#889196 (C++17) No.2365 Present of good number

提出ソース

結果

問題	No.2365 Present of good number
ユーザー	poyon
提出日時	2023-07-08 15:56:34
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	9 ms / 2,000 ms
コード長	13,966 bytes
コンパイル時間	3,203 ms
コンパイル使用メモリ	227,564 KB
実行使用メモリ	7,124 KB
最終ジャッジ日時	2023-09-29 17:18:13
合計ジャッジ時間	4,864 ms
ジャッジサーバーID （参考情報）	judge15 / judge12

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	8 ms 6,964 KB
testcase_01	AC	8 ms 6,932 KB
testcase_02	AC	9 ms 6,904 KB
testcase_03	AC	8 ms 6,964 KB
testcase_04	AC	8 ms 6,956 KB
testcase_05	AC	9 ms 6,928 KB
testcase_06	AC	8 ms 6,860 KB
testcase_07	AC	8 ms 6,984 KB
testcase_08	AC	8 ms 7,000 KB
testcase_09	AC	8 ms 6,988 KB
testcase_10	AC	8 ms 6,960 KB
testcase_11	AC	9 ms 6,960 KB
testcase_12	AC	9 ms 6,940 KB
testcase_13	AC	8 ms 7,124 KB
testcase_14	AC	8 ms 6,972 KB
testcase_15	AC	8 ms 6,908 KB
testcase_16	AC	8 ms 6,908 KB
testcase_17	AC	8 ms 6,932 KB
testcase_18	AC	9 ms 6,872 KB
testcase_19	AC	8 ms 6,960 KB
testcase_20	AC	9 ms 6,868 KB
testcase_21	AC	9 ms 6,856 KB
testcase_22	AC	8 ms 6,956 KB
testcase_23	AC	8 ms 6,876 KB
testcase_24	AC	9 ms 6,924 KB
testcase_25	AC	8 ms 6,880 KB
testcase_26	AC	8 ms 6,916 KB
testcase_27	AC	8 ms 6,840 KB
testcase_28	AC	9 ms 6,880 KB
testcase_29	AC	8 ms 6,956 KB
testcase_30	AC	8 ms 6,844 KB
testcase_31	AC	8 ms 6,960 KB
testcase_32	AC	8 ms 6,920 KB
testcase_33	AC	9 ms 6,956 KB
testcase_34	AC	9 ms 7,032 KB
testcase_35	AC	8 ms 6,960 KB
testcase_36	AC	8 ms 6,920 KB
testcase_37	AC	9 ms 6,960 KB
testcase_38	AC	8 ms 6,868 KB
testcase_39	AC	9 ms 6,984 KB
testcase_40	AC	8 ms 6,936 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

raw source code

// clang-format off
#ifdef _LOCAL
    #include <pch.hpp>
#else
    #include <bits/stdc++.h>
    #define cerr if (false) cerr
    #define debug_bar
    #define debug(...)
    #define debug2(vv)
    #define debug3(vvv)
#endif

