QOJ.ac

QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#132492#6417. Classical Summation ProblemUFRJ#AC ✓340ms19260kbC++201.3kb2023-07-30 00:36:352023-07-30 00:36:37

Judging History

你现在查看的是最新测评结果

  • [2023-08-10 23:21:45]
  • System Update: QOJ starts to keep a history of the judgings of all the submissions.
  • [2023-07-30 00:36:37]
  • 评测
  • 测评结果:AC
  • 用时:340ms
  • 内存:19260kb
  • [2023-07-30 00:36:35]
  • 提交

answer

#include "bits/stdc++.h"

using namespace std;

using lint = int64_t;
const int mod = 998244353;
const int lim = 1e6 + 10;

lint power(lint x, lint n){
    x %= mod;
    lint res = 1;
    for(;n;n>>=1){
        if(n&1) res = res * x % mod;
        x = x * x % mod;
    }
    return res;
}

lint fac[lim], ifac[lim];

void prep(){
    fac[0] = 1;
    for(int i=1;i<lim;i++) fac[i] = (fac[i-1] * i) % mod;
    ifac[lim-1] = power(fac[lim-1], mod - 2);
    for(int i=lim-2;i>=0;i--) ifac[i] = (ifac[i+1] * (i + 1)) % mod;
}

int main() {
    cin.tie(nullptr)->sync_with_stdio(false);
    prep();
    lint n, k;
    cin>>n>>k;
    lint ans = power(n, k) * (n + 1) % mod * power(2, mod - 2) % mod;
    if(k&1){
        cout<<ans<<"\n";
    }
    else{
        lint cnt = 0;
        for(int i=1;i<=n;i++){
            lint cur = (n + 1 - i) % mod * ( (power(i, k/2) - power(i - 1, k/2) + mod) * power(n - i + 1, k/2) % mod - 
                (power(n - i + 1, k/2) - power(n - i, k/2) + mod) * power(i, k/2) % mod + mod) % mod;
            cnt = (cnt + cur) % mod;
        }
        cnt = cnt * fac[k] % mod * ifac[k/2] % mod * ifac[k/2] % mod * power(2, mod - 2) % mod;
        ans = (ans - cnt + mod) % mod;
        cout<<ans<<"\n";
    }
    return 0;
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 6ms
memory: 19088kb

input:

3 2

output:

14

result:

ok 1 number(s): "14"

Test #2:

score: 0
Accepted
time: 12ms
memory: 19100kb

input:

5 3

output:

375

result:

ok 1 number(s): "375"

Test #3:

score: 0
Accepted
time: 1ms
memory: 19096kb

input:

2 2

output:

5

result:

ok 1 number(s): "5"

Test #4:

score: 0
Accepted
time: 12ms
memory: 19008kb

input:

10 9

output:

508778235

result:

ok 1 number(s): "508778235"

Test #5:

score: 0
Accepted
time: 4ms
memory: 19156kb

input:

69 3

output:

11497815

result:

ok 1 number(s): "11497815"

Test #6:

score: 0
Accepted
time: 8ms
memory: 19048kb

input:

994 515

output:

33689623

result:

ok 1 number(s): "33689623"

Test #7:

score: 0
Accepted
time: 8ms
memory: 19224kb

input:

4476 6182

output:

114894183

result:

ok 1 number(s): "114894183"

Test #8:

score: 0
Accepted
time: 11ms
memory: 19092kb

input:

58957 12755

output:

932388891

result:

ok 1 number(s): "932388891"

Test #9:

score: 0
Accepted
time: 58ms
memory: 19000kb

input:

218138 28238

output:

392861201

result:

ok 1 number(s): "392861201"

Test #10:

score: 0
Accepted
time: 176ms
memory: 19048kb

input:

644125 316810

output:

420621854

result:

ok 1 number(s): "420621854"

Test #11:

score: 0
Accepted
time: 188ms
memory: 19104kb

input:

