結果
| 問題 |
No.2963 Mecha DESU
|
| コンテスト | |
| ユーザー |
 apricity
|
| 提出日時 | 2024-11-16 16:04:33 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 476 ms / 2,000 ms |
| コード長 | 9,642 bytes |
| コンパイル時間 | 1,622 ms |
| コンパイル使用メモリ | 134,032 KB |
| 最終ジャッジ日時 | 2025-02-25 04:30:18 |
|
ジャッジサーバーID （参考情報） |
judge4 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 57 |
ソースコード
#include<iostream>
#include<string>
#include<vector>
#include<algorithm>
#include<numeric>
#include<cmath>
#include<utility>
#include<tuple>
#include<cstdint>
#include<cstdio>
#include<iomanip>
#include<map>
#include<queue>
#include<set>
#include<stack>
#include<deque>
#include<unordered_map>
#include<unordered_set>
#include<bitset>
#include<cctype>
#include<chrono>
#include<random>
#include<cassert>
#include<cstddef>
#include<iterator>
#include<string_view>
#include<type_traits>
#ifdef LOCAL
# include "debug_print.hpp"
# define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
# define debug(...) (static_cast<void>(0))
#endif
using namespace std;
#define rep1(a) for(int i = 0; i < a; i++)
#define rep2(i, a) for(int i = 0; i < a; i++)
#define rep3(i, a, b) for(int i = a; i < b; i++)
#define rep4(i, a, b, c) for(int i = a; i < b; i += c)
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep1(a) for(int i = (a)-1; i >= 0; i--)
#define rrep2(i, a) for(int i = (a)-1; i >= 0; i--)
#define rrep3(i, a, b) for(int i = (b)-1; i >= a; i--)
#define rrep4(i, a, b, c) for(int i = (b)-1; i >= a; i -= c)
#define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)
#define ALL(v) v.begin(), v.end()
#define RALL(v) v.rbegin(), v.rend()
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );
#define pb push_back
using ll = long long;
using D = double;
using LD = long double;
using P = pair<int, int>;
using vi = vector<int>;
using vl = vector<ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vector<vc<T>>;
template <class T> using vvvc = vector<vvc<T>>;
template <class T> using vvvvc = vector<vvvc<T>>;
template <class T> using vvvvvc = vector<vvvvc<T>>;
#define vv(type, name, h, ...) \
vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) \
vector<vector<vector<type>>> name( \
h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
vector<vector<vector<vector<type>>>> name( \
a, vector<vector<vector<type>>>( \
b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
template<typename T> using PQ = priority_queue<T,vector<T>>;
template<typename T> using minPQ = priority_queue<T, vector<T>, greater<T>>;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
void yesno(bool flag) {cout << (flag?"Yes":"No") << "\n";}
template<typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template<typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template<typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template<typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (auto &x : v) is >> x;
return is;
}
void in() {}
template<typename T, class... U>
void in(T &t, U &...u) {
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template<typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
void outr() {}
template<typename T, class... U, char sep = ' '>
void outr(const T &t, const U &...u) {
cout << t;
outr(u...);
}
struct eratosthenes{
vector<bool> isprime;
vector<int> minfactor;
vector<int> mobius;
eratosthenes(int n) : isprime(n+1,true), minfactor(n+1, -1), mobius(n+1,1){
isprime[1] = false;
minfactor[1] = 1;
for(int i = 2; i <= n; i++){
if(!isprime[i]) continue;
minfactor[i] = i;
mobius[i] = -1;
for(int j = i+i; j <= n; j += i){
isprime[j] = false;
if(minfactor[j] == -1) minfactor[j] = i;
if((j/i)%i == 0) mobius[j] = 0;
else mobius[j] *= -1;
}
}
}
vector<pair<int, int>> factorize(int n){
