#886103 (C++17(gcc12)) No.2365 Present of good number

• 問題: No.2365 Present of good number
• ユーザー: iiljj
• 提出日時: 2023-06-30 22:29:26
• 言語: C++17(gcc12) (gcc 12.3.0 + boost 1.87.0)
• 結果: CE (最新)
  AC
  (最初)
• 実行時間: -
• コード長: 19,487 bytes
• コンパイル時間: 3,913 ms
• コンパイル使用メモリ: 180,520 KB
• 最終ジャッジ日時: 2025-02-15 04:12:27
• ジャッジサーバーID （参考情報）: judge1 / judge3

コンパイルメッセージ

main.cpp:359:14: error: expected unqualified-id before 'const'
  359 |     Mat<Num>(const size_t h, size_t w) : vc<vc<Num>>(h, vc<Num>(w, 0)), h(h), w(w) {}
      |              ^~~~~
main.cpp:359:14: error: expected ')' before 'const'
  359 |     Mat<Num>(const size_t h, size_t w) : vc<vc<Num>>(h, vc<Num>(w, 0)), h(h), w(w) {}
      |             ~^~~~~
      |              )
main.cpp:361:45: error: invalid declarator before 'init'
  361 |     Mat<Num>(std::initializer_list<vc<Num>> init) : vc<vc<Num>>() {
      |                                             ^~~~
main.cpp:361:44: error: expected ')' before 'init'
  361 |     Mat<Num>(std::initializer_list<vc<Num>> init) : vc<vc<Num>>() {
      |             ~                              ^~~~~
      |                                            )
main.cpp: In function 'void solve()':
main.cpp:578:11: error: could not convert 'SZ' from 'll' {aka 'long long int'} to 'std::vector<std::vector<mint<1000000006>, std::allocator<mint<1000000006> > >, std::allocator<std::vector<mint<1000000006>, std::allocator<mint<1000000006> > > > >'
  578 |     mat A(SZ, SZ);
      |           ^~
      |           |
      |           ll {aka long long int}
main.cpp:591:11: error: could not convert 'SZ' from 'll' {aka 'long long int'} to 'std::vector<std::vector<mint<1000000006>, std::allocator<mint<1000000006> > >, std::allocator<std::vector<mint<1000000006>, std::allocator<mint<1000000006> > > > >'
  591 |     mat x(SZ, 1);
      |           ^~
      |           |
      |           ll {aka long long int}
main.cpp: In instantiation of 'Mat<Num> Mat<Num>::pow(ll) const [with Num = mint<1000000006>; ll = long long int]':
main.cpp:598:18:   required from here
main.cpp:410:28: error: could not convert '((const Mat<mint<1000000006> >*)this)->Mat<mint<1000000006> >::h' from 'const size_t' {aka 'const long unsigned int'} to 'std::vector<std::vector<mint<1000000006>, std::allocator<mint<1000000006> > >, std::allocator<std::vector<mint<1000000006>,

ソースコード

/* #region Head */

// #include <bits/stdc++.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert> // assert.h
#include <cmath>   // math.h
#include <cstring>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>
using namespace std;

using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pll = pair<ll, ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vc<vc<T>>;
using vll = vc<ll>;
using vvll = vvc<ll>;
using vld = vc<ld>;
using vvld = vvc<ld>;
using vs = vc<string>;
using vvs = vvc<string>;
template <class T, class U> using um = unordered_map<T, U>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqa = priority_queue<T, vc<T>, greater<T>>;
template <class T> using us = unordered_set<T>;

#define TREP(T, i, m, n) for (T i = (m), i##_len = (T)(n); i < i##_len; ++(i))
#define TREPM(T, i, m, n) for (T i = (m), i##_max = (T)(n); i <= i##_max; ++(i))
#define TREPR(T, i, m, n) for (T i = (m), i##_min = (T)(n); i >= i##_min; --(i))
#define TREPD(T, i, m, n, d) for (T i = (m), i##_len = (T)(n); i < i##_len; i += (d))
#define TREPMD(T, i, m, n, d) for (T i = (m), i##_max = (T)(n); i <= i##_max; i += (d))

#define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i))
#define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i))
#define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i))
#define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d))
#define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d))
#define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++)
#define REPIR(itr, ds) for (auto itr = ds.rbegin(); itr != ds.rend(); itr++)
#define ALL(x) begin(x), end(x)
#define SIZE(x) ((ll)(x).size())
#define ISIZE(x) ((int)(x).size())
#define PERM(c)                                                                                                        \
    sort(ALL(c));                                                                                                      \
    for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))
#define UNIQ(v) v.erase(unique(ALL(v)), v.end());
#define CEIL(a, b) (((a) + (b)-1) / (b))

