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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#175818#6417. Classical Summation Problemdanielkou5855AC ✓132ms11232kbC++171.4kb2023-09-11 00:47:022023-09-11 00:47:02

Judging History

你现在查看的是最新测评结果

  • [2023-09-11 00:47:02]
  • 评测
  • 测评结果:AC
  • 用时:132ms
  • 内存:11232kb
  • [2023-09-11 00:47:02]
  • 提交

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

Tip: Click on the bar to expand more detailed information

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"