結果
問題 | No.2318 Phys Bone Maker |
ユーザー | rniya |
提出日時 | 2023-05-26 21:49:23 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 270 ms / 3,000 ms |
コード長 | 21,356 bytes |
コンパイル時間 | 2,504 ms |
コンパイル使用メモリ | 216,772 KB |
実行使用メモリ | 5,376 KB |
最終ジャッジ日時 | 2024-06-07 06:26:52 |
合計ジャッジ時間 | 5,772 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge4 |
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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 |
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testcase_00 | AC | 2 ms
5,248 KB |
testcase_01 | AC | 2 ms
5,248 KB |
testcase_02 | AC | 268 ms
5,376 KB |
testcase_03 | AC | 2 ms
5,376 KB |
testcase_04 | AC | 2 ms
5,376 KB |
testcase_05 | AC | 2 ms
5,376 KB |
testcase_06 | AC | 2 ms
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testcase_07 | AC | 2 ms
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testcase_08 | AC | 2 ms
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testcase_09 | AC | 2 ms
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testcase_10 | AC | 2 ms
5,376 KB |
testcase_11 | AC | 3 ms
5,376 KB |
testcase_12 | AC | 2 ms
5,376 KB |
testcase_13 | AC | 2 ms
5,376 KB |
testcase_14 | AC | 2 ms
5,376 KB |
testcase_15 | AC | 2 ms
5,376 KB |
testcase_16 | AC | 5 ms
5,376 KB |
testcase_17 | AC | 2 ms
5,376 KB |
testcase_18 | AC | 2 ms
5,376 KB |
testcase_19 | AC | 2 ms
5,376 KB |
testcase_20 | AC | 2 ms
5,376 KB |
testcase_21 | AC | 2 ms
5,376 KB |
testcase_22 | AC | 2 ms
5,376 KB |
testcase_23 | AC | 4 ms
5,376 KB |
testcase_24 | AC | 2 ms
5,376 KB |
testcase_25 | AC | 4 ms
5,376 KB |
testcase_26 | AC | 2 ms
5,376 KB |
testcase_27 | AC | 1 ms
5,376 KB |
testcase_28 | AC | 2 ms
5,376 KB |
testcase_29 | AC | 2 ms
5,376 KB |
testcase_30 | AC | 4 ms
5,376 KB |
testcase_31 | AC | 2 ms
5,376 KB |
testcase_32 | AC | 7 ms
5,376 KB |
testcase_33 | AC | 2 ms
5,376 KB |
testcase_34 | AC | 2 ms
5,376 KB |
testcase_35 | AC | 47 ms
5,376 KB |
testcase_36 | AC | 162 ms
5,376 KB |
testcase_37 | AC | 140 ms
5,376 KB |
testcase_38 | AC | 122 ms
5,376 KB |
testcase_39 | AC | 240 ms
5,376 KB |
testcase_40 | AC | 206 ms
5,376 KB |
testcase_41 | AC | 270 ms
5,376 KB |
testcase_42 | AC | 229 ms
5,376 KB |
testcase_43 | AC | 2 ms
5,376 KB |
testcase_44 | AC | 14 ms
5,376 KB |
testcase_45 | AC | 14 ms
5,376 KB |
testcase_46 | AC | 196 ms
5,376 KB |
testcase_47 | AC | 13 ms
5,376 KB |
ソースコード
#include <bits/stdc++.h> #ifdef LOCAL #include <debug.hpp> #else #define debug(...) void(0) #endif #include <type_traits> #ifdef _MSC_VER #include <intrin.h> #endif #ifdef _MSC_VER #include <intrin.h> #endif namespace atcoder { namespace internal { // @param m `1 <= m` // @return x mod m constexpr long long safe_mod(long long x, long long m) { x %= m; if (x < 0) x += m; return x; } // Fast modular multiplication by barrett reduction // Reference: https://en.wikipedia.org/wiki/Barrett_reduction // NOTE: reconsider after Ice Lake struct barrett { unsigned int _m; unsigned long long im; // @param m `1 <= m < 2^31` explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {} // @return m unsigned int umod() const { return _m; } // @param a `0 <= a < m` // @param b `0 <= b < m` // @return `a * b % m` unsigned int mul(unsigned int a, unsigned int b) const { // [1] m = 1 // a = b = im = 0, so okay // [2] m >= 2 // im = ceil(2^64 / m) // -> im * m = 2^64 + r (0 <= r < m) // let z = a*b = c*m + d (0 <= c, d < m) // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2 // ((ab * im) >> 64) == c or c + 1 unsigned long long z = a; z *= b; #ifdef _MSC_VER unsigned long long x; _umul128(z, im, &x); #else unsigned long long x = (unsigned long long)(((unsigned __int128)(z)*im) >> 64); #endif unsigned int v = (unsigned int)(z - x * _m); if (_m <= v) v += _m; return v; } }; // @param n `0 <= n` // @param m `1 <= m` // @return `(x ** n) % m` constexpr long long pow_mod_constexpr(long long x, long long n, int m) { if (m == 1) return 0; unsigned int _m = (unsigned int)(m); unsigned long long r = 1; unsigned long long y = safe_mod(x, m); while (n) { if (n & 1) r = (r * y) % _m; y = (y * y) % _m; n >>= 1; } return r; } // Reference: // M. Forisek and J. Jancina, // Fast Primality Testing for Integers That Fit into a Machine Word // @param n `0 <= n` constexpr bool is_prime_constexpr(int n) { if (n <= 1) return false; if (n == 2 || n == 7 || n == 61) return true; if (n % 2 == 0) return false; long long d = n - 1; while (d % 2 == 0) d /= 2; constexpr long long bases[3] = {2, 7, 61}; for (long long a : bases) { long long t = d; long long y = pow_mod_constexpr(a, t, n); while (t != n - 1 && y != 1 && y != n - 1) { y = y * y % n; t <<= 1; } if (y != n - 1 && t % 2 == 0) { return false; } } return true; } template <int n> constexpr bool is_prime = is_prime_constexpr(n); // @param b `1 <= b` // @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) { a = safe_mod(a, b); if (a == 0) return {b, 0}; // Contracts: // [1] s - m0 * a = 0 (mod b) // [2] t - m1 * a = 0 (mod b) // [3] s * |m1| + t * |m0| <= b long long s = b, t = a; long long m0 = 0, m1 = 1; while (t) { long long u = s / t; s -= t * u; m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b // [3]: // (s - t * u) * |m1| + t * |m0 - m1 * u| // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u) // = s * |m1| + t * |m0| <= b auto tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp; } // by [3]: |m0| <= b/g // by g != b: |m0| < b/g if (m0 < 0) m0 += b / s; return {s, m0}; } // Compile time primitive root // @param m must be prime // @return primitive root (and minimum in now) constexpr int primitive_root_constexpr(int m) { if (m == 2) return 1; if (m == 167772161) return 3; if (m == 469762049) return 3; if (m == 754974721) return 11; if (m == 998244353) return 3; int divs[20] = {}; divs[0] = 2; int cnt = 1; int x = (m - 1) / 2; while (x % 2 == 0) x /= 2; for (int i = 3; (long long)(i)*i <= x; i += 2) { if (x % i == 0) { divs[cnt++] = i; while (x % i == 0) { x /= i; } } } if (x > 1) { divs[cnt++] = x; } for (int g = 2;; g++) { bool ok = true; for (int i = 0; i < cnt; i++) { if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) { ok = false; break; } } if (ok) return g; } } template <int m> constexpr int primitive_root = primitive_root_constexpr(m); // @param n `n < 2^32` // @param m `1 <= m < 2^32` // @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64) unsigned long long floor_sum_unsigned(unsigned long long n, unsigned long long m, unsigned long long a, unsigned long long b) { unsigned long long ans = 0; while (true) { if (a >= m) { ans += n * (n - 1) / 2 * (a / m); a %= m; } if (b >= m) { ans += n * (b / m); b %= m; } unsigned long long y_max = a * n + b; if (y_max < m) break; // y_max < m * (n + 1) // floor(y_max / m) <= n n = (unsigned long long)(y_max / m); b = (unsigned long long)(y_max % m); std::swap(m, a); } return ans; } } // namespace internal } // namespace atcoder namespace atcoder { namespace internal { #ifndef _MSC_VER template <class T> using is_signed_int128 = typename std::conditional<std::is_same<T, __int128_t>::value || std::is_same<T, __int128>::value, std::true_type, std::false_type>::type; template <class T> using is_unsigned_int128 = typename std::conditional<std::is_same<T, __uint128_t>::value || std::is_same<T, unsigned __int128>::value, std::true_type, std::false_type>::type; template <class T> using make_unsigned_int128 = typename std::conditional<std::is_same<T, __int128_t>::value, __uint128_t, unsigned __int128>; template <class T> using is_integral = typename std::conditional<std::is_integral<T>::value || is_signed_int128<T>::value || is_unsigned_int128<T>::value, std::true_type, std::false_type>::type; template <class T> using is_signed_int = typename std::conditional<(is_integral<T>::value && std::is_signed<T>::value) || is_signed_int128<T>::value, std::true_type, std::false_type>::type; template <class T> using is_unsigned_int = typename std::conditional<(is_integral<T>::value && std::is_unsigned<T>::value) || is_unsigned_int128<T>::value, std::true_type, std::false_type>::type; template <class T> using to_unsigned = typename std::conditional< is_signed_int128<T>::value, make_unsigned_int128<T>, typename std::conditional<std::is_signed<T>::value, std::make_unsigned<T>, std::common_type<T>>::type>::type; #else template <class T> using is_integral = typename std::is_integral<T>; template <class T> using is_signed_int = typename std::conditional<is_integral<T>::value && std::is_signed<T>::value, std::true_type, std::false_type>::type; template <class T> using is_unsigned_int = typename std::conditional<is_integral<T>::value && std::is_unsigned<T>::value, std::true_type, std::false_type>::type; template <class T> using to_unsigned = typename std::conditional<is_signed_int<T>::value, std::make_unsigned<T>, std::common_type<T>>::type; #endif