#define endl '\n'

constexpr ll INF = 1'010'000'000'000'000'017LL;
constexpr int IINF = 1'000'000'007LL;
constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7
// constexpr ll MOD = 998244353;
constexpr ld EPS = 1e-12;
constexpr ld PI = 3.14159265358979323846;

template <typename T> istream &operator>>(istream &is, vc<T> &vec) { // vector 入力
    for (T &x : vec) is >> x;
    return is;
}
template <typename T> ostream &operator<<(ostream &os, const vc<T> &vec) { // vector 出力 (for dump)
    os << "{";
    REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", ");
    os << "}";
    return os;
}
template <typename T> ostream &operator>>(ostream &os, const vc<T> &vec) { // vector 出力 (inline)
    REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " ");
    return os;
}

template <typename T, size_t _Nm> istream &operator>>(istream &is, array<T, _Nm> &arr) { // array 入力
    REP(i, 0, SIZE(arr)) is >> arr[i];
    return is;
}
template <typename T, size_t _Nm> ostream &operator<<(ostream &os, const array<T, _Nm> &arr) { // array 出力 (for dump)
    os << "{";
    REP(i, 0, SIZE(arr)) os << arr[i] << (i == i_len - 1 ? "" : ", ");
    os << "}";
    return os;
}

template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &pair_var) { // pair 入力
    is >> pair_var.first >> pair_var.second;
    return is;
}
template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &pair_var) { // pair 出力
    os << "(" << pair_var.first << ", " << pair_var.second << ")";
    return os;
}

// map, um, set, us 出力
template <class T> ostream &out_iter(ostream &os, const T &map_var) {
    os << "{";
    REPI(itr, map_var) {
        os << *itr;
        auto itrcp = itr;
        if (++itrcp != map_var.end()) os << ", ";
    }
    return os << "}";
}
template <typename T, typename U> ostream &operator<<(ostream &os, const map<T, U> &map_var) {
    return out_iter(os, map_var);
}
template <typename T, typename U> ostream &operator<<(ostream &os, const um<T, U> &map_var) {
    os << "{";
    REPI(itr, map_var) {
        auto [key, value] = *itr;
        os << "(" << key << ", " << value << ")";
        auto itrcp = itr;
        if (++itrcp != map_var.end()) os << ", ";
    }
    os << "}";
    return os;
}
template <typename T> ostream &operator<<(ostream &os, const set<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, const us<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, const pq<T> &pq_var) {
    pq<T> pq_cp(pq_var);
    os << "{";
    if (!pq_cp.empty()) {
        os << pq_cp.top(), pq_cp.pop();
        while (!pq_cp.empty()) os << ", " << pq_cp.top(), pq_cp.pop();
    }
    return os << "}";
}

// tuple 出力
template <size_t N = 0, bool end_line = false, typename... Args> ostream &operator<<(ostream &os, tuple<Args...> &a) {
    if constexpr (N < std::tuple_size_v<tuple<Args...>>) {
        os << get<N>(a);
        if constexpr (N + 1 < std::tuple_size_v<tuple<Args...>>) {
            os << ' ';
        } else if constexpr (end_line) {
            os << '\n';
        }
        return operator<< <N + 1, end_line>(os, a);
    }
    return os;
}
template <typename... Args> void print_tuple(tuple<Args...> &a) { operator<< <0, true>(std::cout, a); }

void pprint() { std::cout << endl; }
template <class Head, class... Tail> void pprint(Head &&head, Tail &&...tail) {
    std::cout << head;
    if (sizeof...(Tail) > 0) std::cout << ' ';
    pprint(move(tail)...);
}

// dump
#define DUMPOUT cerr
void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail> void dump_func(Head &&head, Tail &&...tail) {
    DUMPOUT << head;
    if (sizeof...(Tail) > 0) DUMPOUT << ", ";
    dump_func(move(tail)...);
}

// chmax (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>> bool chmax(T &xmax, const U &x, Comp comp = {}) {
    if (comp(xmax, x)) {
        xmax = x;
        return true;
    }
    return false;
}

// chmin (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>> bool chmin(T &xmin, const U &x, Comp comp = {}) {
    if (comp(x, xmin)) {
        xmin = x;
        return true;
    }
    return false;
}

