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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#174390#6417. Classical Summation ProblemalexzhanUSAC ✓467ms3608kbC++172.1kb2023-09-10 07:01:512023-09-10 07:01:52

Judging History

你现在查看的是最新测评结果

  • [2023-09-10 07:01:52]
  • 评测
  • 测评结果:AC
  • 用时:467ms
  • 内存:3608kb
  • [2023-09-10 07:01:51]
  • 提交

answer

#include <iostream>
#include <vector>

using namespace std;

long long modulo = 998244353;

long long binaryExponentiation(long long value, long long power) {
    vector<long long> powers(31);
    powers[0] = value;
    for (int i = 1; i <= 30; i++) {
        powers[i] = powers[i - 1] * powers[i - 1];
        powers[i] %= modulo;
    }
    long long answer = 1;
    for (int i = 0; i <= 30; i++) {
        if ((power & (1 << i)) > 0) {
            answer *= powers[i];
            answer %= modulo;
        }
    }
    return answer;
}

long long divide(long long a, long long b) {
    // find a/b mod modulo
    // find b ^ (modulo - 2)
    long long inverse = binaryExponentiation(b, modulo - 2);
    return ((inverse * a) % modulo);
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int n, k;
    cin >> n >> k;
    long long answer = n + 1;
    for (int i = 0; i < k; i++) {
        answer *= n;
        answer %= modulo;
    }
    if (answer % 2 == 0) {
        answer /= 2;
    } else {
        answer = (answer + modulo) / 2;
    }
    if (k % 2 == 1) {
        cout << answer << "\n";
    } else {
        long long factorial1 = 1;
        for (int i = (k/2) + 1; i <= k; i++) {
            factorial1 *= i;
            factorial1 %= modulo;
        }
        long long factorial2 = 1;
        for (int i = 1; i <= (k/2); i++) {
            factorial2 *= i;
            factorial2 %= modulo;
        }
        long long combination = factorial1;
        combination = divide(combination, factorial2);

        long long value = 0;
        for (int i = 1; i < n; i++) {
            long long tmp = binaryExponentiation(i, k/2);
            tmp *= binaryExponentiation(n - i, k/2);
            tmp %= modulo;
            tmp *= combination;
            tmp %= modulo;
            value += tmp;
            value %= modulo;
        }
        if (value % 2 == 0) {
            value /= 2;
        } else {
            value = (value + modulo) / 2;
        }
        answer -= value;
        answer %= modulo;
        if (answer < 0) {
            answer += modulo;
        }
        cout << answer << "\n";
    }
    return 0;
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 1ms
memory: 3400kb

input:

3 2

output:

14

result:

ok 1 number(s): "14"

Test #2:

score: 0
Accepted
time: 0ms
memory: 3436kb

input:

5 3

output:

375

result:

ok 1 number(s): "375"

Test #3:

score: 0
Accepted
time: 0ms
memory: 3456kb

input:

2 2

output:

5

result:

ok 1 number(s): "5"

Test #4:

score: 0
Accepted
time: 0ms
memory: 3524kb

input:

10 9

output:

508778235

result:

ok 1 number(s): "508778235"

Test #5:

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

input:

69 3

output:

11497815

result:

ok 1 number(s): "11497815"

Test #6:

score: 0
Accepted
time: 2ms
memory: 3428kb

input:

994 515

output:

33689623

result:

ok 1 number(s): "33689623"

Test #7:

score: 0
Accepted
time: 3ms
memory: 3564kb

input:

4476 6182

output:

114894183

result:

ok 1 number(s): "114894183"

Test #8:

score: 0
Accepted
time: 0ms
memory: 3448kb

input:

58957 12755

output:

932388891

result:

ok 1 number(s): "932388891"

Test #9:

score: 0
Accepted
time: 98ms
memory: 3608kb

input:

218138 28238

output:

392861201

result:

ok 1 number(s): "392861201"

Test #10:

score: 0
Accepted
time: 292ms
memory: 3448kb

input:

644125 316810

output:

