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#486936#6417. Classical Summation Problemucup-team1525#AC ✓158ms11552kbC++201.3kb2024-07-22 12:50:122024-07-22 12:50:13

Judging History

你现在查看的是最新测评结果

  • [2024-07-22 12:50:13]
  • 评测
  • 测评结果:AC
  • 用时:158ms
  • 内存:11552kb
  • [2024-07-22 12:50:12]
  • 提交

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;
}

详细

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"