// ローカル用
#ifndef ONLINE_JUDGE
#define DEBUG_
#endif

#ifndef MYLOCAL
#undef DEBUG_
#endif

#ifdef DEBUG_
#define DEB
#define dump(...)                                                                                                      \
    DUMPOUT << "  " << string(#__VA_ARGS__) << ": "                                                                    \
            << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl                                        \
            << "    ",                                                                                                 \
        dump_func(__VA_ARGS__)
#else
#define DEB if (false)
#define dump(...)
#endif

#define VAR(type, ...)                                                                                                 \
    type __VA_ARGS__;                                                                                                  \
    assert((std::cin >> __VA_ARGS__));

template <typename T> istream &operator,(istream &is, T &rhs) { return is >> rhs; }
template <typename T> ostream &operator,(ostream &os, const T &rhs) { return os << ' ' << rhs; }

struct AtCoderInitialize {
    static constexpr int IOS_PREC = 15;
    static constexpr bool AUTOFLUSH = false;
    AtCoderInitialize() {
        ios_base::sync_with_stdio(false), std::cin.tie(nullptr), std::cout.tie(nullptr);
        std::cout << fixed << setprecision(IOS_PREC);
        if (AUTOFLUSH) std::cout << unitbuf;
    }
} ATCODER_INITIALIZE;

void Yn(bool p) { std::cout << (p ? "Yes" : "No") << endl; }
void YN(bool p) { std::cout << (p ? "YES" : "NO") << endl; }

template <typename T> constexpr void operator--(vc<T> &v, int) noexcept {
    for (int i = 0; i < ISIZE(v); ++i) v[i]--;
}
template <typename T> constexpr void operator++(vc<T> &v, int) noexcept {
    for (int i = 0; i < ISIZE(v); ++i) v[i]++;
}

/* #endregion */

// #include <atcoder/all>
// using namespace atcoder;

/* #region mint */

// 自動で MOD を取る整数
template <ll MOD> struct mint {
    ll x;
    constexpr mint(ll x = 0) : x((x % MOD + MOD) % MOD) {}
    constexpr mint &operator+=(const mint &a) {
        if ((x += a.x) >= MOD) x -= MOD;
        return *this;
    }
    constexpr mint &operator-=(const mint &a) {
        if ((x += MOD - a.x) >= MOD) x -= MOD;
        return *this;
    }
    constexpr mint &operator*=(const mint &a) {
        (x *= a.x) %= MOD;
        return *this;
    }
    constexpr mint operator+(const mint &a) const {
        mint res(*this);
        return res += a;
    }
    constexpr mint operator-(const mint &a) const {
        mint res(*this);
        return res -= a;
    }
    constexpr mint operator*(const mint &a) const {
        mint res(*this);
        return res *= a;
    }
    // O(log(t))
    constexpr mint pow_rec(ll t) const {
        if (!t) return 1;
        mint a = pow(t >> 1); // ⌊t/2⌋ 乗
        a *= a;               // ⌊t/2⌋*2 乗
        if (t & 1)            // ⌊t/2⌋*2 == t-1 のとき
            a *= *this;       // ⌊t/2⌋*2+1 乗 => t 乗
        return a;
    }

    constexpr mint pow(ll t) const {
        mint a(*this);
        mint res = 1;
        while (t) {
            if (t & 1) res *= a;
            t >>= 1, a *= a;
        }
        return res;
    }

    // for prime mod
    constexpr mint inv_prime() const {
        return pow(MOD - 2); // オイラーの定理から， x^(-1) ≡ x^(p-2)
    }
    constexpr mint inv() const {
        ll a = this->x, b = MOD, u = 1, v = 0, t = 0;
        mint res;
        while (b) {
            t = a / b;
            a -= t * b;
            swap(a, b);
            u -= t * v;
            swap(u, v);
        }
        if (u < 0) u += MOD;
        res = u;
        return res;
    }
    constexpr mint &operator/=(const mint &a) { return (*this) *= a.inv(); }
    constexpr mint operator/(const mint &a) const {
        mint res(*this);
        return res /= a;
    }
    constexpr bool operator==(const mint &a) const { return this->x == a.x; }
    constexpr bool operator==(const ll a) const { return this->x == a; }
    constexpr bool operator!=(const mint &a) const { return this->x != a.x; }
    constexpr bool operator!=(const ll a) const { return this->x != a; }

    mint operator+() const { return *this; }
    mint operator-() const { return *this * (-1); }

    // mint 入力
    friend istream &operator>>(istream &is, mint &x) {
        is >> x.x;
        return is;
    }