612914 505428

output:

973686286

result:

ok 1 number(s): "973686286"

Test #12:

score: 0
Accepted
time: 8ms
memory: 19004kb

input:

998216 938963

output:

251335926

result:

ok 1 number(s): "251335926"

Test #13:

score: 0
Accepted
time: 11ms
memory: 19056kb

input:

990516 996933

output:

549551960

result:

ok 1 number(s): "549551960"

Test #14:

score: 0
Accepted
time: 330ms
memory: 19092kb

input:

999019 999012

output:

637189128

result:

ok 1 number(s): "637189128"

Test #15:

score: 0
Accepted
time: 332ms
memory: 19208kb

input:

999928 999950

output:

185229465

result:

ok 1 number(s): "185229465"

Test #16:

score: 0
Accepted
time: 3ms
memory: 19184kb

input:

999999 999999

output:

384164916

result:

ok 1 number(s): "384164916"

Test #17:

score: 0
Accepted
time: 310ms
memory: 19112kb

input:

999999 1000000

output:

696165930

result:

ok 1 number(s): "696165930"

Test #18:

score: 0
Accepted
time: 8ms
memory: 19208kb

input:

1000000 999999

output:

219071706

result:

ok 1 number(s): "219071706"

Test #19:

score: 0
Accepted
time: 306ms
memory: 19224kb

input:

1000000 1000000

output:

128206597

result:

ok 1 number(s): "128206597"

Test #20:

score: 0
Accepted
time: 12ms
memory: 19052kb

input:

2 10

output:

1410

result:

ok 1 number(s): "1410"

Test #21:

score: 0
Accepted
time: 9ms
memory: 19204kb

input:

84 16

output:

297627153

result:

ok 1 number(s): "297627153"

Test #22:

score: 0
Accepted
time: 11ms
memory: 19088kb

input:

643 800

output:

489237163

result:

ok 1 number(s): "489237163"

Test #23:

score: 0
Accepted
time: 12ms
memory: 19096kb

input:

9903 880

output:

595167333

result:

ok 1 number(s): "595167333"

Test #24:

score: 0
Accepted
time: 25ms
memory: 19088kb

input:

97446 89750

output:

410205549

result:

ok 1 number(s): "410205549"

Test #25:

score: 0
Accepted
time: 65ms
memory: 19004kb

input:

186460 646474

output:

32638530

result:

ok 1 number(s): "32638530"

Test #26:

score: 0
Accepted
time: 152ms
memory: 19228kb

input:

508940 244684

output:

598321755

result:

ok 1 number(s): "598321755"

Test #27:

score: 0
Accepted
time: 164ms
memory: 19044kb

input:

583646 557758

output:

858695621

result:

ok 1 number(s): "858695621"

Test #28:

score: 0
Accepted
time: 305ms
memory: 19052kb

input:

969610 992608

output:

256683498

result:

ok 1 number(s): "256683498"

Test #29:

score: 0
Accepted
time: 315ms
memory: 19100kb

input:

995106 996434

output:

411791999

result:

ok 1 number(s): "411791999"

Test #30:

score: 0
Accepted
time: 310ms
memory: 19096kb

input:

999961 999872

output:

61222370

result:

ok 1 number(s): "61222370"

Test #31:

score: 0
Accepted
time: 324ms
memory: 19260kb

input:

999977 999908

output:

831096762

result:

ok 1 number(s): "831096762"

Test #32:

score: 0
Accepted
time: 340ms
memory: 19096kb

input:

999992 999998

output:

562977678

result:

ok 1 number(s): "562977678"

Test #33:

score: 0
Accepted
time: 28ms
memory: 19208kb

input:

1000000 2

output:

118436113

result:

ok 1 number(s): "118436113"

Test #34:

score: 0
Accepted
time: 12ms
memory: 19088kb

input:

2 1000000

output:

298823641

result:

ok 1 number(s): "298823641"