結果
| 問題 |
No.2039 Copy and Avoid
|
| コンテスト | |
| ユーザー |
 suisen
|
| 提出日時 | 2022-08-12 22:43:48 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 39 ms / 2,000 ms |
| コード長 | 26,519 bytes |
| コンパイル時間 | 4,124 ms |
| コンパイル使用メモリ | 371,824 KB |
| 最終ジャッジ日時 | 2025-01-30 21:31:13 |
|
ジャッジサーバーID （参考情報） |
judge3 / judge4 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 31 |
ソースコード
#include <bits/stdc++.h>
#ifdef _MSC_VER
# include <intrin.h>
#else
# include <x86intrin.h>
#endif
#include <limits>
#include <type_traits>
namespace suisen {
// ! utility
template <typename ...Types>
using constraints_t = std::enable_if_t<std::conjunction_v<Types...>, std::nullptr_t>;
template <bool cond_v, typename Then, typename OrElse>
constexpr decltype(auto) constexpr_if(Then&& then, OrElse&& or_else) {
if constexpr (cond_v) {
return std::forward<Then>(then);
} else {
return std::forward<OrElse>(or_else);
}
}
// ! function
template <typename ReturnType, typename Callable, typename ...Args>
using is_same_as_invoke_result = std::is_same<std::invoke_result_t<Callable, Args...>, ReturnType>;
template <typename F, typename T>
using is_uni_op = is_same_as_invoke_result<T, F, T>;
template <typename F, typename T>
using is_bin_op = is_same_as_invoke_result<T, F, T, T>;
template <typename Comparator, typename T>
using is_comparator = std::is_same<std::invoke_result_t<Comparator, T, T>, bool>;
// ! integral
template <typename T, typename = constraints_t<std::is_integral<T>>>
constexpr int bit_num = std::numeric_limits<std::make_unsigned_t<T>>::digits;
template <typename T, unsigned int n>
struct is_nbit { static constexpr bool value = bit_num<T> == n; };
template <typename T, unsigned int n>
static constexpr bool is_nbit_v = is_nbit<T, n>::value;
// ?
template <typename T>
struct safely_multipliable {};
template <>
struct safely_multipliable<int> { using type = long long; };
template <>
struct safely_multipliable<long long> { using type = __int128_t; };
template <>
struct safely_multipliable<unsigned int> { using type = unsigned long long; };
template <>
struct safely_multipliable<unsigned long int> { using type = __uint128_t; };
template <>
struct safely_multipliable<unsigned long long> { using type = __uint128_t; };
template <>
struct safely_multipliable<float> { using type = float; };
template <>
struct safely_multipliable<double> { using type = double; };
template <>
struct safely_multipliable<long double> { using type = long double; };
template <typename T>
using safely_multipliable_t = typename safely_multipliable<T>::type;
template <typename T, typename = void>
struct rec_value_type {
using type = T;
};
template <typename T>
struct rec_value_type<T, std::void_t<typename T::value_type>> {
using type = typename rec_value_type<typename T::value_type>::type;
};
template <typename T>
using rec_value_type_t = typename rec_value_type<T>::type;
} // namespace suisen
// ! type aliases
using i128 = __int128_t;
using u128 = __uint128_t;
template <typename T>
using pq_greater = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template <typename T, typename U>
using umap = std::unordered_map<T, U>;
// ! macros (capital: internal macro)
#define OVERLOAD2(_1,_2,name,...) name
#define OVERLOAD3(_1,_2,_3,name,...) name
#define OVERLOAD4(_1,_2,_3,_4,name,...) name
#define REP4(i,l,r,s) for(std::remove_reference_t<std::remove_const_t<decltype(r)>>i=(l);i<(r);i+=(s))
#define REP3(i,l,r) REP4(i,l,r,1)
#define REP2(i,n) REP3(i,0,n)
#define REPINF3(i,l,s) for(std::remove_reference_t<std::remove_const_t<decltype(l)>>i=(l);;i+=(s))
#define REPINF2(i,l) REPINF3(i,l,1)
#define REPINF1(i) REPINF2(i,0)
#define RREP4(i,l,r,s) for(std::remove_reference_t<std::remove_const_t<decltype(r)>>i=(l)+fld((r)-(l)-1,s)*(s);i>=(l);i-=(s))
#define RREP3(i,l,r) RREP4(i,l,r,1)
#define RREP2(i,n) RREP3(i,0,n)
#define rep(...) OVERLOAD4(__VA_ARGS__, REP4 , REP3 , REP2 )(__VA_ARGS__)
#define rrep(...) OVERLOAD4(__VA_ARGS__, RREP4 , RREP3 , RREP2 )(__VA_ARGS__)
#define repinf(...) OVERLOAD3(__VA_ARGS__, REPINF3, REPINF2, REPINF1)(__VA_ARGS__)
#define CAT_I(a, b) a##b
#define CAT(a, b) CAT_I(a, b)
#define UNIQVAR(tag) CAT(tag, __LINE__)