    // mint 出力
    friend ostream &operator<<(ostream &os, const mint x) {
        os << x.x;
        return os;
    }
};

/* #endregion */

/* #region Mat */

template <typename T> constexpr bool false_v = false;

// 行列，==, !=, [] あたりは vector と一緒
template <class Num> class Mat : public vc<vc<Num>> {
  public:
    // using vc<vc<Num>>::vector;
    size_t h, w;

    // コンストラクタ
    Mat<Num>(const size_t h, size_t w) : vc<vc<Num>>(h, vc<Num>(w, 0)), h(h), w(w) {}
    // Mat<Num>(const Mat<Num> &mt) : vc<vc<Num>>(mt), h(mt.h), w(mt.w) {}
    Mat<Num>(std::initializer_list<vc<Num>> init) : vc<vc<Num>>() {
        for (auto iter = init.begin(); iter != init.end(); ++iter) this->emplace_back(*iter);
        h = this->size(), w = (*this)[0].size();
    }

    // 行列に別の行列を足す
    Mat &operator+=(const Mat &another) {
        assert(this->h == another.h && this->w == another.w);
        REP(i, 0, this->h) REP(j, 0, this->w)(*this)[i][j] += another[i][j];
        return *this;
    }

    // 行列から別の行列を引く
    Mat &operator-=(const Mat &another) {
        assert(this->h == another.h && this->w == another.w);
        REP(i, 0, this->h) REP(j, 0, this->w)(*this)[i][j] -= another[i][j];
        return *this;
    }

    // 行列に別の行列を右から掛ける
    Mat &operator*=(const Mat &another) {
        assert(w == another.h);
        Mat<Num> ret(this->h, another.w);
        REP(i, 0, this->h) REP(j, 0, another.w) REP(k, 0, this->w) ret[i][j] += (*this)[i][k] * another[k][j];
        *this = ret;
        return *this;
    }

    // 行列に別の行列を足す
    Mat operator+(const Mat &another) const {
        Mat<Num> ret(*this);
        return ret += another;
    }

    // 行列から別の行列を引く
    Mat operator-(const Mat &another) const {
        Mat<Num> ret(*this);
        return ret -= another;
    }

    // 行列に別の行列を右から掛ける
    Mat operator*(const Mat &another) const {
        Mat<Num> ret(*this);
        return ret *= another;
    }

    // 行列の n 乗を計算する
    Mat pow(ll n) const {
        assert(this->h == this->w);
        Mat<Num> ret(this->h, this->w);
        Mat<Num> a(*this);
        REP(i, 0, this->h) ret[i][i] = 1;
        while (n) {
            if (n & 1) ret = a * ret;
            a = a * a, n >>= 1;
        }
        return ret;
    }

    template <class... T> Mat assign(T... nums) {
        vc<Num> num_list = vc<Num>{nums...};
        assert(num_list.size() == this->h * this->w);
        REP(i, 0, this->h) REP(j, 0, this->w)(*this)[i][j] = num_list[this->w * i + j];
        return *this;
    }

    void fill(Num num) { REP(i, 0, this->h) REP(j, 0, this->w)(*this)[i][j] = num; }

    void print() { REP(i, 0, h) REP(j, 0, w) cout << (*this)[i][j] << (j == (ll)w - 1 ? '\n' : ' '); }
};

/* #endregion */

struct Sieve {
    int n;
    int sqrtn;
    vc<int> sieve; // sieve[i] := i の最小の素因数

    // コンストラクタ．前処理を行う．
    Sieve(int n) : n(n), sqrtn((int)sqrtl(n)), sieve(n + 1) {
        iota(ALL(sieve), 0); // 各要素をインデックスで初期化（0, 1, ..., n）．使用するのは 2, 3, ...
        REPM(i, 2, sqrtn) {
            if (sieve[i] < i) continue; // i は合成数
            // assert(i は素数)
            sieve[i] = i;
            // n 以下の任意の i の倍数 j について，j が i 未満の素数で割れなかった場合
            REPMD(j, i * i, n, i) if (sieve[j] == j) sieve[j] = i; // j の最小の素因数は i
        }
    }

    // 素因数分解クエリ，O(log n)
    vc<int> pfd(int m) const {
        assert(m <= n);
        vc<int> prime_factors;
        while (m > 1) {
            prime_factors.push_back(sieve[m]);
            m /= sieve[m];
        }
        return prime_factors;
    }

    // 素因数分解クエリ，O(log n)
    map<int, int> pfd_map(int m) const {
        assert(m <= n);
        map<int, int> prime_factors; //
        while (m > 1) {
            prime_factors[sieve[m]]++;
            m /= sieve[m];
        }
        return prime_factors;
    }

