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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#305953#6417. Classical Summation ProblemckisekiAC ✓152ms3740kbC++201.4kb2024-01-16 06:26:572024-01-16 06:26:58

Judging History

你现在查看的是最新测评结果

  • [2024-01-16 06:26:58]
  • 评测
  • 测评结果:AC
  • 用时:152ms
  • 内存:3740kb
  • [2024-01-16 06:26:57]
  • 提交

answer

#include <bits/stdc++.h>
using namespace std;

const int mod = 998244353;

int modadd(int a, int b) {
    return a + b < mod ? a + b : a + b - mod;
}

int modsub(int a, int b) {
    return a - b < 0 ? a - b + mod : a - b;
}

int modmul(int64_t a, int64_t b) {
    return static_cast<int>(a * b % mod);
}

int modpow(int e, int64_t p) {
    int r = 1;
    while (p) {
        if (p & 1) r = modmul(r, e);
        e = modmul(e, e);
        p >>= 1;
    }
    return r;
}

int C(int n, int k) {
    int res = 1;
    int div = 1;
    for (int i = 0; i < k; i++)
        res = modmul(res, n - i);
    for (int i = 1; i <= k; i++)
        div = modmul(div, i);
    return modmul(res, modpow(div, mod - 2));
}

int main() {
    cin.tie(nullptr)->sync_with_stdio(false);
    int n, k;
    cin >> n >> k;

    int ans = 0;

    ans = modpow(n, k);

    const int inv2 = (mod + 1) / 2;
    if (k % 2 == 1) {
        int tmp = modmul(modpow(n, k), (n - 1));
        ans = modadd(ans, modmul(tmp, inv2));
    } else {
        int tmp = modmul(modpow(n, k), (n - 1));
        int sum = 0;
        for (int i = 1; i <= n - 1; i++) {
            sum = modadd(sum, modmul(modpow(i, k/2), modpow(n - i, k / 2)));
        }
        tmp = modsub(tmp, modmul(C(k, k/2), sum));
        ans = modadd(ans, modmul(tmp, inv2));
    }

    cout << ans << '\n';

    return 0;
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 1ms
memory: 3680kb

input:

3 2

output:

14

result:

ok 1 number(s): "14"

Test #2:

score: 0
Accepted
time: 1ms
memory: 3660kb

input:

5 3

output:

375

result:

ok 1 number(s): "375"

Test #3:

score: 0
Accepted
time: 1ms
memory: 3604kb

input:

2 2

output:

5

result:

ok 1 number(s): "5"

Test #4:

score: 0
Accepted
time: 0ms
memory: 3620kb

input:

10 9

output:

508778235

result:

ok 1 number(s): "508778235"

Test #5:

score: 0
Accepted
time: 1ms
memory: 3740kb

input:

69 3

output:

11497815

result:

ok 1 number(s): "11497815"

Test #6:

score: 0
Accepted
time: 1ms
memory: 3664kb

input:

994 515

output:

33689623

result:

ok 1 number(s): "33689623"

Test #7:

score: 0
Accepted
time: 1ms
memory: 3656kb

input:

4476 6182

output:

114894183

result:

ok 1 number(s): "114894183"

Test #8:

score: 0
Accepted
time: 1ms
memory: 3600kb

input:

58957 12755

output:

932388891

result:

ok 1 number(s): "932388891"

Test #9:

score: 0
Accepted
time: 22ms
memory: 3612kb

input:

218138 28238

output:

392861201

result:

ok 1 number(s): "392861201"

Test #10:

score: 0
Accepted
time: 85ms
memory: 3608kb

input:

644125 316810

output:

420621854

result:

ok 1 number(s): "420621854"

Test #11:

score: 0
Accepted
time: 82ms
memory: 3600kb

input:

612914 505428

output:

973686286

result:

ok 1 number(s): "973686286"

Test #12:

score: 0
Accepted
time: 0ms
memory: 3664kb

input:

998216 938963

output:

251335926

result:

ok 1 number(s): "251335926"

Test #13:

score: 0
Accepted
time: 0ms
memory: 3732kb

input:

990516 996933

output:

549551960

result:

ok 1 number(s): "549551960"

Test #14:

score: 0
Accepted
time: 145ms
memory: 3728kb

input:

999019 999012

output:

637189128

result:

ok 1 number(s): "637189128"

Test #15:

score: 0
Accepted
time: 150ms
memory: 3668kb

input:

999928 999950

output:

185229465

result:

ok 1 number(s): "185229465"

Test #16:

score: 0
Accepted
time: 0ms
memory: 3676kb

input:

999999 999999

output:

384164916

result:

ok 1 number(s): "384164916"

Test #17:

score: 0
Accepted
time: 141ms
memory: 3684kb

input:

999999 1000000

output:

696165930

result:

ok 1 number(s): "696165930"

Test #18:

score: 0
Accepted
time: 0ms
memory: 3600kb

input:

1000000 999999

output:

219071706

result:

ok 1 number(s): "219071706"

Test #19:

score: 0
Accepted
time: 145ms
memory: 3688kb

input:

1000000 1000000

output:

128206597

result:

ok 1 number(s): "128206597"

Test #20:

score: 0
Accepted
time: 0ms
memory: 3692kb

input:

2 10

output:

1410

result:

ok 1 number(s): "1410"

Test #21:

score: 0
Accepted
time: 0ms
memory: 3660kb

input:

84 16

output:

297627153

result:

ok 1 number(s): "297627153"

Test #22:

score: 0
Accepted
time: 0ms
memory: 3664kb

input:

643 800

output:

489237163

result:

ok 1 number(s): "489237163"

Test #23:

score: 0
Accepted
time: 0ms
memory: 3664kb

input:

9903 880

output:

595167333

result:

ok 1 number(s): "595167333"

Test #24:

score: 0
Accepted
time: 12ms
memory: 3608kb

input:

97446 89750

output:

410205549

result:

ok 1 number(s): "410205549"

Test #25:

score: 0
Accepted
time: 29ms
memory: 3644kb

input:

186460 646474

output:

32638530

result:

ok 1 number(s): "32638530"

Test #26:

score: 0
Accepted
time: 62ms
memory: 3580kb

input:

508940 244684

output:

598321755

result:

ok 1 number(s): "598321755"

Test #27:

score: 0
Accepted
time: 81ms
memory: 3604kb

input:

583646 557758

output:

858695621

result:

ok 1 number(s): "858695621"

Test #28:

score: 0
Accepted
time: 142ms
memory: 3668kb

input:

969610 992608

output:

256683498

result:

ok 1 number(s): "256683498"

Test #29:

score: 0
Accepted
time: 149ms
memory: 3652kb

input:

995106 996434

output:

411791999

result:

ok 1 number(s): "411791999"

Test #30:

score: 0
Accepted
time: 142ms
memory: 3664kb

input:

999961 999872

output:

61222370

result:

ok 1 number(s): "61222370"

Test #31:

score: 0
Accepted
time: 144ms
memory: 3604kb

input:

999977 999908

output:

831096762

result:

ok 1 number(s): "831096762"

Test #32:

score: 0
Accepted
time: 152ms
memory: 3680kb

input:

999992 999998

output:

562977678

result:

ok 1 number(s): "562977678"

Test #33:

score: 0
Accepted
time: 3ms
memory: 3616kb

input:

1000000 2

output:

118436113

result:

ok 1 number(s): "118436113"

Test #34:

score: 0
Accepted
time: 5ms
memory: 3604kb

input:

2 1000000

output:

298823641

result:

ok 1 number(s): "298823641"