#define loop(n) for (std::remove_reference_t<std::remove_const_t<decltype(n)>> UNIQVAR(loop_variable) = n; UNIQVAR(loop_variable) --> 0;)
#define all(iterable) std::begin(iterable), std::end(iterable)
#define input(type, ...) type __VA_ARGS__; read(__VA_ARGS__)
#ifdef LOCAL
# define debug(...) debug_internal(#__VA_ARGS__, __VA_ARGS__)
template <class T, class... Args>
void debug_internal(const char* s, T&& first, Args&&... args) {
constexpr const char* prefix = "[\033[32mDEBUG\033[m] ";
constexpr const char* open_brakets = sizeof...(args) == 0 ? "" : "(";
constexpr const char* close_brakets = sizeof...(args) == 0 ? "" : ")";
std::cerr << prefix << open_brakets << s << close_brakets << ": " << open_brakets << std::forward<T>(first);
((std::cerr << ", " << std::forward<Args>(args)), ...);
std::cerr << close_brakets << "\n";
}
#else
# define debug(...) void(0)
#endif
// ! I/O utilities
// __int128_t
std::ostream& operator<<(std::ostream& dest, __int128_t value) {
std::ostream::sentry s(dest);
if (s) {
__uint128_t tmp = value < 0 ? -value : value;
char buffer[128];
char* d = std::end(buffer);
do {
--d;
*d = "0123456789"[tmp % 10];
tmp /= 10;
} while (tmp != 0);
if (value < 0) {
--d;
*d = '-';
}
int len = std::end(buffer) - d;
if (dest.rdbuf()->sputn(d, len) != len) {
dest.setstate(std::ios_base::badbit);
}
}
return dest;
}
// __uint128_t
std::ostream& operator<<(std::ostream& dest, __uint128_t value) {
std::ostream::sentry s(dest);
if (s) {
char buffer[128];
char* d = std::end(buffer);
do {
--d;
*d = "0123456789"[value % 10];
value /= 10;
} while (value != 0);
int len = std::end(buffer) - d;
if (dest.rdbuf()->sputn(d, len) != len) {
dest.setstate(std::ios_base::badbit);
}
}
return dest;
}
// pair
template <typename T, typename U>
std::ostream& operator<<(std::ostream& out, const std::pair<T, U>& a) {
return out << a.first << ' ' << a.second;
}
// tuple
template <unsigned int N = 0, typename ...Args>
std::ostream& operator<<(std::ostream& out, const std::tuple<Args...>& a) {
if constexpr (N >= std::tuple_size_v<std::tuple<Args...>>) {
return out;
} else {
out << std::get<N>(a);
if constexpr (N + 1 < std::tuple_size_v<std::tuple<Args...>>) {
out << ' ';
}
return operator<<<N + 1>(out, a);
}
}
// vector
template <typename T>
std::ostream& operator<<(std::ostream& out, const std::vector<T>& a) {
for (auto it = a.begin(); it != a.end();) {
out << *it;
if (++it != a.end()) out << ' ';
}
return out;
}
// array
template <typename T, size_t N>
std::ostream& operator<<(std::ostream& out, const std::array<T, N>& a) {
for (auto it = a.begin(); it != a.end();) {
out << *it;
if (++it != a.end()) out << ' ';
}
return out;
}
inline void print() { std::cout << '\n'; }
template <typename Head, typename... Tail>
inline void print(const Head& head, const Tail &...tails) {
std::cout << head;
if (sizeof...(tails)) std::cout << ' ';
print(tails...);
}
template <typename Iterable>
auto print_all(const Iterable& v, std::string sep = " ", std::string end = "\n") -> decltype(std::cout << *v.begin(), void()) {
for (auto it = v.begin(); it != v.end();) {
std::cout << *it;
if (++it != v.end()) std::cout << sep;
}
std::cout << end;
}
__int128_t parse_i128(std::string& s) {
__int128_t ret = 0;
for (int i = 0; i < int(s.size()); i++) if ('0' <= s[i] and s[i] <= '9') ret = 10 * ret + s[i] - '0';
if (s[0] == '-') ret = -ret;
return ret;
}
__uint128_t parse_u128(std::string& s) {
__uint128_t ret = 0;
for (int i = 0; i < int(s.size()); i++) if ('0' <= s[i] and s[i] <= '9') ret = 10 * ret + s[i] - '0';
return ret;
}
// __int128_t
std::istream& operator>>(std::istream& in, __int128_t& v) {
std::string s;
in >> s;
v = parse_i128(s);
return in;
}
// __uint128_t
std::istream& operator>>(std::istream& in, __uint128_t& v) {
std::string s;
in >> s;
v = parse_u128(s);
return in;
}
// pair
template <typename T, typename U>
std::istream& operator>>(std::istream& in, std::pair<T, U>& a) {
return in >> a.first >> a.second;
}
// tuple
template <unsigned int N = 0, typename ...Args>
std::istream& operator>>(std::istream& in, std::tuple<Args...>& a) {
if constexpr (N >= std::tuple_size_v<std::tuple<Args...>>) {
return in;
} else {
return operator>><N + 1>(in >> std::get<N>(a), a);
}
}
// vector
template <typename T>
