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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#500703#6417. Classical Summation Problemucup-team2307#AC ✓161ms19336kbC++201.4kb2024-08-01 18:18:032024-08-01 18:18:07

Judging History

你现在查看的是最新测评结果

  • [2024-08-01 18:18:07]
  • 评测
  • 测评结果:AC
  • 用时:161ms
  • 内存:19336kb
  • [2024-08-01 18:18:03]
  • 提交

answer

#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("avx,avx2,sse,sse2")
#include<bits/stdc++.h>
#define all(x) begin(x), end(x)
using namespace std;
using ll = long long;
const int N = 2e6 + 66, mod = 998244353;
int fact[N], ifact[N];
void calc() {
	ifact[0] = fact[0] = ifact[1] = 1;
	for(int i = 2; i < N; i++) {
		ifact[i] = mod - (mod / i) * 1ll * ifact[mod % i] % mod; 
	}
	for(int i = 1; i < N; i++) {
		fact[i] = fact[i - 1] * 1ll * i % mod;
		ifact[i] = ifact[i - 1] * 1ll * ifact[i] % mod;
	}
}
int nck(int n, int k) {
	if(k < 0 || k > n) return 0;
	int ans = fact[n] * 1ll * ifact[k] % mod;
	return ans * 1ll * ifact[n-k]%mod;
}
int bp(int a, int p) {
	int r = 1;
	for(; p; p>>=1, a = a*1ll*a%mod)
		if(p&1) r = r*1ll*a%mod;
	return r;
}
 main() {
	cin.tie(0)->sync_with_stdio(0);
	//E[med] = sum_{x=0...inf} P[med > x] = sum_k=...n/2-1 P[cnt_(<=x) = k]
	calc();
	int n, k;
	cin >> n >> k;
	if(k & 1) {
		ll ans = bp(n, k) * 1ll * (n + 1) % mod;
		ans = ans * 1ll * ((mod+1)/2) % mod;
		cout << ans << '\n';
		return 0;
	}
	ll exp_diff = 0;
	for(int i = 1; i < n; i++) {
		exp_diff += bp(i, k/2)*1ll*bp(n-i, k/2) % mod;
	}
	exp_diff = (exp_diff % mod) * 1ll * nck(k, k/2) % mod;
	ll exp_sum = (n + 1) * 1ll * bp(n, k) % mod;
	ll smoll = (mod + exp_sum - exp_diff) * 1ll * ((mod+1)/2) % mod;
	cout << smoll << '\n';
	
}/*
2 piles sum <= 2
0 0
0 1
0 2
1 1
*/

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 11ms
memory: 19240kb

input:

3 2

output:

14

result:

ok 1 number(s): "14"

Test #2:

score: 0
Accepted
time: 17ms
memory: 19332kb

input:

5 3

output:

375

result:

ok 1 number(s): "375"

Test #3:

score: 0
Accepted
time: 15ms
memory: 19312kb

input:

2 2

output:

5

result:

ok 1 number(s): "5"

Test #4:

score: 0
Accepted
time: 11ms
memory: 19240kb

input:

10 9

output:

508778235

result:

ok 1 number(s): "508778235"

Test #5:

score: 0
Accepted
time: 15ms
memory: 19180kb

input:

69 3

output:

11497815

result:

ok 1 number(s): "11497815"

Test #6:

score: 0
Accepted
time: 19ms
memory: 19256kb

input:

994 515

output:

33689623

result:

ok 1 number(s): "33689623"

Test #7:

score: 0
Accepted
time: 10ms
memory: 19260kb

input:

4476 6182

output:

114894183

result:

ok 1 number(s): "114894183"

Test #8:

score: 0
Accepted
time: 15ms
memory: 19256kb

input:

58957 12755

output:

932388891

result:

ok 1 number(s): "932388891"

Test #9:

score: 0
Accepted
time: 36ms
memory: 19164kb

input:

218138 28238

output:

392861201

result:

ok 1 number(s): "392861201"

Test #10:

score: 0
Accepted
time: 101ms
memory: 19216kb

input:

644125 316810

output:

420621854

result:

ok 1 number(s): "420621854"

Test #11:

score: 0
Accepted
time: 97ms
memory: 19240kb

input:

612914 505428

output:

973686286

result:

ok 1 number(s): "973686286"

Test #12:

score: 0
Accepted
time: 15ms
memory: 19184kb

input:

998216 938963

output:

251335926

result:

ok 1 number(s): "251335926"

Test #13:

score: 0
Accepted
time: 15ms
memory: 19332kb

input:

990516 996933

output:

549551960

result:

ok 1 number(s): "549551960"

Test #14:

score: 0
Accepted
time: 154ms
memory: 19332kb

input:

999019 999012

output:

637189128

result:

ok 1 number(s): "637189128"

Test #15:

score: 0
Accepted
time: 159ms
memory: 19244kb

input:

999928 999950

output:

185229465

result:

ok 1 number(s): "185229465"

Test #16:

score: 0
Accepted
time: 18ms
memory: 19236kb

input:

999999 999999

output:

384164916

result:

ok 1 number(s): "384164916"

Test #17:

score: 0
Accepted
time: 150ms
memory: 19240kb

input:

999999 1000000

output:

696165930

result:

ok 1 number(s): "696165930"

Test #18:

score: 0
Accepted
time: 19ms
memory: 19200kb

input:

1000000 999999

output:

219071706

result:

ok 1 number(s): "219071706"

Test #19:

score: 0
Accepted
time: 150ms
memory: 19180kb

input:

1000000 1000000

output:

128206597

result:

ok 1 number(s): "128206597"

Test #20:

score: 0
Accepted
time: 19ms
memory: 19264kb

input:

2 10

output:

1410

result:

ok 1 number(s): "1410"

Test #21:

score: 0
Accepted
time: 18ms
memory: 19272kb

input:

84 16

output:

297627153

result:

ok 1 number(s): "297627153"

Test #22:

score: 0
Accepted
time: 14ms
memory: 19204kb

input:

643 800

output:

489237163

result:

ok 1 number(s): "489237163"

Test #23:

score: 0
Accepted
time: 14ms
memory: 19184kb

input:

9903 880

output:

595167333

result:

ok 1 number(s): "595167333"

Test #24:

score: 0
Accepted
time: 26ms
memory: 19332kb

input:

97446 89750

output:

410205549

result:

ok 1 number(s): "410205549"

Test #25:

score: 0
Accepted
time: 44ms
memory: 19204kb

input:

186460 646474

output:

32638530

result:

ok 1 number(s): "32638530"

Test #26:

score: 0
Accepted
time: 82ms
memory: 19248kb

input:

508940 244684

output:

598321755

result:

ok 1 number(s): "598321755"

Test #27:

score: 0
Accepted
time: 96ms
memory: 19256kb

input:

583646 557758

output:

858695621

result:

ok 1 number(s): "858695621"

Test #28:

score: 0
Accepted
time: 151ms
memory: 19176kb

input:

969610 992608

output:

256683498

result:

ok 1 number(s): "256683498"

Test #29:

score: 0
Accepted
time: 154ms
memory: 19264kb

input:

995106 996434

output:

411791999

result:

ok 1 number(s): "411791999"

Test #30:

score: 0
Accepted
time: 150ms
memory: 19236kb

input:

999961 999872

output:

61222370

result:

ok 1 number(s): "61222370"

Test #31:

score: 0
Accepted
time: 161ms
memory: 19336kb

input:

999977 999908

output:

831096762

result:

ok 1 number(s): "831096762"

Test #32:

score: 0
Accepted
time: 160ms
memory: 19248kb

input:

999992 999998

output:

562977678

result:

ok 1 number(s): "562977678"

Test #33:

score: 0
Accepted
time: 24ms
memory: 19316kb

input:

1000000 2

output:

118436113

result:

ok 1 number(s): "118436113"

Test #34:

score: 0
Accepted
time: 15ms
memory: 19184kb

input:

2 1000000

output:

298823641

result:

ok 1 number(s): "298823641"