QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#132492 | #6417. Classical Summation Problem | UFRJ# | AC ✓ | 340ms | 19260kb | C++20 | 1.3kb | 2023-07-30 00:36:35 | 2023-07-30 00:36:37 |
Judging History
answer
#include "bits/stdc++.h"
using namespace std;
using lint = int64_t;
const int mod = 998244353;
const int lim = 1e6 + 10;
lint power(lint x, lint n){
x %= mod;
lint res = 1;
for(;n;n>>=1){
if(n&1) res = res * x % mod;
x = x * x % mod;
}
return res;
}
lint fac[lim], ifac[lim];
void prep(){
fac[0] = 1;
for(int i=1;i<lim;i++) fac[i] = (fac[i-1] * i) % mod;
ifac[lim-1] = power(fac[lim-1], mod - 2);
for(int i=lim-2;i>=0;i--) ifac[i] = (ifac[i+1] * (i + 1)) % mod;
}
int main() {
cin.tie(nullptr)->sync_with_stdio(false);
prep();
lint n, k;
cin>>n>>k;
lint ans = power(n, k) * (n + 1) % mod * power(2, mod - 2) % mod;
if(k&1){
cout<<ans<<"\n";
}
else{
lint cnt = 0;
for(int i=1;i<=n;i++){
lint cur = (n + 1 - i) % mod * ( (power(i, k/2) - power(i - 1, k/2) + mod) * power(n - i + 1, k/2) % mod -
(power(n - i + 1, k/2) - power(n - i, k/2) + mod) * power(i, k/2) % mod + mod) % mod;
cnt = (cnt + cur) % mod;
}
cnt = cnt * fac[k] % mod * ifac[k/2] % mod * ifac[k/2] % mod * power(2, mod - 2) % mod;
ans = (ans - cnt + mod) % mod;
cout<<ans<<"\n";
}
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 6ms
memory: 19088kb
input:
3 2
output:
14
result:
ok 1 number(s): "14"
Test #2:
score: 0
Accepted
time: 12ms
memory: 19100kb
input:
5 3
output:
375
result:
ok 1 number(s): "375"
Test #3:
score: 0
Accepted
time: 1ms
memory: 19096kb
input:
2 2
output:
5
result:
ok 1 number(s): "5"
Test #4:
score: 0
Accepted
time: 12ms
memory: 19008kb
input:
10 9
output:
508778235
result:
ok 1 number(s): "508778235"
Test #5:
score: 0
Accepted
time: 4ms
memory: 19156kb
input:
69 3
output:
11497815
result:
ok 1 number(s): "11497815"
Test #6:
score: 0
Accepted
time: 8ms
memory: 19048kb
input:
994 515
output:
33689623
result:
ok 1 number(s): "33689623"
Test #7:
score: 0
Accepted
time: 8ms
memory: 19224kb
input:
4476 6182
output:
114894183
result:
ok 1 number(s): "114894183"
Test #8:
score: 0
Accepted
time: 11ms
memory: 19092kb
input:
58957 12755
output:
932388891
result:
ok 1 number(s): "932388891"
Test #9:
score: 0
Accepted
time: 58ms
memory: 19000kb
input:
218138 28238
output:
392861201
result:
ok 1 number(s): "392861201"
Test #10:
score: 0
Accepted
time: 176ms
memory: 19048kb
input:
644125 316810
output:
420621854
result:
ok 1 number(s): "420621854"
Test #11:
score: 0
Accepted
time: 188ms
memory: 19104kb
input:
612914 505428
output:
973686286
result:
ok 1 number(s): "973686286"
Test #12:
score: 0
Accepted
time: 8ms
memory: 19004kb
input:
998216 938963
output:
251335926
result:
ok 1 number(s): "251335926"
Test #13:
score: 0
Accepted
time: 11ms
memory: 19056kb
input:
990516 996933
output:
549551960
result:
ok 1 number(s): "549551960"
Test #14:
score: 0
Accepted
time: 330ms
memory: 19092kb
input:
999019 999012
output:
637189128
result:
ok 1 number(s): "637189128"
Test #15:
score: 0
Accepted
time: 332ms
memory: 19208kb
input:
999928 999950
output:
185229465
result:
ok 1 number(s): "185229465"
Test #16:
score: 0
Accepted
time: 3ms
memory: 19184kb
input:
999999 999999
output:
384164916
result:
ok 1 number(s): "384164916"
Test #17:
score: 0
Accepted
time: 310ms
memory: 19112kb
input:
999999 1000000
output:
696165930
result:
ok 1 number(s): "696165930"
Test #18:
score: 0
Accepted
time: 8ms
memory: 19208kb
input:
1000000 999999
output:
219071706
result:
ok 1 number(s): "219071706"
Test #19:
score: 0
Accepted
time: 306ms
memory: 19224kb
input:
1000000 1000000
output:
128206597
result:
ok 1 number(s): "128206597"
Test #20:
score: 0
Accepted
time: 12ms
memory: 19052kb
input:
2 10
output:
1410
result:
ok 1 number(s): "1410"
Test #21:
score: 0
Accepted
time: 9ms
memory: 19204kb
input:
84 16
output:
297627153
result:
ok 1 number(s): "297627153"
Test #22:
score: 0
Accepted
time: 11ms
memory: 19088kb
input:
643 800
output:
489237163
result:
ok 1 number(s): "489237163"
Test #23:
score: 0
Accepted
time: 12ms
memory: 19096kb
input:
9903 880
output:
595167333
result:
ok 1 number(s): "595167333"
Test #24:
score: 0
Accepted
time: 25ms
memory: 19088kb
input:
97446 89750
output:
410205549
result:
ok 1 number(s): "410205549"
Test #25:
score: 0
Accepted
time: 65ms
memory: 19004kb
input:
186460 646474
output:
32638530
result:
ok 1 number(s): "32638530"
Test #26:
score: 0
Accepted
time: 152ms
memory: 19228kb
input:
508940 244684
output:
598321755
result:
ok 1 number(s): "598321755"
Test #27:
score: 0
Accepted
time: 164ms
memory: 19044kb
input:
583646 557758
output:
858695621
result:
ok 1 number(s): "858695621"
Test #28:
score: 0
Accepted
time: 305ms
memory: 19052kb
input:
969610 992608
output:
256683498
result:
ok 1 number(s): "256683498"
Test #29:
score: 0
Accepted
time: 315ms
memory: 19100kb
input:
995106 996434
output:
411791999
result:
ok 1 number(s): "411791999"
Test #30:
score: 0
Accepted
time: 310ms
memory: 19096kb
input:
999961 999872
output:
61222370
result:
ok 1 number(s): "61222370"
Test #31:
score: 0
Accepted
time: 324ms
memory: 19260kb
input:
999977 999908
output:
831096762
result:
ok 1 number(s): "831096762"
Test #32:
score: 0
Accepted
time: 340ms
memory: 19096kb
input:
999992 999998
output:
562977678
result:
ok 1 number(s): "562977678"
Test #33:
score: 0
Accepted
time: 28ms
memory: 19208kb
input:
1000000 2
output:
118436113
result:
ok 1 number(s): "118436113"
Test #34:
score: 0
Accepted
time: 12ms
memory: 19088kb
input:
2 1000000
output:
298823641
result:
ok 1 number(s): "298823641"