using namespace std;
using ll = long long;
using ld = long double;
using str = string;
using P = pair<ll,ll>;
using VP = vector<P>;
using VVP = vector<VP>;
using VC = vector<char>;
using VS = vector<string>;
using VVS = vector<VS>;
using VI = vector<int>;
using VVI = vector<VI>;
using VVVI = vector<VVI>;
using VLL = vector<ll>;
using VVLL = vector<VLL>;
using VVVLL = vector<VVLL>;
using VB = vector<bool>;
using VVB = vector<VB>;
using VVVB = vector<VVB>;
using VD = vector<double>;
using VVD = vector<VD>;
using VVVD = vector<VVD>;
#define FOR(i,l,r) for (ll i = (l); i < (r); ++i)
#define RFOR(i,l,r) for (ll i = (r)-1; (l) <= i; --i)
#define REP(i,n) FOR(i,0,n)
#define RREP(i,n) RFOR(i,0,n)
#define FORE(e,c) for (auto&& e : c)
#define ALL(c) (c).begin(), (c).end()
#define SORT(c) sort(ALL(c))
#define RSORT(c) sort((c).rbegin(), (c).rend())
#define MIN(c) *min_element(ALL(c))
#define MAX(c) *max_element(ALL(c))
#define COUNT(c,v) count(ALL(c),(v))
#define len(c) ((ll)(c).size())
#define BIT(b,i) (((b)>>(i)) & 1)
#define PCNT(b) ((ll)__builtin_popcountll(b))
#define LB(c,v) distance((c).begin(), lower_bound(ALL(c), (v)))
#define UB(c,v) distance((c).begin(), upper_bound(ALL(c), (v)))
#define UQ(c) do { SORT(c); (c).erase(unique(ALL(c)), (c).end()); (c).shrink_to_fit(); } while (0)
#define END(...) do { print(__VA_ARGS__); exit(0); } while (0)
constexpr ld EPS = 1e-10;
constexpr ld PI  = acosl(-1.0);
constexpr int inf = (1 << 30) - (1 << 15);   // 1,073,709,056
constexpr ll INF = (1LL << 62) - (1LL << 31);  // 4,611,686,016,279,904,256
template<class... T> void input(T&... a) { (cin >> ... >> a); }
void print() { cout << '\n'; }
template<class T> void print(const T& a) { cout << a << '\n'; }
template<class P1, class P2> void print(const pair<P1, P2>& a) { cout << a.first << " " << a.second << '\n'; }
template<class T, class... Ts> void print(const T& a, const Ts&... b) { cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; }
template<class T> void cout_line(const vector<T>& ans, int l, int r) { for (int i = l; i < r; i++) { if (i != l) { cout << ' '; } cout << ans[i]; } cout << '\n'; }
template<class T> void print(const vector<T>& a) { cout_line(a, 0, a.size()); }
template<class S, class T> bool chmin(S& a, const T b) { if (b < a) { a = b; return 1; } return 0; }
template<class S, class T> bool chmax(S& a, const T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> T SUM(const vector<T>& A) { return accumulate(ALL(A), T(0)); }
template<class T> vector<T> cumsum(const vector<T>& A, bool offset = false) { int N = A.size(); vector<T> S(N+1, 0); for (int i = 0; i < N; i++) { S[i+1] = S[i] + A[i]; } if (not offset) { S.erase(S.begin()); } return S; }
template<class T> string to_binary(T x, int B = 0) { string s; while (x) { s += ('0' + (x & 1)); x >>= 1; } while ((int)s.size() < B) { s += '0'; } reverse(s.begin(), s.end()); return s; }
template<class F> ll binary_search(const F& is_ok, ll ok, ll ng) { while (abs(ok - ng) > 1) { ll m = (ok + ng) / 2; (is_ok(m) ? ok : ng) = m; } return ok; }
template<class F> double binary_search_real(const F& is_ok, double ok, double ng, int iter = 90) { for (int i = 0; i < iter; i++) { double m = (ok + ng) / 2; (is_ok(m) ? ok : ng) = m; } return ok; }
template<class T> using PQ_max = priority_queue<T>;
template<class T> using PQ_min = priority_queue<T, vector<T>, greater<T>>;
template<class T> T pick(stack<T>& s) { assert(not s.empty()); T x = s.top(); s.pop(); return x; }
template<class T> T pick(queue<T>& q) { assert(not q.empty()); T x = q.front(); q.pop(); return x; }
template<class T> T pick_front(deque<T>& dq) { assert(not dq.empty()); T x = dq.front(); dq.pop_front(); return x; }
template<class T> T pick_back(deque<T>& dq) { assert(not dq.empty()); T x = dq.back(); dq.pop_back(); return x; }
template<class T> T pick(PQ_min<T>& pq) { assert(not pq.empty()); T x = pq.top(); pq.pop(); return x; }
template<class T> T pick(PQ_max<T>& pq) { assert(not pq.empty()); T x = pq.top(); pq.pop(); return x; }
template<class T> T pick(vector<T>& v) { assert(not v.empty()); T x = v.back(); v.pop_back(); return x; }
int to_int(const char c) { if (islower(c)) { return (c - 'a'); } if (isupper(c)) { return (c - 'A'); } if (isdigit(c)) { return (c - '0'); } assert(false); }
char to_a(const int i) { assert(0 <= i && i < 26); return ('a' + i); }
char to_A(const int i) { assert(0 <= i && i < 26); return ('A' + i); }
char to_d(const int i) { assert(0 <= i && i <= 9); return ('0' + i); }
ll min(int a, ll b) { return min((ll)a, b); }
ll min(ll a, int b) { return min(a, (ll)b); }
ll max(int a, ll b) { return max((ll)a, b); }
ll max(ll a, int b) { return max(a, (ll)b); }
ll mod(ll x, ll m) { assert(m > 0); return (x % m + m) % m; }
ll ceil(ll a, ll b) { if (b < 0) { return ceil(-a, -b); } assert(b > 0); return (a < 0 ? a / b : (a + b - 1) / b); }
ll floor(ll a, ll b) { if (b < 0) { return floor(-a, -b); } assert(b > 0); return (a > 0 ? a / b : (a - b + 1) / b); }
ll powint(ll x, ll n) { assert(n >= 0); if (n == 0) { return 1; }; ll res = powint(x, n>>1); res *= res; if (n & 1) { res *= x; } return res; }
pair<ll,ll> divmod(ll a, ll b) { assert(b != 0); ll q = floor(a, b); return make_pair(q, a - q * b); }
ll bitlen(ll b) { if (b <= 0) { return 0; } return (64LL - __builtin_clzll(b)); }
ll digitlen(ll n) { assert(n >= 0); if (n == 0) { return 1; } ll sum = 0; while (n > 0) { sum++; n /= 10; } return sum; }
ll msb(ll b) { return (b <= 0 ? -1 : (63 - __builtin_clzll(b))); }
ll lsb(ll b) { return (b <= 0 ? -1 : __builtin_ctzll(b)); }
// --------------------------------------------------------