template <class T> using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>; template <class T> using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>; template <class T> using to_unsigned_t = typename to_unsigned<T>::type; } // namespace internal } // namespace atcoder namespace atcoder { namespace internal { struct modint_base {}; struct static_modint_base : modint_base {}; template <class T> using is_modint = std::is_base_of<modint_base, T>; template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>; } // namespace internal template <int m, std::enable_if_t<(1 <= m)>* = nullptr> struct static_modint : internal::static_modint_base { using mint = static_modint; public: static constexpr int mod() { return m; } static mint raw(int v) { mint x; x._v = v; return x; } static_modint() : _v(0) {} template <class T, internal::is_signed_int_t<T>* = nullptr> static_modint(T v) { long long x = (long long)(v % (long long)(umod())); if (x < 0) x += umod(); _v = (unsigned int)(x); } template <class T, internal::is_unsigned_int_t<T>* = nullptr> static_modint(T v) { _v = (unsigned int)(v % umod()); } unsigned int val() const { return _v; } mint& operator++() { _v++; if (_v == umod()) _v = 0; return *this; } mint& operator--() { if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int) { mint result = *this; ++*this; return result; } mint operator--(int) { mint result = *this; --*this; return result; } mint& operator+=(const mint& rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator-=(const mint& rhs) { _v -= rhs._v; if (_v >= umod()) _v += umod(); return *this; } mint& operator*=(const mint& rhs) { unsigned long long z = _v; z *= rhs._v; _v = (unsigned int)(z % umod()); return *this; } mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv() const { if (prime) { assert(_v); return pow(umod() - 2); } else { auto eg = internal::inv_gcd(_v, m); assert(eg.first == 1); return eg.second; } } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } private: unsigned int _v; static constexpr unsigned int umod() { return m; } static constexpr bool prime = internal::is_prime<m>; }; template <int id> struct dynamic_modint : internal::modint_base { using mint = dynamic_modint; public: static int mod() { return (int)(bt.umod()); } static void set_mod(int m) { assert(1 <= m); bt = internal::barrett(m); } static mint raw(int v) { mint x; x._v = v; return x; } dynamic_modint() : _v(0) {} template <class T, internal::is_signed_int_t<T>* = nullptr> dynamic_modint(T v) { long long x = (long long)(v % (long long)(mod())); if (x < 0) x += mod(); _v = (unsigned int)(x); } template <class T, internal::is_unsigned_int_t<T>* = nullptr> dynamic_modint(T v) { _v = (unsigned int)(v % mod()); } unsigned int val() const { return _v; } mint& operator++() { _v++; if (_v == umod()) _v = 0; return *this; } mint& operator--() { if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int) { mint result = *this; ++*this; return result; } mint operator--(int) { mint result = *this; --*this; return result; } mint& operator+=(const mint& rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator-=(const mint& rhs) { _v += mod() - rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator*=(const mint& rhs) { _v = bt.mul(_v, rhs._v); return *this; } mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv() const { auto eg = internal::inv_gcd(_v, mod()); assert(eg.first == 1); return eg.second; } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } private: unsigned int _v; static internal::barrett bt; static unsigned int umod() { return bt.umod(); } }; template <int id> internal::barrett dynamic_modint<id>::bt(998244353); using modint998244353 = static_modint<998244353>; using modint1000000007 = static_modint<1000000007>; using modint = dynamic_modint<-1>; namespace internal { template <class T> using is_static_modint = std::is_base_of<internal::static_modint_base, T>; template <class T> using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>; template <class> struct is_dynamic_modint : public std::false_type {}; template <int id> struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {}; template <class T> using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>; } // namespace internal } // namespace atcoder namespace elementary_math { template <typename T> std::vector<T> divisor(T n) { std::vector<T> res; for (T i = 1; i * i <= n; i++) { if (n % i == 0) { res.emplace_back(i); if (i * i != n) res.emplace_back(n / i); } } return res; } template <typename T> std::vector<std::pair<T, int>> prime_factor(T n) { std::vector<std::pair<T, int>> res; for (T p = 2; p * p <= n; p++) { if (n % p == 0) { res.emplace_back(p, 0); while (n % p == 0) { res.back().second++; n /= p; } } } if (n > 1) res.emplace_back(n, 1); return res; } std::vector<int> osa_k(int n) { std::vector<int> min_factor(n + 1, 0); for (int i = 2; i <= n; i++) { if (min_factor[i]) continue; for (int j = i; j <= n; j += i) { if (!min_factor[j]) { min_factor[j] = i; } } } return min_factor; } std::vector<int> prime_factor(const std::vector<int>& min_factor, int n) { std::vector<int> res; while (n > 1) { res.emplace_back(min_factor[n]); n /= min_factor[n]; } return res; } long long modpow(long long x, long long n, long long mod) { assert(0 <= n && 1 <= mod && mod < (1LL << 31)); if (mod == 1) return 0; x %= mod; long long res = 1; while (n > 0) { if (n & 1) res = res * x % mod; x = x * x % mod; n >>= 1; } return res; } long long extgcd(long long a, long long b, long long& x, long long& y) { long long d = a; if (b != 0) { d = extgcd(b, a % b, y, x); y -= (a / b) * x; } else x = 1, y = 0; return d; } long long inv_mod(long long a, long long mod) { assert(1 <= mod); long long x, y; if (extgcd(a, mod, x, y) != 1) return -1; return (mod + x % mod) % mod; } template <typename T> T euler_phi(T n) { auto pf = prime_factor(n); T res = n; for (const auto& p : pf) { res /= p.first; res *= p.first - 1; } return res; } std::vector<int> euler_phi_table(int n) { std::vector<int> res(n + 1, 0); iota(res.begin(), res.end(), 0); for (int i = 2; i <= n; i++) { if (res[i] != i) continue; for (int j = i; j <= n; j += i) res[j] = res[j] / i * (i - 1); } return res; } // minimum i > 0 s.t. x^i \equiv 1 \pmod{m} template <typename T> T order(T x, T m) { T n = euler_phi(m); auto cand = divisor(n); sort(cand.begin(), cand.end()); for (auto& i : cand) { if (modpow(x, i, m) == 1) { return i; } } return -1; } template <typename T> std::vector<std::tuple<T, T, T>> quotient_ranges(T n) { std::vector<std::tuple<T, T, T>> res; T m = 1; for (; m * m <= n; m++) res.emplace_back(m, m, n / m); for (; m >= 1; m--) { T l = n / (m + 1) + 1, r = n / m; if (l <= r and std::get<1>(res.back()) < l) res.emplace_back(l, r, n / l); } return res; } } // namespace elementary_math using namespace std; typedef long long ll; #define all(x) begin(x), end(x) constexpr int INF = (1 << 30) - 1; constexpr long long IINF = (1LL << 60) - 1; constexpr int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1}; template <class T> istream& operator>>(istream& is, vector<T>& v) { for (auto& x : v) is >> x; return is; } template <class T> ostream& operator<<(ostream& os, const vector<T>& v) { auto sep = ""; for (const auto& x : v) os << exchange(sep, " ") << x; return os; } template <class T, class U = T> bool chmin(T& x, U&& y) { return y < x and (x = forward<U>(y), true); } template <class T, class U = T> bool chmax(T& x, U&& y) { return x < y and (x = forward<U>(y), true); } template <class T> void mkuni(vector<T>& v) { sort(begin(v), end(v)); v.erase(unique(begin(v), end(v)), end(v)); } template <class T> int lwb(const vector<T>& v, const T& x) { return lower_bound(begin(v), end(v), x) - begin(v); } template <typename T> T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; } template <typename T> T lcm(T x, T y) { return x / gcd(x, y) * y; } using mint = atcoder::modint998244353; int main() { ios::sync_with_stdio(false); cin.tie(nullptr); ll N; cin >> N; auto divs = elementary_math::prime_factor(N); int n = divs.size(); vector<ll> ds; vector<vector<int>> facs; auto dfs = [&](auto self, int d, ll cur, vector<int>& v) -> void { if (d == n) { ds.emplace_back(cur); facs.emplace_back(v); return; } for (int i = 0; i <= divs[d].second; i++, cur *= divs[d].first) { v.emplace_back(i); self(self, d + 1, cur, v); v.pop_back(); } }; vector<int> init; dfs(dfs, 0, 1, init); int len = ds.size(); vector<mint> dp(len, 0); dp[0] = 1; for (int i = 0; i < len; i++) { for (int j = i + 1; j < len; j++) { mint prod = 1; bool ok = true; for (int k = 0; k < n; k++) { if (facs[i][k] > facs[j][k]) { ok = false; break; } else if (facs[i][k] == facs[j][k]) prod *= facs[i][k] + 1; } if (not ok) continue; dp[j] += dp[i] * prod; } } mint ans = dp.back(); cout << ans.val() << '\n'; return 0; }