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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#175818 | #6417. Classical Summation Problem | danielkou5855 | AC ✓ | 132ms | 11232kb | C++17 | 1.4kb | 2023-09-11 00:47:02 | 2023-09-11 00:47:02 |
Judging History
answer
// Source: https://usaco.guide/general/io
#include <bits/stdc++.h>
#define ll long long
using namespace std;
const int MOD = 998244353;
ll exp(ll a, ll b) {
ll res = 1;
while (b > 0) {
if (b & 1)
res = res * a % MOD;
a = a * a % MOD;
b >>= 1;
}
return res % MOD;
}
vector<ll> factorial;
void generate_factorial(int m) {
factorial.resize(m + 1);
factorial[0] = 1;
for (ll i = 1; i <= m; i++) {
factorial[i] = factorial[i - 1] * i; factorial[i] += MOD; factorial[i] %= MOD;
}
}
ll choose(ll a, ll b) {
ll tmp = factorial[a];
tmp *= exp(factorial[a - b], MOD - 2); tmp += MOD; tmp %= MOD;
tmp *= exp(factorial[b], MOD - 2); tmp += MOD; tmp %= MOD;
return tmp;
}
signed main() {
int N, K; cin >> N >> K;
generate_factorial(max(N + 1, K));
if (K % 2 == 1) {
ll ans = (N + 1) * exp(N, K) % MOD;
ans *= exp(2, MOD - 2); ans %= MOD;
cout << ans << "\n";
return 0;
}
ll ans = 0;
for (int i = 1; i < N; i++) {
ll tmp = choose(K, K / 2) * exp(i, K / 2) % MOD;
tmp = tmp * exp(N - i, K / 2) % MOD;
ans += tmp; ans %= MOD;
}
ll tmp2 = (N + 1) * exp(N, K) % MOD;
tmp2 -= ans; tmp2 += MOD; tmp2 %= MOD;
tmp2 *= exp(2, MOD - 2); tmp2 %= MOD;
cout << tmp2 << "\n";
}
Details
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Test #1:
score: 100
Accepted
time: 0ms
memory: 3704kb
input:
3 2
output:
14
result:
ok 1 number(s): "14"
Test #2:
score: 0
Accepted
time: 0ms
memory: 3644kb
input:
5 3
output:
375
result:
ok 1 number(s): "375"
Test #3:
score: 0
Accepted
time: 1ms
memory: 3648kb
input:
2 2
output:
5
result:
ok 1 number(s): "5"
Test #4:
score: 0
Accepted
time: 1ms
memory: 3584kb
input:
10 9
output:
508778235
result:
ok 1 number(s): "508778235"
Test #5:
score: 0
Accepted
time: 0ms
memory: 3652kb
input:
69 3
output:
11497815
result:
ok 1 number(s): "11497815"
Test #6:
score: 0
Accepted
time: 1ms
memory: 3596kb
input:
994 515
output:
33689623
result:
ok 1 number(s): "33689623"
Test #7:
score: 0
Accepted
time: 1ms
memory: 3772kb
input:
4476 6182
output:
114894183
result:
ok 1 number(s): "114894183"
Test #8:
score: 0
Accepted
time: 1ms
memory: 3712kb
input:
58957 12755
output:
932388891
result:
ok 1 number(s): "932388891"
Test #9:
score: 0
Accepted
time: 18ms
memory: 4996kb
input:
218138 28238
output:
392861201
result:
ok 1 number(s): "392861201"
Test #10:
score: 0
Accepted
time: 75ms
memory: 8160kb
input:
644125 316810
output:
420621854
result:
ok 1 number(s): "420621854"
Test #11:
score: 0
Accepted
time: 76ms
memory: 8036kb
input:
612914 505428
output:
973686286
result:
ok 1 number(s): "973686286"
Test #12:
score: 0
Accepted
time: 3ms
memory: 10856kb
input:
998216 938963
output:
251335926
result:
ok 1 number(s): "251335926"
Test #13:
score: 0
Accepted
time: 3ms
memory: 10860kb
input:
990516 996933
output:
549551960
result:
ok 1 number(s): "549551960"
Test #14:
score: 0
Accepted
time: 131ms
memory: 11000kb
input:
999019 999012
output:
637189128
result:
ok 1 number(s): "637189128"
Test #15:
score: 0
Accepted
time: 132ms
memory: 11168kb
input:
999928 999950
output:
185229465
result:
ok 1 number(s): "185229465"
Test #16:
score: 0
Accepted
time: 7ms
memory: 11128kb
input:
999999 999999
output:
384164916
result:
ok 1 number(s): "384164916"
Test #17:
score: 0
Accepted
time: 124ms
memory: 11168kb
input:
999999 1000000
output:
696165930
result:
ok 1 number(s): "696165930"
Test #18:
score: 0
Accepted
time: 7ms
memory: 11224kb
input:
1000000 999999
output:
219071706
result:
ok 1 number(s): "219071706"
Test #19:
score: 0
Accepted
time: 117ms
memory: 10968kb
input:
1000000 1000000
output:
128206597
result:
ok 1 number(s): "128206597"
Test #20:
score: 0
Accepted
time: 1ms
memory: 3640kb
input:
2 10
output:
1410
result:
ok 1 number(s): "1410"
Test #21:
score: 0
Accepted
time: 0ms
memory: 3644kb
input:
84 16
output:
297627153
result:
ok 1 number(s): "297627153"
Test #22:
score: 0
Accepted
time: 1ms
memory: 3636kb
input:
643 800
output:
489237163
result:
ok 1 number(s): "489237163"
Test #23:
score: 0
Accepted
time: 0ms
memory: 3784kb
input:
9903 880
output:
595167333
result:
ok 1 number(s): "595167333"
Test #24:
score: 0
Accepted
time: 7ms
memory: 3928kb
input:
97446 89750
output:
410205549
result:
ok 1 number(s): "410205549"
Test #25:
score: 0
Accepted
time: 27ms
memory: 8320kb
input:
186460 646474
output:
32638530
result:
ok 1 number(s): "32638530"
Test #26:
score: 0
Accepted
time: 56ms
memory: 7044kb
input:
508940 244684
output:
598321755
result:
ok 1 number(s): "598321755"
Test #27:
score: 0
Accepted
time: 64ms
memory: 7820kb
input:
583646 557758
output:
858695621
result:
ok 1 number(s): "858695621"
Test #28:
score: 0
Accepted
time: 123ms
memory: 10916kb
input:
969610 992608
output:
256683498
result:
ok 1 number(s): "256683498"
Test #29:
score: 0
Accepted
time: 126ms
memory: 10848kb
input:
995106 996434
output:
411791999
result:
ok 1 number(s): "411791999"
Test #30:
score: 0
Accepted
time: 118ms
memory: 10928kb
input:
999961 999872
output:
61222370
result:
ok 1 number(s): "61222370"
Test #31:
score: 0
Accepted
time: 125ms
memory: 11232kb
input:
999977 999908
output:
831096762
result:
ok 1 number(s): "831096762"
Test #32:
score: 0
Accepted
time: 130ms
memory: 11088kb
input:
999992 999998
output:
562977678
result:
ok 1 number(s): "562977678"
Test #33:
score: 0
Accepted
time: 15ms
memory: 11120kb
input:
1000000 2
output:
118436113
result:
ok 1 number(s): "118436113"
Test #34:
score: 0
Accepted
time: 7ms
memory: 11120kb
input:
2 1000000
output:
298823641
result:
ok 1 number(s): "298823641"