vector<pair<int, int>> res;
while(n > 1){
int p = minfactor[n];
int e = 0;
while(minfactor[n] == p){
n /= p;
e++;
}
res.push_back({p,e});
}
return res;
}
vector<int> divisor(int n){
vector<int> res;
res.pb(1);
auto v = factorize(n);
for(auto x : v){
int s = res.size();
for(int i = 0; i < s; i++){
int m = 1;
for(int _ = 0; _ < x.second; _++){
m *= x.first;
res.push_back(res[i]*m);
}
}
}
return res;
}
template<class T> void fzt(vector<T> &f){
int n = f.size();
for(int p = 2; p < n; p++){
if(!isprime[p]) continue;
for(int q = (n-1)/p; q > 0; q--){
f[q] += f[p*q];
}
}
}
template<class T> void fmt(vector<T> &f){
int n = f.size();
for(int p = 2; p < n; p++){
if(!isprime[p]) continue;
for(int q = 1; q*p < n; q++){
f[q] -= f[p*q];
}
}
// for(int p = 2; p < n; p++){
// if(!isprime[p]) continue;
// for(int q = (n-1)/p; q > 0; q--){
// f[p*q] -= f[q];
// }
// }
}
template<class T> vector<T> conv(const vector<T> &f, const vector<T> &g){
int n = max(f.size(), g.size());
vector<T> nf(n), ng(n), h(n);
for(int i = 0; i < (int)f.size(); i++) nf[i] = f[i];
for(int i = 0; i < (int)g.size(); i++) ng[i] = g[i];
fzt(nf); fzt(ng);
for(int i = 0; i < n; i++) h[i] = nf[i]*ng[i];
fmt(h);
return h;
}
};
template <uint32_t mod>
struct LazyMontgomeryModInt {
using mint = LazyMontgomeryModInt;
using i32 = int32_t;
using u32 = uint32_t;
using u64 = uint64_t;
static constexpr u32 get_r() {
u32 ret = mod;
for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
return ret;
}
static constexpr u32 r = get_r();
static constexpr u32 n2 = -u64(mod) % mod;
static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
static_assert(r * mod == 1, "this code has bugs.");
u32 a;
constexpr LazyMontgomeryModInt() : a(0) {}
constexpr LazyMontgomeryModInt(const int64_t &b)
: a(reduce(u64(b % mod + mod) * n2)){};
static constexpr u32 reduce(const u64 &b) {
return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
}
constexpr mint &operator+=(const mint &b) {
if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator-=(const mint &b) {
if (i32(a -= b.a) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator*=(const mint &b) {
a = reduce(u64(a) * b.a);
return *this;
}
constexpr mint &operator/=(const mint &b) {
*this *= b.inverse();
return *this;
}
constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
constexpr bool operator==(const mint &b) const {
return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
}
constexpr bool operator!=(const mint &b) const {
return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
}
constexpr mint operator-() const { return mint() - mint(*this); }
constexpr mint operator+() const { return mint(*this); }
constexpr mint pow(u64 n) const {
mint ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
constexpr mint inverse() const {
int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0;
while (y > 0) {
t = x / y;
x -= t * y, u -= t * v;
tmp = x, x = y, y = tmp;
tmp = u, u = v, v = tmp;
}
return mint{u};
}
friend ostream &operator<<(ostream &os, const mint &b) {
return os << b.get();
}
friend istream &operator>>(istream &is, mint &b) {
int64_t t;
is >> t;
b = LazyMontgomeryModInt<mod>(t);
return (is);
}
constexpr u32 get() const {
u32 ret = reduce(a);
return ret >= mod ? ret - mod : ret;
}
static constexpr u32 get_mod() { return mod; }
};
const int mod = 998244353;
//const int mod = 1000000007;
using mint = LazyMontgomeryModInt<mod>;
int main(){
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int n,m,k; in(n,m,k);
eratosthenes si(1000005);
vector<int> a(m); in(a);
vector<int> cnt(1000001);
rep(i,m) cnt[a[i]]++;
mint ans = 0;
mint minv = mint(m).inverse();
rep(i,1,n+1){
int f = m;
for(auto x : si.divisor(i)) f -= cnt[x];
ans += (minv*f).pow(k);
}
out(mint(n)-ans);
}