++i)
{
d1=MD2(MD(1ll*MD(cst+rest)*pw[i-1]%mod+1ll*MD2(pw[n]-pw[n-1])*invpw[i-1]%mod)-ds);
d2=MD2(1ll*cst*rest%mod*pw[i-2]%mod-delta);
dp[i]=1ll*MD(1ll*d1*dp[i-1]%mod+1ll*d2*dp[i-2]%mod)*invs[i]%mod;
}
for (int i=0;i<=n;++i) dp[i]=1ll*dp[i]*invqfac[n-i]%mod;
for (int i=1;i<=n;++i) dst=1ll*dst*q%(mod-1);
for (int i=0,res=1;i<=n;++i,res=1ll*res*dst%(mod-1)) Adder(ans,1ll*dp[n-i]*get_fast_pow(res)%mod);
printf("%lld\n",1ll*ans*qfac[n]%mod);
return 0;
}
詳細信息
Subtask #1:
score: 10
Accepted
Test #1:
score: 10
Accepted
time: 5ms
memory: 4488kb
input:
1 2 540053233
output:
9
result:
ok 1 number(s): "9"
Test #2:
score: 0
Accepted
time: 5ms
memory: 4528kb
input:
2 2 156542707
output:
43046970
result:
ok 1 number(s): "43046970"
Test #3:
score: 0
Accepted
time: 5ms
memory: 4348kb
input:
1 2 186225229
output:
9
result:
ok 1 number(s): "9"
Test #4:
score: 0
Accepted
time: 1ms
memory: 4344kb
input:
3 3 109884329
output:
100602209
result:
ok 1 number(s): "100602209"
Test #5:
score: 0
Accepted
time: 5ms
memory: 4356kb
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: 2ms
memory: 4424kb
input:
20 21992843 328859143
output:
110137213
result:
ok 1 number(s): "110137213"
Test #7:
score: 0
Accepted
time: 5ms
memory: 4288kb
input:
22 332524739 654888401
output:
410922781
result:
ok 1 number(s): "410922781"
Test #8:
score: 0
Accepted
time: 5ms
memory: 4452kb
input:
26 302215049 566649113
output:
221720840
result:
ok 1 number(s): "221720840"
Test #9:
score: 0
Accepted
time: 2ms
memory: 4452kb
input:
15 111009527 722130737
output:
648834664
result:
ok 1 number(s): "648834664"
Test #10:
score: 0
Accepted
time: 2ms
memory: 4364kb
input:
82 110032063 394529383
output:
111730592
result:
ok 1 number(s): "111730592"
Test #11:
score: 0
Accepted
time: 2ms
memory: 4352kb
input:
9 11172911 259650437
output:
68381774
result:
ok 1 number(s): "68381774"
Test #12:
score: 0
Accepted
time: 5ms
memory: 4348kb
input:
86 12016027 354886243
output:
263687778
result:
ok 1 number(s): "263687778"
Test #13:
score: 0
Accepted
time: 5ms
memory: 4592kb
input:
91 273689959 454097881
output:
114436127
result:
ok 1 number(s): "114436127"
Test #14:
score: 0
Accepted
time: 5ms
memory: 4492kb
input:
73 148878967 694206977
output:
176215101
result:
ok 1 number(s): "176215101"
Test #15:
score: 0
Accepted
time: 2ms
memory: 4404kb
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: 4500kb
input:
2778 122825869 147297463
output:
43419574
result:
ok 1 number(s): "43419574"
Test #17:
score: 0
Accepted
time: 1ms
memory: 4360kb
input:
289 7729669 589652893
output:
552952137
result:
ok 1 number(s): "552952137"
Test #18:
score: 0
Accepted
time: 6ms
memory: 4484kb
input:
2281 35651417 203950963
output:
21659018
result:
ok 1 number(s): "21659018"
Test #19:
score: 0
Accepted
time: 6ms
memory: 4508kb
input:
1684 258745639 373223677
output:
355596229
result:
ok 1 number(s): "355596229"
Test #20:
score: 0
Accepted
time: 6ms
memory: 4524kb
input:
2107 86850989 455823859
output:
245960059
result:
ok 1 number(s): "245960059"
Test #21:
score: 0
Accepted
time: 2ms
memory: 4528kb
input:
1323 43290799 791120419
