結果
| 問題 | No.1396 Giri |
| ユーザー |
 lorent_kyopro
|
| 提出日時 | 2021-02-14 21:31:59 |
| 言語 | C++17 (gcc 13.2.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 218 ms / 2,000 ms |
| コード長 | 19,064 bytes |
| コンパイル時間 | 2,190 ms |
| コンパイル使用メモリ | 209,704 KB |
| 実行使用メモリ | 15,312 KB |
| 最終ジャッジ日時 | 2023-09-29 14:39:28 |
| 合計ジャッジ時間 | 4,553 ms |
|
ジャッジサーバーID （参考情報） |
judge15 / judge11 |
（要ログイン）
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 | 1 ms
4,376 KB |
| testcase_01 | AC | 1 ms
4,376 KB |
| testcase_02 | AC | 202 ms
15,220 KB |
| testcase_03 | AC | 1 ms
4,380 KB |
| testcase_04 | AC | 2 ms
4,380 KB |
| testcase_05 | AC | 202 ms
15,308 KB |
| testcase_06 | AC | 1 ms
4,380 KB |
| testcase_07 | AC | 2 ms
4,376 KB |
| testcase_08 | AC | 1 ms
4,380 KB |
| testcase_09 | AC | 1 ms
4,376 KB |
| testcase_10 | AC | 1 ms
4,380 KB |
| testcase_11 | AC | 1 ms
4,380 KB |
| testcase_12 | AC | 1 ms
4,376 KB |
| testcase_13 | AC | 1 ms
4,376 KB |
| testcase_14 | AC | 1 ms
4,380 KB |
| testcase_15 | AC | 1 ms
4,376 KB |
| testcase_16 | AC | 1 ms
4,380 KB |
| testcase_17 | AC | 4 ms
4,376 KB |
| testcase_18 | AC | 16 ms
4,380 KB |
| testcase_19 | AC | 113 ms
9,444 KB |
| testcase_20 | AC | 156 ms
11,972 KB |
| testcase_21 | AC | 185 ms
14,008 KB |
| testcase_22 | AC | 202 ms
14,928 KB |
| testcase_23 | AC | 204 ms
15,164 KB |
| testcase_24 | AC | 208 ms
15,260 KB |
| testcase_25 | AC | 218 ms
15,312 KB |
ソースコード
// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (int)n; ++i)
#define rrep(i, n) for (int i = (int)n - 1; i >= 0; --i)
#define ALL(v) v.begin(), v.end()
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
using namespace std;
using ll = long long;
using ld = long double;
const array<int, 8> di = {0, 1, 0, -1, 1, 1, -1, -1}, dj = {1, 0, -1, 0, 1, -1, -1, 1};
const array<string, 2> YESNO = {"NO", "YES"};
const array<string, 2> YesNo = {"No", "Yes"};
const array<string, 2> yesno = {"no", "yes"};
void YES(bool b = true) { cout << YESNO[b] << '\n'; }
void Yes(bool b = true) { cout << YesNo[b] << '\n'; }
void yes(bool b = true) { cout << yesno[b] << '\n'; }
template<typename T, typename U>
inline bool chmax(T& a, const U& b) {
if (a < b){
a = b;
return true;
}
return false;
}
template<typename T, typename U>
inline bool chmin(T& a, const U& b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template<typename T>
T MAX(const vector<T>& v) { return *max_element(v.begin(), v.end()); }
template<typename T>
T MIN(const vector<T>& v) { return *min_element(v.begin(), v.end()); }
template<typename T>
T SUM(const vector<T>& v) { return accumulate(v.begin(), v.end(), T()); }
template<typename T>
void UNIQUE(vector<T>& v) {
sort(v.begin(), v.end());
v.erase(unique(v.begin(), v.end()), v.end());
}
template<typename T>
T POW(T a, int n) {
T res = 1;
for (; n > 0; n >>= 1, a *= a) if (n & 1) res *= a;
return res;
}
template<typename T>
int lb(const vector<T>& v, T x) {
return distance(v.begin(), lower_bound(v.begin(), v.end(), x));
}
template<typename T>
int ub(const vector<T>& v, T x) {
return distance(v.begin(), upper_bound(v.begin(), v.end(), x));
}
/**
* @brief 多次元 vector の作成
* @author えびちゃん
*/
namespace detail {
template<typename T, int N>
auto make_vec(vector<int>& sizes, T const& x) {
if constexpr (N == 1) {