// エラトステネスの篩
struct eratosthenes {
  public:
    // 前計算
    //   - O(N log log N)
    eratosthenes(int N) : N(N) {
        D.resize(N+1);
        iota(D.begin(), D.end(), 0);
        for (int p : {2, 3, 5}) {
            for (int i = p*p; i <= N; i += p) { if (D[i] == i) { D[i] = p; } }
        }
        vector<int> inc = {4, 2, 4, 2, 4, 6, 2, 6};
        int p = 7, idx = 0;
        int root = floor(sqrt(N) + 0.5);
        while (p <= root) {
            if (D[p] == p) {
                for (int i = p*p; i <= N; i += p) { if (D[i] == i) { D[i] = p; } }
            }
            p += inc[idx++];
            if (idx == 8) { idx = 0; }
        }
    }

    // 素数判定
    //   - O(1)
    bool is_prime(int x) const {
        assert(1 <= x && x <= N);
        if (x == 1) { return false; }
        return D[x] == x;
    }

    // 素因数分解
    //   - O(log x), 厳密には O(Σi ei)
    vector<pair<int,int>> factorize(int x) const {
        assert(1 <= x && x <= N);
        vector<pair<int,int>> F;
        while (x != 1) {
            int p = D[x];
            int e = 0;
            while (x % p == 0) { x /= p; e++; }
            F.emplace_back(p, e);
        }
        return F;
    }

