結果

問題 No.2963 Mecha DESU
ユーザー apricityapricity
提出日時 2024-11-16 16:04:33
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 483 ms / 2,000 ms
コード長 9,642 bytes
コンパイル時間 1,538 ms
コンパイル使用メモリ 138,688 KB
実行使用メモリ 15,488 KB
最終ジャッジ日時 2024-11-16 16:04:53
合計ジャッジ時間 18,290 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge5
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 44 ms
15,104 KB
testcase_01 AC 44 ms
15,104 KB
testcase_02 AC 44 ms
14,976 KB
testcase_03 AC 43 ms
15,104 KB
testcase_04 AC 44 ms
14,976 KB
testcase_05 AC 44 ms
15,104 KB
testcase_06 AC 45 ms
14,976 KB
testcase_07 AC 44 ms
15,104 KB
testcase_08 AC 44 ms
15,104 KB
testcase_09 AC 44 ms
15,104 KB
testcase_10 AC 44 ms
15,104 KB
testcase_11 AC 45 ms
14,976 KB
testcase_12 AC 42 ms
15,104 KB
testcase_13 AC 467 ms
15,488 KB
testcase_14 AC 456 ms
15,360 KB
testcase_15 AC 478 ms
15,488 KB
testcase_16 AC 454 ms
15,488 KB
testcase_17 AC 453 ms
15,488 KB
testcase_18 AC 450 ms
15,360 KB
testcase_19 AC 478 ms
15,488 KB
testcase_20 AC 282 ms
15,360 KB
testcase_21 AC 89 ms
15,360 KB
testcase_22 AC 82 ms
15,232 KB
testcase_23 AC 58 ms
15,360 KB
testcase_24 AC 320 ms
15,232 KB
testcase_25 AC 308 ms
15,360 KB
testcase_26 AC 404 ms
15,104 KB
testcase_27 AC 206 ms
15,104 KB
testcase_28 AC 402 ms
15,488 KB
testcase_29 AC 271 ms
15,488 KB
testcase_30 AC 62 ms
15,104 KB
testcase_31 AC 141 ms
15,360 KB
testcase_32 AC 94 ms
15,104 KB
testcase_33 AC 331 ms
15,360 KB
testcase_34 AC 367 ms
15,360 KB
testcase_35 AC 124 ms
15,232 KB
testcase_36 AC 331 ms
15,232 KB
testcase_37 AC 74 ms
15,360 KB
testcase_38 AC 147 ms
15,104 KB
testcase_39 AC 347 ms
15,232 KB
testcase_40 AC 223 ms
15,104 KB
testcase_41 AC 367 ms
15,360 KB
testcase_42 AC 315 ms
15,232 KB
testcase_43 AC 483 ms
15,488 KB
testcase_44 AC 426 ms
15,360 KB
testcase_45 AC 375 ms
15,104 KB
testcase_46 AC 203 ms
15,232 KB
testcase_47 AC 294 ms
14,976 KB
testcase_48 AC 126 ms
15,232 KB
testcase_49 AC 278 ms
15,104 KB
testcase_50 AC 445 ms
15,488 KB
testcase_51 AC 473 ms
15,488 KB
testcase_52 AC 444 ms
15,360 KB
testcase_53 AC 420 ms
15,488 KB
testcase_54 AC 456 ms
15,360 KB
testcase_55 AC 45 ms
15,104 KB
testcase_56 AC 45 ms
15,104 KB
testcase_57 AC 373 ms
15,104 KB
testcase_58 AC 53 ms
15,488 KB
testcase_59 AC 43 ms
14,976 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#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);
}
0