return vector(sizes[0], x);
} else {
int size = sizes[N-1];
sizes.pop_back();
return vector(size, make_vec<T, N-1>(sizes, x));
}
}
}
template<typename T, int N>
auto make_vec(int const(&sizes)[N], T const& x = T()) {
vector<int> s(N);
for (int i = 0; i < N; ++i) s[i] = sizes[N-i-1];
return detail::make_vec<T, N>(s, x);
}
template<typename T>
ostream& operator<<(ostream& os, const vector<T>& v) {
for (auto it = v.begin(); it != v.end(); ++it) {
if (it == v.begin()) os << *it;
else os << ' ' << *it;
}
return os;
}
template<typename T, typename U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
os << p.first << ' ' << p.second;
return os;
}
__attribute__((constructor))
void setup() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout << fixed << setprecision(15);
}
#include <cassert>
#include <numeric>
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
#include <utility>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
struct barrett {
unsigned int _m;
unsigned long long im;
explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
unsigned int umod() const { return _m; }
unsigned int mul(unsigned int a, unsigned int b) const {
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;
}
};
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;
}
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);
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};
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
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
if (m0 < 0) m0 += b / s;
return {s, m0};
}
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);
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;
n = (unsigned long long)(y_max / m);
b = (unsigned long long)(y_max % m);
std::swap(m, a);
}
return ans;
}
} // namespace internal
} // namespace atcoder
#include <cassert>
#include <numeric>
#include <type_traits>
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
using namespace atcoder;
// using mint = modint1000000007;
using mint = modint998244353;
struct sieve {
int n;
vector<int> f, primes;
sieve(int n) : n(n), f(n + 1) {
for (int i = 2; i <= n; ++i) {
if (f[i] == 0) {
f[i] = i;
primes.push_back(i);
}
for (size_t j = 0; j < primes.size() && primes[j] * i <= n && primes[j] <= f[i]; ++j) {
f[primes[j] * i] = primes[j];
}
}
}
bool is_prime(int x) {
assert(x <= n);
if (x <= 1) return false;
return f[x] == x;
}
vector<int> factorize_list(int x) {
assert(1 <= x && x <= n);
vector<int> res;
while (x != 1) {
res.push_back(f[x]);
x /= f[x];
}
return res;
}
vector<pair<int, int>> factorize(int x) {
assert(1 <= x && x <= n);
vector<int> factors = factorize_list(x);
vector<pair<int, int>> res;
if (factors.empty()) return res;
res.emplace_back(factors.front(), 0);
for (int p : factors) {
if (res.back().first == p) res.back().second++;
else res.emplace_back(p, 1);
}
return res;
}
};
int main() {
int n;
cin >> n;
sieve s(n);
vector<pair<int, int>> cnt(n + 1);
for (int x = 1; x <= n; ++x) {
auto f = s.factorize(x);
for (auto [p, k] : f) {
if (cnt[p].fi == k) cnt[p].se++;
else if (cnt[p].fi < k) cnt[p] = {k, 1};
}
}
int mx = 1;
mint ans = 1;
for (int p = 1; p <= n; ++p) {
if (cnt[p].fi != 0) {
ans *= mint(p).pow(cnt[p].fi);
if (cnt[p].se == 1) mx = p;
}
}
ans /= mx;
cout << ans.val() << '\n';
}