QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#407931 | #6417. Classical Summation Problem | grass8cow# | AC ✓ | 53ms | 11756kb | C++17 | 1.1kb | 2024-05-09 15:00:13 | 2024-05-09 15:00:14 |
Judging History
answer
#include<bits/stdc++.h>
using namespace std;
int n,m;
const int mod=998244353;
int qpow(int a,int b){
int c=1;
for(;b;b>>=1){
if(b&1)c=1ll*a*c%mod;
a=1ll*a*a%mod;
}
return c;
}
const int N=1e6;
int jc[1010000],ij[1010000];
int C(int a,int b){
if(a<0||a<b||b<0)return 0;
return 1ll*jc[a]*ij[b]%mod*ij[a-b]%mod;
}
void sieve(){
jc[0]=1;
for(int i=1;i<=N;i++)jc[i]=1ll*i*jc[i-1]%mod;
ij[N]=qpow(jc[N],mod-2);
for(int i=N;i;i--)ij[i-1]=1ll*i*ij[i]%mod;
}
int main(){
sieve();
scanf("%d%d",&n,&m);
int ans=0;
/*for(int t=1;t<n;t++)for(int i=0;i<=(m-1)/2;i++)
(ans+=1ll*C(m,i)*qpow(t,i)%mod*qpow(n-t,m-i)%mod)%=mod;*/
int al=qpow(n,m);
for(int t=1;t*2<n;t++){
(ans+=al)%=mod;
if(!(m&1))(ans-=1ll*C(m,m/2)*qpow(1ll*t*(n-t)%mod,m/2)%mod)%=mod;
//同时计算t和n-t的贡献
}
if(!(n&1)){
int zk=qpow(n/2,m);
for(int i=0;i<=(m-1)/2;i++)(ans+=1ll*C(m,i)*zk%mod)%=mod;
}
printf("%d\n",((ans+qpow(n,m))%mod+mod)%mod);
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 12ms
memory: 11636kb
input:
3 2
output:
14
result:
ok 1 number(s): "14"
Test #2:
score: 0
Accepted
time: 12ms
memory: 11672kb
input:
5 3
output:
375
result:
ok 1 number(s): "375"
Test #3:
score: 0
Accepted
time: 12ms
memory: 11488kb
input:
2 2
output:
5
result:
ok 1 number(s): "5"
Test #4:
score: 0
Accepted
time: 12ms
memory: 11684kb
input:
10 9
output:
508778235
result:
ok 1 number(s): "508778235"
Test #5:
score: 0
Accepted
time: 9ms
memory: 11608kb
input:
69 3
output:
11497815
result:
ok 1 number(s): "11497815"
Test #6:
score: 0
Accepted
time: 12ms
memory: 11724kb
input:
994 515
output:
33689623
result:
ok 1 number(s): "33689623"
Test #7:
score: 0
Accepted
time: 8ms
memory: 11656kb
input:
4476 6182
output:
114894183
result:
ok 1 number(s): "114894183"
Test #8:
score: 0
Accepted
time: 8ms
memory: 11508kb
input:
58957 12755
output:
932388891
result:
ok 1 number(s): "932388891"
Test #9:
score: 0
Accepted
time: 19ms
memory: 11684kb
input:
218138 28238
output:
392861201
result:
ok 1 number(s): "392861201"
Test #10:
score: 0
Accepted
time: 27ms
memory: 11560kb
input:
644125 316810
output:
420621854
result:
ok 1 number(s): "420621854"
Test #11:
score: 0
Accepted
time: 29ms
memory: 11660kb
input:
612914 505428
output:
973686286
result:
ok 1 number(s): "973686286"
Test #12:
score: 0
Accepted
time: 12ms
memory: 11628kb
input:
998216 938963
output:
251335926
result:
ok 1 number(s): "251335926"
Test #13:
score: 0
Accepted
time: 12ms
memory: 11524kb
input:
990516 996933
output:
549551960
result:
ok 1 number(s): "549551960"
Test #14:
score: 0
Accepted
time: 52ms
memory: 11684kb
input:
999019 999012
output:
637189128
result:
ok 1 number(s): "637189128"
Test #15:
score: 0
Accepted
time: 45ms
memory: 11652kb
input:
999928 999950
output:
185229465
result:
ok 1 number(s): "185229465"
Test #16:
score: 0
Accepted
time: 13ms
memory: 11520kb
input:
999999 999999
output:
384164916
result:
ok 1 number(s): "384164916"
Test #17:
score: 0
Accepted
time: 46ms
memory: 11592kb
input:
999999 1000000
output:
696165930
result:
ok 1 number(s): "696165930"
Test #18:
score: 0
Accepted
time: 15ms
memory: 11528kb
input:
1000000 999999
output:
219071706
result:
ok 1 number(s): "219071706"
Test #19:
score: 0
Accepted
time: 53ms
memory: 11720kb
input:
1000000 1000000
output:
128206597
result:
ok 1 number(s): "128206597"
Test #20:
score: 0
Accepted
time: 8ms
memory: 11756kb
input:
2 10
output:
1410
result:
ok 1 number(s): "1410"
Test #21:
score: 0
Accepted
time: 11ms
memory: 11664kb
input:
84 16
output:
297627153
result:
ok 1 number(s): "297627153"
Test #22:
score: 0
Accepted
time: 8ms
memory: 11668kb
input:
643 800
output:
489237163
result:
ok 1 number(s): "489237163"
Test #23:
score: 0
Accepted
time: 12ms
memory: 11608kb
input:
9903 880
output:
595167333
result:
ok 1 number(s): "595167333"
Test #24:
score: 0
Accepted
time: 14ms
memory: 11724kb
input:
97446 89750
output:
410205549
result:
ok 1 number(s): "410205549"
Test #25:
score: 0
Accepted
time: 20ms
memory: 11528kb
input:
186460 646474
output:
32638530
result:
ok 1 number(s): "32638530"
Test #26:
score: 0
Accepted
time: 30ms
memory: 11556kb
input:
508940 244684
output:
598321755
result:
ok 1 number(s): "598321755"
Test #27:
score: 0
Accepted
time: 27ms
memory: 11608kb
input:
583646 557758
output:
858695621
result:
ok 1 number(s): "858695621"
Test #28:
score: 0
Accepted
time: 45ms
memory: 11656kb
input:
969610 992608
output:
256683498
result:
ok 1 number(s): "256683498"
Test #29:
score: 0
Accepted
time: 53ms
memory: 11544kb
input:
995106 996434
output:
411791999
result:
ok 1 number(s): "411791999"
Test #30:
score: 0
Accepted
time: 50ms
memory: 11716kb
input:
999961 999872
output:
61222370
result:
ok 1 number(s): "61222370"
Test #31:
score: 0
Accepted
time: 47ms
memory: 11752kb
input:
999977 999908
output:
831096762
result:
ok 1 number(s): "831096762"
Test #32:
score: 0
Accepted
time: 49ms
memory: 11672kb
input:
999992 999998
output:
562977678
result:
ok 1 number(s): "562977678"
Test #33:
score: 0
Accepted
time: 11ms
memory: 11608kb
input:
1000000 2
output:
118436113
result:
ok 1 number(s): "118436113"
Test #34:
score: 0
Accepted
time: 14ms
memory: 11644kb
input:
2 1000000
output:
298823641
result:
ok 1 number(s): "298823641"