std::istream& operator>>(std::istream& in, std::vector<T>& a) {
for (auto it = a.begin(); it != a.end(); ++it) in >> *it;
return in;
}
// array
template <typename T, size_t N>
std::istream& operator>>(std::istream& in, std::array<T, N>& a) {
for (auto it = a.begin(); it != a.end(); ++it) in >> *it;
return in;
}
template <typename ...Args>
void read(Args &...args) {
(std::cin >> ... >> args);
}
// ! integral utilities
// Returns pow(-1, n)
template <typename T>
constexpr inline int pow_m1(T n) {
return -(n & 1) | 1;
}
// Returns pow(-1, n)
template <>
constexpr inline int pow_m1<bool>(bool n) {
return -int(n) | 1;
}
// Returns floor(x / y)
template <typename T>
constexpr inline T fld(const T x, const T y) {
return (x ^ y) >= 0 ? x / y : (x - (y + pow_m1(y >= 0))) / y;
}
template <typename T>
constexpr inline T cld(const T x, const T y) {
return (x ^ y) <= 0 ? x / y : (x + (y + pow_m1(y >= 0))) / y;
}
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 16>> = nullptr>
__attribute__((target("popcnt"))) constexpr inline int popcount(const T x) { return _mm_popcnt_u32(x); }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 32>> = nullptr>
__attribute__((target("popcnt"))) constexpr inline int popcount(const T x) { return _mm_popcnt_u32(x); }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 64>> = nullptr>
__attribute__((target("popcnt"))) constexpr inline int popcount(const T x) { return _mm_popcnt_u64(x); }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 16>> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x) : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 32>> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x) : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 64>> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clzll(x) : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 16>> = nullptr>
constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x) : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 32>> = nullptr>
constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x) : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 64>> = nullptr>
constexpr inline int count_tz(const T x) { return x ? __builtin_ctzll(x) : suisen::bit_num<T>; }
template <typename T>
constexpr inline int floor_log2(const T x) { return suisen::bit_num<T> -1 - count_lz(x); }
template <typename T>
constexpr inline int ceil_log2(const T x) { return floor_log2(x) + ((x & -x) != x); }
template <typename T>
constexpr inline int kth_bit(const T x, const unsigned int k) { return (x >> k) & 1; }
template <typename T>
constexpr inline int parity(const T x) { return popcount(x) & 1; }
// ! container
template <typename T, typename Comparator, suisen::constraints_t<suisen::is_comparator<Comparator, T>> = nullptr>
auto priqueue_comp(const Comparator comparator) {
return std::priority_queue<T, std::vector<T>, Comparator>(comparator);
}
template <typename Iterable>
auto isize(const Iterable& iterable) -> decltype(int(iterable.size())) {
return iterable.size();
}
template <typename T, typename Gen, suisen::constraints_t<suisen::is_same_as_invoke_result<T, Gen, int>> = nullptr>
auto generate_vector(int n, Gen generator) {
std::vector<T> v(n);
for (int i = 0; i < n; ++i) v[i] = generator(i);
return v;
}
template <typename T>
auto generate_range_vector(T l, T r) {
return generate_vector(r - l, [l](int i) { return l + i; });
}
template <typename T>
auto generate_range_vector(T n) {
return generate_range_vector(0, n);
}
template <typename T>
void sort_unique_erase(std::vector<T>& a) {
std::sort(a.begin(), a.end());
a.erase(std::unique(a.begin(), a.end()), a.end());
}
template <typename InputIterator, typename BiConsumer>
auto foreach_adjacent_values(InputIterator first, InputIterator last, BiConsumer f) -> decltype(f(*first++, *last), void()) {
if (first != last) for (auto itr = first, itl = itr++; itr != last; itl = itr++) f(*itl, *itr);
}
template <typename Container, typename BiConsumer>
auto foreach_adjacent_values(Container c, BiConsumer f) -> decltype(c.begin(), c.end(), void()) {
foreach_adjacent_values(c.begin(), c.end(), f);
}
// ! other utilities
// x <- min(x, y). returns true iff `x` has chenged.
