QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#486936 | #6417. Classical Summation Problem | ucup-team1525# | AC ✓ | 158ms | 11552kb | C++20 | 1.3kb | 2024-07-22 12:50:12 | 2024-07-22 12:50:13 |
Judging History
answer
#include <bits/stdc++.h>
using namespace std;
const int mod = 998244353;
const int inv2 = (mod + 1) / 2;
const int N = 1e6 + 65;
int n, k;
int fac[N], invfac[N];
int ksm(int a, int b) {
int ret = 1;
while (b) {
if (b & 1)
ret = 1ll * ret * a % mod;
b >>= 1, a = 1ll * a * a % mod;
}
return ret;
}
int C(int n, int m) {
return 1ll * fac[n] * invfac[m] % mod * invfac[n - m] % mod;
}
int main() {
cin >> n >> k;
fac[0] = invfac[0] = 1;
for (int i = 1; i < N; i++) fac[i] = 1ll * fac[i - 1] * i % mod;
invfac[N - 1] = ksm(fac[N - 1], mod - 2);
for (int i = N - 2; i >= 1; i--) invfac[i] = 1ll * invfac[i + 1] * (i + 1) % mod;
if (k & 1) {
cout << 1ll * (n + 1) * inv2 % mod * ksm(n, k) % mod << endl;
} else {
int ans = 1ll * (n + 1) * inv2 % mod;
int res = 0;
for (int i = 1; i < n; i++) {
int p = 1ll * ksm(i, k / 2) * ksm(n - i, k / 2) % mod * C(k, k / 2) % mod;
res = (res + 1ll * p) % mod;
}
res = 1ll * res * inv2 % mod;
res = 1ll * res * ksm(ksm(n, k), mod - 2) % mod;
ans -= res;
ans = (ans % mod + mod) % mod;
ans = 1ll * ans * ksm(n, k) % mod;
cout << ans << "\n";
}
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 10ms
memory: 11408kb
input:
3 2
output:
14
result:
ok 1 number(s): "14"
Test #2:
score: 0
Accepted
time: 10ms
memory: 11464kb
input:
5 3
output:
375
result:
ok 1 number(s): "375"
Test #3:
score: 0
Accepted
time: 10ms
memory: 11468kb
input:
2 2
output:
5
result:
ok 1 number(s): "5"
Test #4:
score: 0
Accepted
time: 10ms
memory: 11480kb
input:
10 9
output:
508778235
result:
ok 1 number(s): "508778235"
Test #5:
score: 0
Accepted
time: 6ms
memory: 11520kb
input:
69 3
output:
11497815
result:
ok 1 number(s): "11497815"
Test #6:
score: 0
Accepted
time: 10ms
memory: 11480kb
input:
994 515
output:
33689623
result:
ok 1 number(s): "33689623"
Test #7:
score: 0
Accepted
time: 10ms
memory: 11524kb
input:
4476 6182
output:
114894183
result:
ok 1 number(s): "114894183"
Test #8:
score: 0
Accepted
time: 10ms
memory: 11464kb
input:
58957 12755
output:
932388891
result:
ok 1 number(s): "932388891"
Test #9:
score: 0
Accepted
time: 32ms
memory: 11408kb
input:
218138 28238
output:
392861201
result:
ok 1 number(s): "392861201"
Test #10:
score: 0
Accepted
time: 93ms
memory: 11544kb
input:
644125 316810
output:
420621854
result:
ok 1 number(s): "420621854"
Test #11:
score: 0
Accepted
time: 90ms
memory: 11464kb
input:
612914 505428
output:
973686286
result:
ok 1 number(s): "973686286"
Test #12:
score: 0
Accepted
time: 10ms
memory: 11460kb
input:
998216 938963
output:
251335926
result:
ok 1 number(s): "251335926"
Test #13:
score: 0
Accepted
time: 10ms
memory: 11524kb
input:
990516 996933
output:
549551960
result:
ok 1 number(s): "549551960"
Test #14:
score: 0
Accepted
time: 155ms
memory: 11384kb
input:
999019 999012
output:
637189128
result:
ok 1 number(s): "637189128"
Test #15:
score: 0
Accepted
time: 158ms
memory: 11552kb
input:
999928 999950
output:
185229465
result:
ok 1 number(s): "185229465"
Test #16:
score: 0
Accepted
time: 10ms
memory: 11396kb
input:
999999 999999
output:
384164916
result:
ok 1 number(s): "384164916"
Test #17:
score: 0
Accepted
time: 145ms
memory: 11472kb
input:
999999 1000000
output:
696165930
result:
ok 1 number(s): "696165930"
Test #18:
score: 0
Accepted
time: 3ms
memory: 11400kb
input:
1000000 999999
output:
219071706
result:
ok 1 number(s): "219071706"
Test #19:
score: 0
Accepted
time: 153ms
memory: 11468kb
input:
1000000 1000000
output:
128206597
result:
ok 1 number(s): "128206597"
Test #20:
score: 0
Accepted
time: 10ms
memory: 11464kb
input:
2 10
output:
1410
result:
ok 1 number(s): "1410"
Test #21:
score: 0
Accepted
time: 7ms
memory: 11408kb
input:
84 16
output:
297627153
result:
ok 1 number(s): "297627153"
Test #22:
score: 0
Accepted
time: 6ms
memory: 11480kb
input:
643 800
output:
489237163
result:
ok 1 number(s): "489237163"
Test #23:
score: 0
Accepted
time: 10ms
memory: 11472kb
input:
9903 880
output:
595167333
result:
ok 1 number(s): "595167333"
Test #24:
score: 0
Accepted
time: 21ms
memory: 11468kb
input:
97446 89750
output:
410205549
result:
ok 1 number(s): "410205549"
Test #25:
score: 0
Accepted
time: 28ms
memory: 11544kb
input:
186460 646474
output:
32638530
result:
ok 1 number(s): "32638530"
Test #26:
score: 0
Accepted
time: 75ms
memory: 11468kb
input:
508940 244684
output:
598321755
result:
ok 1 number(s): "598321755"
Test #27:
score: 0
Accepted
time: 89ms
memory: 11484kb
input:
583646 557758
output:
858695621
result:
ok 1 number(s): "858695621"
Test #28:
score: 0
Accepted
time: 148ms
memory: 11532kb
input:
969610 992608
output:
256683498
result:
ok 1 number(s): "256683498"
Test #29:
score: 0
Accepted
time: 151ms
memory: 11548kb
input:
995106 996434
output:
411791999
result:
ok 1 number(s): "411791999"
Test #30:
score: 0
Accepted
time: 153ms
memory: 11468kb
input:
999961 999872
output:
61222370
result:
ok 1 number(s): "61222370"
Test #31:
score: 0
Accepted
time: 155ms
memory: 11512kb
input:
999977 999908
output:
831096762
result:
ok 1 number(s): "831096762"
Test #32:
score: 0
Accepted
time: 154ms
memory: 11536kb
input:
999992 999998
output:
562977678
result:
ok 1 number(s): "562977678"
Test #33:
score: 0
Accepted
time: 18ms
memory: 11520kb
input:
1000000 2
output:
118436113
result:
ok 1 number(s): "118436113"
Test #34:
score: 0
Accepted
time: 6ms
memory: 11472kb
input:
2 1000000
output:
298823641
result:
ok 1 number(s): "298823641"