QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#583528 | #6417. Classical Summation Problem | ship2077# | AC ✓ | 148ms | 11756kb | C++23 | 1002b | 2024-09-22 20:23:47 | 2024-09-22 20:23:49 |
Judging History
answer
#include<bits/stdc++.h>
using namespace std;
constexpr int M=1e6+5,mod=998244353;
int fac[M],ifac[M];
int qpow(int x,int n){
int s=1; while (n){
if (n&1) s=1ll*s*x%mod;
x=1ll*x*x%mod; n>>=1;
} return s;
}
void init(int n){
for (int i=fac[0]=1;i<=n;i++) fac[i]=1ll*fac[i-1]*i%mod;
ifac[n]=qpow(fac[n],mod-2);
for (int i=n;i;i--) ifac[i-1]=1ll*ifac[i]*i%mod;
}
int c(int n,int m){return n<m||m<0?0:1ll*fac[n]*ifac[m]%mod*ifac[n-m]%mod;}
int main(){ int n,k;
scanf("%d%d",&n,&k);init(max(n,k));
int p=(k+1>>1)-1,ans=0;
ans=1ll*(n+1>>1)*qpow(n,k)%mod;
if (n%2==0){
const int i=n>>1;
for (int j=0;j<=p;j++)
ans=(ans+1ll*qpow(i,j)*qpow(n-i,k-j)%mod*c(k,j))%mod;
}
if (k%2==0){
for (int i=0;i<<1<n;i++){
const int j=k/2;
ans=(ans-1ll*qpow(i,j)*qpow(n-i,k-j)%mod*c(k,j))%mod;
}
}
if (ans<0) ans+=mod;
printf("%d\n",ans);
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 1ms
memory: 5952kb
input:
3 2
output:
14
result:
ok 1 number(s): "14"
Test #2:
score: 0
Accepted
time: 0ms
memory: 5952kb
input:
5 3
output:
375
result:
ok 1 number(s): "375"
Test #3:
score: 0
Accepted
time: 1ms
memory: 5944kb
input:
2 2
output:
5
result:
ok 1 number(s): "5"
Test #4:
score: 0
Accepted
time: 0ms
memory: 5948kb
input:
10 9
output:
508778235
result:
ok 1 number(s): "508778235"
Test #5:
score: 0
Accepted
time: 1ms
memory: 5996kb
input:
69 3
output:
11497815
result:
ok 1 number(s): "11497815"
Test #6:
score: 0
Accepted
time: 1ms
memory: 5948kb
input:
994 515
output:
33689623
result:
ok 1 number(s): "33689623"
Test #7:
score: 0
Accepted
time: 1ms
memory: 5972kb
input:
4476 6182
output:
114894183
result:
ok 1 number(s): "114894183"
Test #8:
score: 0
Accepted
time: 1ms
memory: 6040kb
input:
58957 12755
output:
932388891
result:
ok 1 number(s): "932388891"
Test #9:
score: 0
Accepted
time: 16ms
memory: 10740kb
input:
218138 28238
output:
392861201
result:
ok 1 number(s): "392861201"
Test #10:
score: 0
Accepted
time: 46ms
memory: 10220kb
input:
644125 316810
output:
420621854
result:
ok 1 number(s): "420621854"
Test #11:
score: 0
Accepted
time: 78ms
memory: 11280kb
input:
612914 505428
output:
973686286
result:
ok 1 number(s): "973686286"
Test #12:
score: 0
Accepted
time: 80ms
memory: 11700kb
input:
998216 938963
output:
251335926
result:
ok 1 number(s): "251335926"
Test #13:
score: 0
Accepted
time: 86ms
memory: 11700kb
input:
990516 996933
output:
549551960
result:
ok 1 number(s): "549551960"
Test #14:
score: 0
Accepted
time: 79ms
memory: 11648kb
input:
999019 999012
output:
637189128
result:
ok 1 number(s): "637189128"
Test #15:
score: 0
Accepted
time: 145ms
memory: 11692kb
input:
999928 999950
output:
185229465
result:
ok 1 number(s): "185229465"
Test #16:
score: 0
Accepted
time: 11ms
memory: 11752kb
input:
999999 999999
output:
384164916
result:
ok 1 number(s): "384164916"
Test #17:
score: 0
Accepted
time: 71ms
memory: 11712kb
input:
999999 1000000
output:
696165930
result:
ok 1 number(s): "696165930"
Test #18:
score: 0
Accepted
time: 86ms
memory: 11756kb
input:
1000000 999999
output:
219071706
result:
ok 1 number(s): "219071706"
Test #19:
score: 0
Accepted
time: 146ms
memory: 11708kb
input:
1000000 1000000
output:
128206597
result:
ok 1 number(s): "128206597"
Test #20:
score: 0
Accepted
time: 0ms
memory: 5848kb
input:
2 10
output:
1410
result:
ok 1 number(s): "1410"
Test #21:
score: 0
Accepted
time: 1ms
memory: 5992kb
input:
84 16
output:
297627153
result:
ok 1 number(s): "297627153"
Test #22:
score: 0
Accepted
time: 1ms
memory: 5952kb
input:
643 800
output:
489237163
result:
ok 1 number(s): "489237163"
Test #23:
score: 0
Accepted
time: 1ms
memory: 5964kb
input:
9903 880
output:
595167333
result:
ok 1 number(s): "595167333"
Test #24:
score: 0
Accepted
time: 13ms
memory: 8296kb
input:
97446 89750
output:
410205549
result:
ok 1 number(s): "410205549"
Test #25:
score: 0
Accepted
time: 63ms
memory: 10268kb
input:
186460 646474
output:
32638530
result:
ok 1 number(s): "32638530"
Test #26:
score: 0
Accepted
time: 49ms
memory: 9804kb
input:
508940 244684
output:
598321755
result:
ok 1 number(s): "598321755"
Test #27:
score: 0
Accepted
time: 77ms
memory: 11016kb
input:
583646 557758
output:
858695621
result:
ok 1 number(s): "858695621"
Test #28:
score: 0
Accepted
time: 142ms
memory: 11604kb
input:
969610 992608
output:
256683498
result:
ok 1 number(s): "256683498"
Test #29:
score: 0
Accepted
time: 148ms
memory: 11700kb
input:
995106 996434
output:
411791999
result:
ok 1 number(s): "411791999"
Test #30:
score: 0
Accepted
time: 68ms
memory: 11708kb
input:
999961 999872
output:
61222370
result:
ok 1 number(s): "61222370"
Test #31:
score: 0
Accepted
time: 78ms
memory: 11636kb
input:
999977 999908
output:
831096762
result:
ok 1 number(s): "831096762"
Test #32:
score: 0
Accepted
time: 146ms
memory: 11700kb
input:
999992 999998
output:
562977678
result:
ok 1 number(s): "562977678"
Test #33:
score: 0
Accepted
time: 7ms
memory: 11632kb
input:
1000000 2
output:
118436113
result:
ok 1 number(s): "118436113"
Test #34:
score: 0
Accepted
time: 86ms
memory: 11708kb
input:
2 1000000
output:
298823641
result:
ok 1 number(s): "298823641"