    // 約数列挙
    //   - O(Πi(1+ei))
    //   - ソートされていないことに注意
    vector<int> calc_divisors(int x) const {
        assert(1 <= x && x <= N);

        int n = 1;  // 約数の個数
        vector<pair<int,int>> F;
        while (x != 1) {
            int p = D[x];
            int e = 0;
            while (x % p == 0) { x /= p; e++; }
            F.emplace_back(p, e);
            n *= (1 + e);
        }

        vector<int> divisors(n,1);
        int sz = 1;  // 現在の約数の個数
        for (const auto& [p, e] : F) {
            for (int i = 0; i < sz * e; i++) {
                divisors[sz + i] = divisors[i] * p;
            }
            sz *= (1 + e);
        }
        return divisors;
    }

    // 最小素因数 (least prime factor)
    //   - O(1)
    int lpf(int x) const { assert(1 <= x && x <= N); return D[x]; }

    // オイラーの φ 関数
    // 1 から x までの整数のうち x と互いに素なものの個数 φ(x)
    //   - O(log x), 厳密には O(Σi ei)
    int euler_phi(int x) const {
        assert(1 <= x && x <= N);
        int res = x;
        while (x != 1) {
            int p = D[x];
            res -= res / p;
            while (x % p == 0) { x /= p; }
        }
        return res;
    }

    // メビウス関数のテーブルを計算する
    //   - O(N)
    vector<int> calc_moebius() const {
        vector<int> moebius(N+1, 0);
        moebius[1] = 1;
        for (int x = 2; x <= N; x++) {
            int y = x / D[x];
            if (D[x] != D[y]) { moebius[x] = -moebius[y]; }
        }
        return moebius;
    }

  private:
    int N;
    vector<int> D;  // 最小素因数 (least prime factor)
};

#include <atcoder/modint>
using namespace atcoder;

// constexpr ll MOD = 1000003;
// using mint = modint;
// mint::set_mod(MOD);  // write in main()

using mint = modint1000000007;
// using mint = modint998244353;

using VM = vector<mint>;
using VVM = vector<VM>;
using VVVM = vector<VVM>;
using VVVVM = vector<VVVM>;

template<int M> istream &operator>>(istream &is, static_modint<M> &m) { ll v; is >> v; m = v; return is; }
template<int M> istream &operator>>(istream &is, dynamic_modint<M> &m) { ll v; is >> v; m = v; return is; }
template<int M> ostream &operator<<(ostream &os, const static_modint<M> &m) { return os << m.val(); }
template<int M> ostream &operator<<(ostream &os, const dynamic_modint<M> &m) { return os << m.val(); }

// It is assumed that M (= mod) is prime number
struct combination {
  public:
    combination() : combination(1) {}
    combination(int n) : N(1), _fact(2,1), _ifact(2,1) {
        M = mint().mod();
        assert(0 < n && n < M);
        if (N < n) { build(n); }
    }

    mint P(int n, int k) {
        if (N < n) { build(n); }
        if (n < 0 || k < 0 || n < k) { return 0; }
        return _fact[n] * _ifact[n-k];
    }
    mint C(int n, int k) {
        if (N < n) { build(n); }
        if (n < 0 || k < 0 || n < k) { return 0; }
        return _fact[n] * _ifact[n-k] * _ifact[k];
    }
    mint H(int n, int k) {
        if (n == 0 && k == 0) { return 1; }
        if (n < 0 || k < 0) { return 0; }
        return C(n + k - 1, k);
    }
    mint fact(int n) {
        if (N < n) { build(n); }
        if (n < 0) { return 0; }
        return _fact[n];
    }
    mint ifact(int n) {
        if (N < n) { build(n); }
        if (n < 0) { return 0; }
        return _ifact[n];
    }
    mint P_naive(ll n, int k) const noexcept {
        if (n < 0 || k < 0 || n < k) { return 0; }
        mint res = 1;
        for (int i = 1; i <= k; i++) { res *= (n - i + 1); }
        return res;
    }
    mint C_naive(ll n, int k) const noexcept {
        if (n < 0 || k < 0 || n < k) { return 0; }
        if (k > n - k) { k = n - k; }
        mint nume = 1, deno = 1;
        for (int i = 1; i <= k; i++) { nume *= (n - i + 1); deno *= i; }
        return nume / deno;
    }
    mint H_naive(ll n, int k) const noexcept {
        if (n == 0 && k == 0) { return 1; }
        if (n < 0 || k < 0) { return 0; }
        return C_naive(n + k - 1, k);
    }
    mint catalan(int n) {
        if (N < 2 * n) { build(2 * n); }
        return _fact[2 * n] * _ifact[n + 1] * _ifact[n];
    }
    template<class... Ts>
    mint C_multinomial(int n, int k, Ts... ks) {
        if (N < n) { build(n); }
        if (n < 0 || k < 0 || n < k) { return 0; }
        return C_multinomial(n, ks...) * _ifact[k];
    }
    mint C_multinomial(int n, int k) {
        if (N < n) { build(n); }
        if (n < 0 || k < 0 || n < k) { return 0; }
        return _fact[n] * _ifact[k];
    }

