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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#213764#2157. 数列WZRYWZWY100411ms17272kbC++111.4kb2024-11-13 18:44:342024-11-13 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;
}

Details

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'