QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#89231 | #5817. 小学生数学题 | sunxuanyu | 60 | 396ms | 209520kb | C++23 | 1.4kb | 2023-03-19 12:17:56 | 2023-03-19 12:18:13 |
Judging History
answer
#include<bits/stdc++.h>
using namespace std;
const int mod = 998244353,maxn = 2e7 + 10;
int sq(int x,int m){
return 1ll * x * x % m;
}
int qp(int a,int k,int m){
if(!k)return 1;
int t = sq(qp(a,k >> 1,m),m);
if(k & 1)return 1ll * t * a % m;
return t;
}
bool num[maxn];
int prime[maxn],sm[maxn],cnt,t[maxn],s[maxn],sv[maxn],inv[maxn];
inline int read(){
char c = getchar();
while(c < '0' || c > '9')c = getchar();
int a = 0;
while(c >= '0' && c <= '9'){
a = a * 10 + c - '0';
c = getchar();
}
return a;
}
void write(int n){
if(!n)return;
write(n / 10);
putchar(n % 10 + '0');
}
int main(){
int n = read(),k = read();
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,mod);
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,mod);
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;
}
write(ans);
}
Details
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Test #1:
score: 10
Accepted
time: 344ms
memory: 199588kb
input:
9450395 1
output:
688545438
result:
ok single line: '688545438'
Test #2:
score: 10
Accepted
time: 396ms
memory: 189852kb
input:
8978812 1
output:
334565356
result:
ok single line: '334565356'
Test #3:
score: 10
Accepted
time: 309ms
memory: 189108kb
input:
8944235 1
output:
982802915
result:
ok single line: '982802915'
Test #4:
score: 10
Accepted
time: 252ms
memory: 150516kb
input:
7081118 3
output:
599009773
result:
ok single line: '599009773'
Test #5:
score: 10
Accepted
time: 288ms
memory: 167456kb
input:
7904241 3
output:
871243720
result:
ok single line: '871243720'
Test #6:
score: 10
Accepted
time: 332ms
memory: 209520kb
input:
9921275 3
output:
549818101
result:
ok single line: '549818101'
Test #7:
score: 0
Time Limit Exceeded
input:
17575748 14135489
output:
result:
Test #8:
score: 0
Time Limit Exceeded
input:
19858362 14822524
output:
result:
Test #9:
score: 0
Time Limit Exceeded
input:
18848696 15530895
output:
result:
Test #10:
score: 0
Time Limit Exceeded
input:
17787945 13890407