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 |
---|---|---|---|---|---|---|---|---|---|
#213764 | #2157. 数列 | WZRYWZWY | 100 | 411ms | 17272kb | C++11 | 1.4kb | 2024-11-13 18:44:34 | 2024-11-13 23:00:29 |
answer
#include<bits/stdc++.h>//https://www.luogu.com.cn/problem/solution/P3200
using namespace std;
const int N=2000005;
//注意是2*n
int mp[N],p[N/10],cnt[N],r;
//mp[]表示每个数最小的质因数,p[]表示质数表,cnt[]用于计算指数,r为取模数
int qpow(int a,int b)
//快速幂:计算a^b%r
{
int ans=1;
do
{
if(b&1)
ans=(long long)ans*a%r;
a=(long long)a*a%r;
}
while(b/=2);
return ans;
}
int main()
{
int n;
cin>>n>>r;
int pn=0;
for(int i=2;i<=2*n;i++)
{
if(!mp[i])
{
p[++pn]=i;
mp[i]=i;
}
for(int j=1;j<=pn&&i*p[j]<=2*n;j++)
{
mp[i*p[j]]=p[j];
if(i%p[j]==0)
break;
}
}
//欧拉线性筛法
for(int i=1;i<=n;i++)
cnt[i]=-1;
//需要除以分母
for(int i=n+2;i<=2*n;i++)
cnt[i]=1;
//乘以分子
for(int i=2*n;i>1;i--)
if(mp[i]<i)
//如果是合数,向下传递,可以保证O(n)
{
cnt[mp[i]]+=cnt[i];
cnt[i/mp[i]]+=cnt[i];
}
int ans=1;
for(int i=2;i<=2*n;i++)
if(mp[i]==i)
//如果是质数计入答案,合数已经处理过了
ans=(long long)ans*qpow(i,cnt[i])%r;
//防止中间过程溢出
cout<<ans<<endl;
return 0;
}
详细
小提示:点击横条可展开更详细的信息
Test #1:
score: 5
Accepted
time: 0ms
memory: 1216kb
input:
921 998054347
output:
345389219
result:
ok single line: '345389219'
Test #2:
score: 5
Accepted
time: 0ms
memory: 1216kb
input:
926 998064329
output:
458756691
result:
ok single line: '458756691'
Test #3:
score: 5
Accepted
time: 0ms
memory: 1224kb
input:
1000 998074327
output:
457273797
result:
ok single line: '457273797'
Test #4:
score: 5
Accepted
time: 0ms
memory: 1220kb
input:
952 998084303
output:
329700115
result:
ok single line: '329700115'
Test #5:
score: 5
Accepted
time: 0ms
memory: 1220kb
input:
989 998094347
output:
94788253
result:
ok single line: '94788253'
Test #6:
score: 5
Accepted
time: 0ms
memory: 1220kb
input:
902 998104313
output:
911969455
result:
ok single line: '911969455'
Test #7:
score: 5
Accepted
time: 0ms
memory: 1216kb
input:
914 998114333
output:
827812986
result:
ok single line: '827812986'
Test #8:
score: 5
Accepted
time: 0ms
memory: 1224kb
input:
986 998124313
output:
169699253
result:
ok single line: '169699253'
Test #9:
score: 5
Accepted
time: 0ms
memory: 1224kb
input:
947 998134339
output:
761932751
result:
ok single line: '761932751'
Test #10:
score: 5
Accepted
time: 0ms
memory: 1224kb
input:
934 998144339
output:
42889072
result:
ok single line: '42889072'
Test #11:
score: 5
Accepted
time: 53ms
memory: 17272kb
input:
991572 998154343
output:
277089318
result:
ok single line: '277089318'
Test #12:
score: 5
Accepted
time: 25ms
memory: 16324kb
input:
932800 998164337
output:
945072504
result:
ok single line: '945072504'
Test #13:
score: 5
Accepted
time: 36ms
memory: 15852kb
input:
903603 998174341
output:
29916736
result:
ok single line: '29916736'
Test #14:
score: 5
Accepted
time: 39ms
memory: 16744kb
input:
958646 998184331
output:
802903490
result:
ok single line: '802903490'
Test #15:
score: 5
Accepted
time: 47ms
memory: 17140kb
input:
983016 998194349
output:
802900579
result:
ok single line: '802900579'
Test #16:
score: 5
Accepted
time: 43ms
memory: 16156kb
input:
922347 998204353
output:
228575331
result:
ok single line: '228575331'
Test #17:
score: 5
Accepted
time: 48ms
memory: 17020kb
input:
976053 998214317
output:
982618317
result:
ok single line: '982618317'
Test #18:
score: 5
Accepted
time: 43ms
memory: 16724kb
input:
957300 998224351
output:
514549818
result:
ok single line: '514549818'
Test #19:
score: 5
Accepted
time: 36ms
memory: 16148kb
input:
921760 998234353
output:
470386410
result:
ok single line: '470386410'
Test #20:
score: 5
Accepted
time: 41ms
memory: 16000kb
input:
912948 998244353
output:
129235345
result:
ok single line: '129235345'