output:
509649562
result:
ok 1 number(s): "509649562"
Test #22:
score: 0
Accepted
time: 3ms
memory: 4536kb
input:
2401 34064903 185314627
output:
70571452
result:
ok 1 number(s): "70571452"
Test #23:
score: 0
Accepted
time: 2ms
memory: 4340kb
input:
1073 82288187 564447959
output:
168200843
result:
ok 1 number(s): "168200843"
Test #24:
score: 0
Accepted
time: 6ms
memory: 4416kb
input:
1926 29995039 129122281
output:
60921463
result:
ok 1 number(s): "60921463"
Test #25:
score: 0
Accepted
time: 6ms
memory: 4460kb
input:
3000 66915659 765705179
output:
222619979
result:
ok 1 number(s): "222619979"
Subtask #4:
score: 20
Accepted
Test #26:
score: 20
Accepted
time: 212ms
memory: 39568kb
input:
998818 198334853 998244353
output:
153251445
result:
ok 1 number(s): "153251445"
Test #27:
score: 0
Accepted
time: 202ms
memory: 36452kb
input:
914379 128814383 998244353
output:
477606145
result:
ok 1 number(s): "477606145"
Test #28:
score: 0
Accepted
time: 194ms
memory: 37720kb
input:
944474 478445339 998244353
output:
174204073
result:
ok 1 number(s): "174204073"
Test #29:
score: 0
Accepted
time: 196ms
memory: 37640kb
input:
948637 711592127 998244353
output:
178256114
result:
ok 1 number(s): "178256114"
Test #30:
score: 0
Accepted
time: 185ms
memory: 36900kb
input:
927564 14465663 998244353
output:
315244613
result:
ok 1 number(s): "315244613"
Test #31:
score: 0
Accepted
time: 204ms
memory: 37260kb
input:
934615 392799073 998244353
output:
892700270
result:
ok 1 number(s): "892700270"
Test #32:
score: 0
Accepted
time: 181ms
memory: 36732kb
input:
917196 124972031 998244353
output:
782017412
result:
ok 1 number(s): "782017412"
Test #33:
score: 0
Accepted
time: 201ms
memory: 38132kb
input:
957149 392606173 998244353
output:
159348443
result:
ok 1 number(s): "159348443"
Test #34:
score: 0
Accepted
time: 202ms
memory: 39396kb
input:
997042 184649453 998244353
output:
464643024
result:
ok 1 number(s): "464643024"
Test #35:
score: 0
Accepted
time: 196ms
memory: 37820kb
input:
953353 14071961 998244353
output:
391688875
result:
ok 1 number(s): "391688875"
Subtask #5:
score: 0
Time Limit Exceeded
Test #36:
score: 10
Accepted
time: 1947ms
memory: 352792kb
input:
9909956 720431399 720431401
output:
86883659
result:
ok 1 number(s): "86883659"
Test #37:
score: 0
Accepted
time: 1983ms
memory: 353420kb
input:
9924163 267052829 267052831
output:
75754681
result:
ok 1 number(s): "75754681"
Test #38:
score: 0
Accepted
time: 1924ms
memory: 354784kb
input:
9967885 197873129 197873131
output:
16653739
result:
ok 1 number(s): "16653739"
Test #39:
score: 0
Accepted
time: 1966ms
memory: 354244kb
input:
9952642 101872151 101872153
output:
0
result:
ok 1 number(s): "0"
Test #40:
score: 0
Accepted
time: 1958ms
memory: 354604kb
input:
9955909 167874431 167874433
output:
130012020
result:
ok 1 number(s): "130012020"
Test #41:
score: -10
Time Limit Exceeded
input:
9994785 399509567 399509569
output:
result:
Subtask #6:
score: 0
Skipped
Dependency #1:
100%
Accepted
Dependency #2:
100%
Accepted
Dependency #3:
100%
Accepted
Dependency #4:
100%
Accepted
Dependency #5:
0%