QOJ.ac

QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#106917#6417. Classical Summation Problembulijiojiodibuliduo#AC ✓226ms17716kbC++3.4kb2023-05-19 19:36:502023-05-19 19:36:51

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.
  • [2023-05-19 19:36:51]
  • 评测
  • 测评结果:AC
  • 用时:226ms
  • 内存:17716kb
  • [2023-05-19 19:36:50]
  • 提交

answer

#include <bits/stdc++.h>
using namespace std;
#define rep(i,a,n) for (int i=a;i<n;i++)
#define per(i,a,n) for (int i=n-1;i>=a;i--)
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define SZ(x) ((int)(x).size())
typedef vector<int> VI;
typedef basic_string<int> BI;
typedef long long ll;
typedef pair<int,int> PII;
typedef double db;
mt19937 mrand(random_device{}()); 
const ll mod=1000000007;
int rnd(int x) { return mrand() % x;}
ll powmod(ll a,ll b) {ll res=1;a%=mod; assert(b>=0); for(;b;b>>=1){if(b&1)res=res*a%mod;a=a*a%mod;}return res;}
ll gcd(ll a,ll b) { return b?gcd(b,a%b):a;}
// head

template<int MOD, int RT> struct mint {
	static const int mod = MOD;
	static constexpr mint rt() { return RT; } // primitive root for FFT
	int v; explicit operator int() const { return v; } // explicit -> don't silently convert to int
	mint():v(0) {}
	mint(ll _v) { v = int((-MOD < _v && _v < MOD) ? _v : _v % MOD);
		if (v < 0) v += MOD; }
	bool operator==(const mint& o) const {
		return v == o.v; }
	friend bool operator!=(const mint& a, const mint& b) { 
		return !(a == b); }
	friend bool operator<(const mint& a, const mint& b) { 
		return a.v < b.v; }
   
	mint& operator+=(const mint& o) { 
		if ((v += o.v) >= MOD) v -= MOD; 
		return *this; }
	mint& operator-=(const mint& o) { 
		if ((v -= o.v) < 0) v += MOD; 
		return *this; }
	mint& operator*=(const mint& o) { 
		v = int((ll)v*o.v%MOD); return *this; }
	mint& operator/=(const mint& o) { return (*this) *= inv(o); }
	friend mint pow(mint a, ll p) {
		mint ans = 1; assert(p >= 0);
		for (; p; p /= 2, a *= a) if (p&1) ans *= a;
		return ans; }
	friend mint inv(const mint& a) { assert(a.v != 0); 
		return pow(a,MOD-2); }
		
	mint operator-() const { return mint(-v); }
	mint& operator++() { return *this += 1; }
	mint& operator--() { return *this -= 1; }
	friend mint operator+(mint a, const mint& b) { return a += b; }
	friend mint operator-(mint a, const mint& b) { return a -= b; }
	friend mint operator*(mint a, const mint& b) { return a *= b; }
	friend mint operator/(mint a, const mint& b) { return a /= b; }
};

const int MOD=998244353; 
using mi = mint<MOD,5>; // 5 is primitive root for both common mods

namespace simp {
	vector<mi> fac,ifac,invn;
	void check(int x) {
		if (fac.empty()) {
			fac={mi(1),mi(1)};
			ifac={mi(1),mi(1)};
			invn={mi(0),mi(1)};
		}
		while (SZ(fac)<=x) {
			int n=SZ(fac),m=SZ(fac)*2;
			fac.resize(m);
			ifac.resize(m);
			invn.resize(m);
			for (int i=n;i<m;i++) {
				fac[i]=fac[i-1]*mi(i);
				invn[i]=mi(MOD-MOD/i)*invn[MOD%i];
				ifac[i]=ifac[i-1]*invn[i];
			}
		}
	}
	mi gfac(int x) {
		check(x); return fac[x];
	}
	mi ginv(int x) {
		check(x); return invn[x];
	}
	mi gifac(int x) {
		check(x); return ifac[x];
	}
	mi binom(int n,int m) {
		if (m < 0 || m > n) return mi(0);
		return gfac(n)*gifac(m)*gifac(n - m);
	}
}

//const int N=501000;
int n,k;
int main() {
	scanf("%d%d",&n,&k);
	if (k%2==1) {
		mi ans=pow(mi(n),k)*(n+1)/2;
		printf("%d\n",(int)ans);
		return 0;
	}
	mi ans=0;
	for (int i=0;i*2<=n;i++) {
		mi w=0;
		if (i*2<n) {
			ans+=pow(mi(n),k)-simp::binom(k,k/2)*pow(mi(i),k/2)*pow(mi(n-i),k/2);
		} else {
			for (int p=0;p<=k/2-1;p++) {
				w+=simp::binom(k,p)*pow(mi(i),p)*pow(mi(n-i),k-p);
			}
		}
		ans+=w;
		//printf("%d %d\n",(int)w,pow(mi(n),k));
	}
	printf("%d\n",(int)ans);

}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 2ms
memory: 3704kb

input:

3 2

output:

14

result:

ok 1 number(s): "14"

Test #2:

score: 0
Accepted
time: 1ms
memory: 3704kb

input:

5 3

output:

375

result:

ok 1 number(s): "375"

