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ID题目提交者结果用时内存语言文件大小提交时间测评时间
#847882#6417. Classical Summation Problemlichenyu_acAC ✓79ms19312kbC++141.0kb2025-01-08 12:16:192025-01-08 12:16:27

Judging History

This is the latest submission verdict.

  • [2025-01-08 12:16:27]
  • Judged
  • Verdict: AC
  • Time: 79ms
  • Memory: 19312kb
  • [2025-01-08 12:16:19]
  • Submitted

answer

#include <bits/stdc++.h>
typedef long long ll;
using namespace std;
const int N = 1e6 + 10, mod = 998244353, inv2 = 499122177;

int n, k;
ll fac[N], ifac[N];

ll power(ll a, ll b) {
	ll ans = 1;
	for (;b ;b >>= 1) {
		if (b & 1) ans = ans * a % mod;
		a = a * a % mod;
	}
	return ans;
}

void init(int n = N - 1) {
	fac[0] = 1;
	for (int i = 1; i <= n; i++) fac[i] = fac[i - 1] * i % mod;
	ifac[n] = power(fac[n], mod - 2);
	for (int i = n - 1; ~i; i--) ifac[i] = ifac[i + 1] * (i + 1) % mod;
}

ll C(ll a, ll b) {
	return fac[a] * ifac[b] % mod * ifac[a - b] % mod;
}

int main() {
	cin >> n >> k;
	ll ans = 0;
	init();
	for (int i = 1; i * 2 < n; i++) {
		ans = (ans + power(n, k)) % mod;
		if (k % 2 == 0) ans = (ans + mod - C(k, k / 2) * power(1ll * i * (n - i) % mod, k / 2) % mod) % mod;
	}
	if (n % 2 == 0) {
		ll tmp = power(n / 2, k);
		for (int i = 0; i <= (k - 1) / 2; i++)
			ans = (ans + C(k, i) * tmp % mod) % mod;
	}
	cout << (ans + power(n, k)) % mod << endl;
	return 0;
}

詳細信息

Test #1:

score: 100
Accepted
time: 11ms
memory: 19148kb

input:

3 2

output:

14

result:

ok 1 number(s): "14"

Test #2:

score: 0
Accepted
time: 11ms
memory: 19220kb

input:

5 3

output:

375

result:

ok 1 number(s): "375"

Test #3:

score: 0
Accepted
time: 7ms
memory: 19216kb

input:

2 2

output:

5

result:

ok 1 number(s): "5"

Test #4:

score: 0
Accepted
time: 11ms
memory: 19312kb

input:

10 9

output:

508778235

result:

ok 1 number(s): "508778235"

Test #5:

score: 0
Accepted
time: 7ms
memory: 19252kb

input:

69 3

output:

11497815

result:

ok 1 number(s): "11497815"

Test #6:

score: 0
Accepted
time: 10ms
memory: 19124kb

input:

994 515

output:

33689623

result:

ok 1 number(s): "33689623"

Test #7:

score: 0
Accepted
time: 5ms
memory: 19244kb

input:

4476 6182

output:

114894183

result:

ok 1 number(s): "114894183"

Test #8:

score: 0
Accepted
time: 8ms
memory: 19220kb

input:

58957 12755

output:

932388891

result:

ok 1 number(s): "932388891"

Test #9:

score: 0
Accepted
time: 21ms
memory: 19156kb

input:

218138 28238

output:

392861201

result:

ok 1 number(s): "392861201"

Test #10:

score: 0
Accepted
time: 48ms
memory: 19164kb

input:

644125 316810

output:

420621854

result:

ok 1 number(s): "420621854"

Test #11:

score: 0
Accepted
time: 50ms
memory: 19236kb

input:

612914 505428

output:

973686286

result:

ok 1 number(s): "973686286"

Test #12:

score: 0
Accepted
time: 43ms
memory: 19248kb

input:

998216 938963

output:

251335926

result:

ok 1 number(s): "251335926"

Test #13:

score: 0
Accepted
time: 41ms
memory: 19312kb

input:

990516 996933

output:

549551960

result:

ok 1 number(s): "549551960"

Test #14:

score: 0
Accepted
time: 72ms
memory: 19244kb

input:

999019 999012

output:

637189128

result:

ok 1 number(s): "637189128"

Test #15:

score: 0
Accepted
time: 78ms
memory: 19120kb

input:

999928 999950

output:

185229465

result:

ok 1 number(s): "185229465"

Test #16:

score: 0
Accepted
time: 36ms
memory: 19252kb

input:

999999 999999

output:

384164916

result:

ok 1 number(s): "384164916"

Test #17:

score: 0
Accepted
time: 67ms
memory: 19124kb

input:

999999 1000000

output:

696165930

result:

ok 1 number(s): "696165930"

Test #18:

score: 0
Accepted
time: 42ms
memory: 19244kb

input:

1000000 999999

output:

219071706

result:

ok 1 number(s): "219071706"

Test #19:

score: 0
Accepted
time: 76ms
memory: 19152kb

input:

1000000 1000000

output:

128206597

result:

ok 1 number(s): "128206597"

Test #20:

score: 0
Accepted
time: 12ms
memory: 19164kb

input:

2 10

output:

1410

result:

ok 1 number(s): "1410"

Test #21:

score: 0
Accepted
time: 11ms
memory: 19220kb

input:

84 16

output:

297627153

result:

ok 1 number(s): "297627153"

Test #22:

score: 0
Accepted
time: 4ms
memory: 19216kb

input:

643 800

output:

489237163

result:

ok 1 number(s): "489237163"

Test #23:

score: 0
Accepted
time: 7ms
memory: 19244kb

input:

9903 880

output:

595167333

result:

ok 1 number(s): "595167333"

Test #24:

score: 0
Accepted
time: 17ms
memory: 19232kb

input:

97446 89750

output:

410205549

result:

ok 1 number(s): "410205549"

Test #25:

score: 0
Accepted
time: 16ms
memory: 19160kb

input:

186460 646474

output:

32638530

result:

ok 1 number(s): "32638530"

Test #26:

score: 0
Accepted
time: 37ms
memory: 19236kb

input:

508940 244684

output:

598321755

result:

ok 1 number(s): "598321755"

Test #27:

score: 0
Accepted
time: 37ms
memory: 19124kb

input:

583646 557758

output:

858695621

result:

ok 1 number(s): "858695621"

Test #28:

score: 0
Accepted
time: 72ms
memory: 19248kb

input:

969610 992608

output:

256683498

result:

ok 1 number(s): "256683498"

Test #29:

score: 0
Accepted
time: 74ms
memory: 19232kb

input:

995106 996434

output:

411791999

result:

ok 1 number(s): "411791999"

Test #30:

score: 0
Accepted
time: 74ms
memory: 19308kb

input:

999961 999872

output:

61222370

result:

ok 1 number(s): "61222370"

Test #31:

score: 0
Accepted
time: 76ms
memory: 19308kb

input:

999977 999908

output:

831096762

result:

ok 1 number(s): "831096762"

Test #32:

score: 0
Accepted
time: 79ms
memory: 19248kb

input:

999992 999998

output:

562977678

result:

ok 1 number(s): "562977678"

Test #33:

score: 0
Accepted
time: 17ms
memory: 19236kb

input:

1000000 2

output:

118436113

result:

ok 1 number(s): "118436113"

Test #34:

score: 0
Accepted
time: 12ms
memory: 19224kb

input:

2 1000000

output:

298823641

result:

ok 1 number(s): "298823641"