420621854

result:

ok 1 number(s): "420621854"

Test #11:

score: 0
Accepted
time: 281ms
memory: 3456kb

input:

612914 505428

output:

973686286

result:

ok 1 number(s): "973686286"

Test #12:

score: 0
Accepted
time: 5ms
memory: 3384kb

input:

998216 938963

output:

251335926

result:

ok 1 number(s): "251335926"

Test #13:

score: 0
Accepted
time: 5ms
memory: 3436kb

input:

990516 996933

output:

549551960

result:

ok 1 number(s): "549551960"

Test #14:

score: 0
Accepted
time: 467ms
memory: 3448kb

input:

999019 999012

output:

637189128

result:

ok 1 number(s): "637189128"

Test #15:

score: 0
Accepted
time: 455ms
memory: 3432kb

input:

999928 999950

output:

185229465

result:

ok 1 number(s): "185229465"

Test #16:

score: 0
Accepted
time: 7ms
memory: 3360kb

input:

999999 999999

output:

384164916

result:

ok 1 number(s): "384164916"

Test #17:

score: 0
Accepted
time: 451ms
memory: 3608kb

input:

999999 1000000

output:

696165930

result:

ok 1 number(s): "696165930"

Test #18:

score: 0
Accepted
time: 7ms
memory: 3440kb

input:

1000000 999999

output:

219071706

result:

ok 1 number(s): "219071706"

Test #19:

score: 0
Accepted
time: 449ms
memory: 3608kb

input:

1000000 1000000

output:

128206597

result:

ok 1 number(s): "128206597"

Test #20:

score: 0
Accepted
time: 1ms
memory: 3440kb

input:

2 10

output:

1410

result:

ok 1 number(s): "1410"

Test #21:

score: 0
Accepted
time: 0ms
memory: 3524kb

input:

84 16

output:

297627153

result:

ok 1 number(s): "297627153"

Test #22:

score: 0
Accepted
time: 1ms
memory: 3428kb

input:

643 800

output:

489237163

result:

ok 1 number(s): "489237163"

Test #23:

score: 0
Accepted
time: 5ms
memory: 3564kb

input:

9903 880

output:

595167333

result:

ok 1 number(s): "595167333"

Test #24:

score: 0
Accepted
time: 46ms
memory: 3548kb

input:

97446 89750

output:

410205549

result:

ok 1 number(s): "410205549"

Test #25:

score: 0
Accepted
time: 89ms
memory: 3376kb

input:

186460 646474

output:

32638530

result:

ok 1 number(s): "32638530"

Test #26:

score: 0
Accepted
time: 232ms
memory: 3436kb

input:

508940 244684

output:

598321755

result:

ok 1 number(s): "598321755"

Test #27:

score: 0
Accepted
time: 266ms
memory: 3456kb

input:

583646 557758

output:

858695621

result:

ok 1 number(s): "858695621"

Test #28:

score: 0
Accepted
time: 445ms
memory: 3440kb

input:

969610 992608

output:

256683498

result:

ok 1 number(s): "256683498"

Test #29:

score: 0
Accepted
time: 465ms
memory: 3452kb

input:

995106 996434

output:

411791999

result:

ok 1 number(s): "411791999"

Test #30:

score: 0
Accepted
time: 455ms
memory: 3456kb

input:

999961 999872

output:

61222370

result:

ok 1 number(s): "61222370"

Test #31:

score: 0
Accepted
time: 464ms
memory: 3432kb

input:

999977 999908

output:

831096762

result:

ok 1 number(s): "831096762"

Test #32:

score: 0
Accepted
time: 460ms
memory: 3568kb

input:

999992 999998

output:

562977678

result:

ok 1 number(s): "562977678"

Test #33:

score: 0
Accepted
time: 430ms
memory: 3448kb

input:

1000000 2

output:

118436113

result:

ok 1 number(s): "118436113"

Test #34:

score: 0
Accepted
time: 10ms
memory: 3440kb

input:

2 1000000

output:

298823641

result:

ok 1 number(s): "298823641"