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QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#89938#5817. 小学生数学题sunxuanyu100 ✓803ms416136kbC++141.1kb2023-03-21 20:20:572023-03-21 20:21:00

Judging History

你现在查看的是最新测评结果

  • [2023-08-10 23:21:45]
  • System Update: QOJ starts to keep a history of the judgings of all the submissions.
  • [2023-03-21 20:21:00]
  • 评测
  • 测评结果:100
  • 用时:803ms
  • 内存:416136kb
  • [2023-03-21 20:20:57]
  • 提交

answer

#include<iostream>
using namespace std;
#define LL long long
const int mod = 998244353,maxn = 2e7 + 10;
int sq(int x,int m){
	return 1ll * x * x % m;
}
int qp(LL a,int k){
	LL ans = 1;
	while(k)
	{
		if(k&1) ans  = ans * a % mod;
		a = a * a % mod;
		k >>= 1;
	}
	return ans;
}
bool num[maxn];
int prime[maxn],sm[maxn],cnt,t[maxn],s[maxn],sv[maxn],inv[maxn];
int main(){
	int n,k;
	cin >> n >> k;
	for(int i = 2;i <= n;i++){
		if(!num[i])prime[++cnt] = i;
		for(int j = 1;j <= cnt && i * prime[j] <= n;j++){
            num[i*prime[j]] = 1;
            sm[i*prime[j]] = prime[j];
            if(!(i % prime[j]))break;
        }
	}
	for(int i = 1;i <= n;i++)
		if(!num[i])t[i] = qp(i,k);
		else t[i] = 1ll * t[sm[i]] * t[i/sm[i]] % mod;

	s[0] = 1;
	for(int i = 1;i <= n;i++)
		s[i] = 1ll * s[i - 1] * t[i] % mod;
	sv[n] = qp(s[n],mod - 2);
	for(int i = n;i >= 1;i--)
		sv[i - 1] = 1ll * sv[i] * t[i] % mod;
	for(int i = 1;i <= n;i++)
		inv[i] = 1ll * sv[i] * s[i - 1] % mod;
	int ans = 0,x = 1;
	for(int i = 1;i <= n;i++){
		x = 1ll * x * i % mod;
		ans = (ans + 1ll * x * inv[i]) % mod;
	}
	cout << ans;
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 10
Accepted
time: 323ms
memory: 200376kb

input:

9450395 1

output:

688545438

result:

ok single line: '688545438'

Test #2:

score: 10
Accepted
time: 267ms
memory: 191836kb

input:

8978812 1

output:

334565356

result:

ok single line: '334565356'

Test #3:

score: 10
Accepted
time: 296ms
memory: 190804kb

input:

8944235 1

output:

982802915

result:

ok single line: '982802915'

Test #4:

score: 10
Accepted
time: 250ms
memory: 151924kb

input:

7081118 3

output:

599009773

result:

ok single line: '599009773'

Test #5:

score: 10
Accepted
time: 253ms
memory: 168916kb

input:

7904241 3

output:

871243720

result:

ok single line: '871243720'

Test #6:

score: 10
Accepted
time: 340ms
memory: 210892kb

input:

9921275 3

output:

549818101

result:

ok single line: '549818101'

Test #7:

score: 10
Accepted
time: 759ms
memory: 369048kb

input:

17575748 14135489

output:

69236780

result:

ok single line: '69236780'

Test #8:

score: 10
Accepted
time: 803ms
memory: 416136kb

input:

19858362 14822524

output:

239890381

result:

ok single line: '239890381'

Test #9:

score: 10
Accepted
time: 727ms
memory: 396272kb

input:

18848696 15530895

output:

88125041

result:

ok single line: '88125041'

Test #10:

score: 10
Accepted
time: 716ms
memory: 373988kb

input:

17787945 13890407

output:

989967864

result:

ok single line: '989967864'

Extra Test:

score: 0
Extra Test Passed