  private:
    int N;
    int M;  // mod
    vector<mint> _fact, _ifact;

    void build(int N_new) {
        assert(N < N_new);
        assert(N_new < M);
        _fact.resize(N_new + 1);
        _ifact.resize(N_new + 1);
        for (int i = N + 1; i <= N_new; i++) { _fact[i] = _fact[i - 1] * i; }
        _ifact[N_new] = _fact[N_new].inv();
        for (int i = N_new - 1; N + 1 <= i; i--) { _ifact[i] = _ifact[i + 1] * (i + 1); }
        N = N_new;
    }
};

#include <atcoder/math>
using namespace atcoder;

// a^b^c mod p を求める
ll a_b_c(ll a, ll b, ll c, ll mod) {
    if (a % mod == 0) { return 0; }
    return pow_mod(a, pow_mod(b, c, mod-1), mod);
}

// clang-format on
int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(15);

    ll N, K;
    input(N, K);

    eratosthenes era(1e6);

    map<P, tuple<ll, ll, mint>> mp;  // ({n, k}, {e2, e3, others})
    auto dp = [&](auto&& self, ll n, ll k) -> tuple<ll, ll, mint> {
        if (k == 0) {
            ll e2 = 0, e3 = 0;
            while (n % 2 == 0) {
                n /= 2;
                e2++;
            }
            while (n % 3 == 0) {
                n /= 3;
                e3++;
            }
            return make_tuple(e2, e3, n);
        }

        auto it = mp.find({n, k});
        if (it != mp.end()) { return it->second; }

        ll e2 = 0, e3 = 0;
        mint others = 1;
        auto F = era.factorize(n);
        for (auto [p, e] : F) {
            auto [f2, f3, rem] = self(self, p + 1, k - 1);
            e2 += f2 * e;
            e3 += f3 * e;
            others *= rem.pow(e);
        }
        return mp[make_pair(n, k)] = make_tuple(e2, e3, others);
    };

    ll K1 = min(20, K);
    ll K2 = max(0, K - K1);
    auto [x, y, others] = dp(dp, N, K1);

    debug(K1, K2);
    debug(x, y, others);
    if (K2 > 0) { assert(others == 1); }

    mint ans = others;
    auto MOD = mint().mod();
    if (K2 & 1) {
        ans *= mint(2).pow(y * pow_mod(2, K2 / 2 + 1, MOD - 1));
        ans *= mint(3).pow(x * pow_mod(2, K2 / 2, MOD - 1));
    } else {
        ans *= mint(2).pow(x * pow_mod(2, K2 / 2, MOD - 1));
        ans *= mint(3).pow(y * pow_mod(2, K2 / 2, MOD - 1));
    }
    print(ans.val());

    return 0;
}

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結果

テストケース

ソースコード