Test #3:

score: 0
Accepted
time: 2ms
memory: 3576kb

input:

2 2

output:

5

result:

ok 1 number(s): "5"

Test #4:

score: 0
Accepted
time: 2ms
memory: 3552kb

input:

10 9

output:

508778235

result:

ok 1 number(s): "508778235"

Test #5:

score: 0
Accepted
time: 2ms
memory: 3648kb

input:

69 3

output:

11497815

result:

ok 1 number(s): "11497815"

Test #6:

score: 0
Accepted
time: 0ms
memory: 3620kb

input:

994 515

output:

33689623

result:

ok 1 number(s): "33689623"

Test #7:

score: 0
Accepted
time: 2ms
memory: 3668kb

input:

4476 6182

output:

114894183

result:

ok 1 number(s): "114894183"

Test #8:

score: 0
Accepted
time: 2ms
memory: 3664kb

input:

58957 12755

output:

932388891

result:

ok 1 number(s): "932388891"

Test #9:

score: 0
Accepted
time: 19ms
memory: 3708kb

input:

218138 28238

output:

392861201

result:

ok 1 number(s): "392861201"

Test #10:

score: 0
Accepted
time: 69ms
memory: 10264kb

input:

644125 316810

output:

420621854

result:

ok 1 number(s): "420621854"

Test #11:

score: 0
Accepted
time: 119ms
memory: 10476kb

input:

612914 505428

output:

973686286

result:

ok 1 number(s): "973686286"

Test #12:

score: 0
Accepted
time: 1ms
memory: 3560kb

input:

998216 938963

output:

251335926

result:

ok 1 number(s): "251335926"

Test #13:

score: 0
Accepted
time: 2ms
memory: 3564kb

input:

990516 996933

output:

549551960

result:

ok 1 number(s): "549551960"

Test #14:

score: 0
Accepted
time: 133ms
memory: 17544kb

input:

999019 999012

output:

637189128

result:

ok 1 number(s): "637189128"

Test #15:

score: 0
Accepted
time: 216ms
memory: 17716kb

input:

999928 999950

output:

185229465

result:

ok 1 number(s): "185229465"

Test #16:

score: 0
Accepted
time: 2ms
memory: 3660kb

input:

999999 999999

output:

384164916

result:

ok 1 number(s): "384164916"

Test #17:

score: 0
Accepted
time: 142ms
memory: 17708kb

input:

999999 1000000

output:

696165930

result:

ok 1 number(s): "696165930"

Test #18:

score: 0
Accepted
time: 2ms
memory: 3540kb

input:

1000000 999999

output:

219071706

result:

ok 1 number(s): "219071706"

Test #19:

score: 0
Accepted
time: 222ms
memory: 17476kb

input:

1000000 1000000

output:

128206597

result:

ok 1 number(s): "128206597"

Test #20:

score: 0
Accepted
time: 2ms
memory: 3620kb

input:

2 10

output:

1410

result:

ok 1 number(s): "1410"

Test #21:

score: 0
Accepted
time: 1ms
memory: 3668kb

input:

84 16

output:

297627153

result:

ok 1 number(s): "297627153"

Test #22:

score: 0
Accepted
time: 2ms
memory: 3728kb

input:

643 800

output:

489237163

result:

ok 1 number(s): "489237163"

Test #23:

score: 0
Accepted
time: 2ms
memory: 3596kb

input:

9903 880

output:

595167333

result:

ok 1 number(s): "595167333"

Test #24:

score: 0
Accepted
time: 21ms
memory: 4864kb

input:

97446 89750

output:

410205549

result:

ok 1 number(s): "410205549"

Test #25:

score: 0
Accepted
time: 94ms
memory: 17620kb

input:

186460 646474

output:

32638530

result:

ok 1 number(s): "32638530"

Test #26:

score: 0
Accepted
time: 80ms
memory: 6772kb

input:

508940 244684

output:

598321755

result:

ok 1 number(s): "598321755"

Test #27:

score: 0
Accepted
time: 132ms
memory: 17500kb

input:

583646 557758

output:

858695621

result:

ok 1 number(s): "858695621"

Test #28:

score: 0
Accepted
time: 226ms
memory: 17476kb

input:

969610 992608

output:

256683498

result:

ok 1 number(s): "256683498"

Test #29:

score: 0
Accepted
time: 219ms
memory: 17704kb

input:

995106 996434

output:

411791999

result:

ok 1 number(s): "411791999"

Test #30:

score: 0
Accepted
time: 135ms
memory: 17472kb

input:

999961 999872

output:

61222370

result:

ok 1 number(s): "61222370"

Test #31:

score: 0
Accepted
time: 132ms
memory: 17532kb

input:

999977 999908

output:

831096762

result:

ok 1 number(s): "831096762"

Test #32:

score: 0
Accepted
time: 221ms
memory: 17700kb

input:

999992 999998

output:

562977678

result:

ok 1 number(s): "562977678"

Test #33:

score: 0
Accepted
time: 18ms
memory: 3560kb

input:

1000000 2

output:

118436113

result:

ok 1 number(s): "118436113"

Test #34:

score: 0
Accepted
time: 105ms
memory: 17628kb

input:

2 1000000

output:

298823641

result:

ok 1 number(s): "298823641"