    // m が素数かどうかを返す
    bool is_prime(const int m) const {
        return sieve[m] == m; //
    }

    // n 以下の素数一覧を返す
    vc<int> primes() const {
        vc<int> ret;
        REPM(i, 2, n) if (is_prime(i)) ret.push_back(i);
        return ret;
    }

    // a の約数を列挙する
    vc<int> devisors(const int a) const {
        assert(a <= n);
        map<int, int> mp = pfd_map(a);
        vc<pair<int, int>> V; // mp をベクトルに変換したもの
        for (auto pa : mp) {
            V.push_back(pa);
        }

        // 戻り値（入れ物）
        vc<int> Y;
        auto dfsd = [&Y, &V](auto &&dfsd, int cur_idx, int cur_val) -> void {
            if (cur_idx == (int)V.size()) {
                // 値が完成
                Y.push_back(cur_val);
                return;
            }
            const auto [v, c] = V[cur_idx];
            // p乗を全通り試す (0, ..., p乗)
            int mul = 1;
            REP(p, 0, c + 1) {
                dfsd(dfsd, cur_idx + 1, cur_val * mul);
                mul *= v;
            }
            return;
        };

        dfsd(dfsd, 0, 1);
        sort(ALL(Y));
        return Y;
    }
};

// Problem
void solve() {
    VAR(ll, n, k); //

    Sieve sieve(n + 2);
    map<int, int> pfactors = sieve.pfd_map(n);
    int max_prime_factor = pfactors.rbegin()->first;
    if (max_prime_factor == 2) {
        max_prime_factor = 3;
    }

    // 使うかもしれない素数を列挙する
    vc<int> primes = sieve.primes();
    while (primes.size() && primes.back() > max_prime_factor) {
        primes.pop_back();
    }
    // dump(SIZE(primes));

    // 到達し得ない素数は除外する
    vc<int> visited(primes.size(), 0);
    auto dfs = [&](auto &&dfs, const int idx) -> void {
        if (visited[idx]) return;
        visited[idx] = 1;
        // next
        map<int, int> cur_pfactors = sieve.pfd_map(primes[idx]);
        // 素因数ごとに見る
        // dump(idx, primes[idx], cur_pfactors);
        for (auto [p, a] : cur_pfactors) {
            // p は素数なので， p+1 は p>3 なら必ず合成数
            map<int, int> nxt_pfactors = sieve.pfd_map(p + 1);
            // dump(p, p + 1, nxt_pfactors);
            for (auto [np, na] : nxt_pfactors) {
                const int nxt_idx = lower_bound(ALL(primes), np) - primes.begin();
                // dump(np, primes, nxt_idx);
                dfs(dfs, nxt_idx);
            }
        }
    };

    for (auto [p, a] : pfactors) {
        const int idx = lower_bound(ALL(primes), p) - primes.begin();
        // dump(idx);
        dfs(dfs, idx);
    }
    // dump(primes);
    // dump(visited);
    // dump(accumulate(ALL(visited), 0));

    vc<int> primes_to_use;
    REP(i, 0, SIZE(primes)) {
        if (visited[i]) {
            primes_to_use.push_back(primes[i]);
        }
    }

    ll SZ = SIZE(primes_to_use);

    // 推移行列を用意する
    using mat = Mat<mint<MOD - 1>>;

    mat A(SZ, SZ);
    REP(i, 0, SZ) {
        const int p = primes_to_use[i];
        map<int, int> cur_pfactors = sieve.pfd_map(p + 1);
        // dump(p, cur_pfactors);
        for (auto [np, na] : cur_pfactors) {
            const int next_idx = lower_bound(ALL(primes_to_use), np) - primes_to_use.begin();
            A[next_idx][i] = na;
        }
    }
    // dump(primes_to_use);
    // A.print();

    mat x(SZ, 1);
    for (const auto [p, a] : pfactors) {
        const int idx = lower_bound(ALL(primes_to_use), p) - primes_to_use.begin();
        x[idx][0] = a;
    }
    // x.print();

    mat y = A.pow(k) * x;
    // y.print();

    mint<MOD> ans = 1;
    REP(i, 0, SZ) {
        if (y[i][0] == 0) continue;
        const int p = primes_to_use[i];
        ans *= mint<MOD>(p).pow(y[i][0].x);
    }
    pprint(ans);
}

// entry point
int main() {
    solve();
    return 0;
}