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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#174360#6417. Classical Summation ProblemalexzhanUSWA 2ms3720kbC++172.1kb2023-09-10 06:51:172023-09-10 06:51:18

Judging History

你现在查看的是最新测评结果

  • [2023-09-10 06:51:18]
  • 评测
  • 测评结果:WA
  • 用时:2ms
  • 内存:3720kb
  • [2023-09-10 06:51:17]
  • 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 = 1; i <= k / 2; i++) {
            factorial1 *= i;
            factorial1 %= modulo;
        }
        long long factorial2 = 1;
        for (int i = 1; i <= k; i++) {
            factorial1 *= i;
            factorial1 %= modulo;
        }
        long long combination = factorial1;
        combination = divide(combination, factorial2);
        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;
        }
        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

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Test #1:

score: 100
Accepted
time: 2ms
memory: 3668kb

input:

3 2

output:

14

result:

ok 1 number(s): "14"

Test #2:

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

input:

5 3

output:

375

result:

ok 1 number(s): "375"

Test #3:

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

input:

2 2

output:

5

result:

ok 1 number(s): "5"

Test #4:

score: 0
Accepted
time: 1ms
memory: 3720kb

input:

10 9

output:

508778235

result:

ok 1 number(s): "508778235"

Test #5:

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

input:

69 3

output:

11497815

result:

ok 1 number(s): "11497815"

Test #6:

score: 0
Accepted
time: 0ms
memory: 3596kb

input:

994 515

output:

33689623

result:

ok 1 number(s): "33689623"

Test #7:

score: -100
Wrong Answer
time: 1ms
memory: 3600kb

input:

4476 6182

output:

480411085

result:

wrong answer 1st numbers differ - expected: '114894183', found: '480411085'