template <typename T>
inline bool chmin(T& x, const T& y) {
if (y >= x) return false;
x = y;
return true;
}
// x <- max(x, y). returns true iff `x` has chenged.
template <typename T>
inline bool chmax(T& x, const T& y) {
if (y <= x) return false;
x = y;
return true;
}
template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
std::string bin(T val, int bit_num = -1) {
std::string res;
if (bit_num >= 0) {
for (int bit = bit_num; bit-- > 0;) res += '0' + ((val >> bit) & 1);
} else {
for (; val; val >>= 1) res += '0' + (val & 1);
std::reverse(res.begin(), res.end());
}
return res;
}
template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
std::vector<T> digits_low_to_high(T val, T base = 10) {
std::vector<T> res;
for (; val; val /= base) res.push_back(val % base);
if (res.empty()) res.push_back(T{ 0 });
return res;
}
template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
std::vector<T> digits_high_to_low(T val, T base = 10) {
auto res = digits_low_to_high(val, base);
std::reverse(res.begin(), res.end());
return res;
}
template <typename T>
std::string join(const std::vector<T>& v, const std::string& sep, const std::string& end) {
std::ostringstream ss;
for (auto it = v.begin(); it != v.end();) {
ss << *it;
if (++it != v.end()) ss << sep;
}
ss << end;
return ss.str();
}
namespace suisen {}
using namespace suisen;
using namespace std;
struct io_setup {
io_setup(int precision = 20) {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
std::cout << std::fixed << std::setprecision(precision);
}
} io_setup_{};
// ! code from here
#include <algorithm>
#include <array>
#include <cassert>
#include <cmath>
#include <optional>
#include <tuple>
#include <vector>
namespace suisen {
// // Returns pow(-1, n)
// template <typename T>
// constexpr inline int pow_m1(T n) {
// return -(n & 1) | 1;
// }
// // Returns pow(-1, n)
// template <>
// constexpr inline int pow_m1<bool>(bool n) {
// return -int(n) | 1;
// }
// // Returns floor(x / y)
// template <typename T>
// constexpr inline T fld(const T x, const T y) {
// return (x ^ y) >= 0 ? x / y : (x - (y + pow_m1(y >= 0))) / y;
// }
// // Returns ceil(x / y)
// template <typename T>
// constexpr inline T cld(const T x, const T y) {
// return (x ^ y) <= 0 ? x / y : (x + (y + pow_m1(y >= 0))) / y;
// }
/**
* O(sqrt(n))
* Returns a vector of { prime, index }.
* It is guaranteed that `prime` is ascending.
*/
template <typename T>
std::vector<std::pair<T, int>> factorize(T n) {
static constexpr std::array primes{ 2, 3, 5, 7, 11, 13 };
static constexpr int next_prime = 17;
static constexpr int siz = std::array{ 1, 2, 8, 48, 480, 5760, 92160 } [primes.size() - 1] ;
static constexpr int period = [] {
int res = 1;
for (auto e : primes) res *= e;
return res;
}();
static constexpr struct S : public std::array<int, siz> {
constexpr S() {
for (int i = next_prime, j = 0; i < period + next_prime; i += 2) {
bool ok = true;
for (int p : primes) ok &= i % p > 0;
if (ok) (*this)[j++] = i - next_prime;
}
}
} s{};
assert(n > 0);
std::vector<std::pair<T, int>> res;
auto f = [&res, &n](int p) {
if (n % p) return;
int cnt = 0;
do n /= p, ++cnt; while (n % p == 0);
res.emplace_back(p, cnt);
};
for (int p : primes) f(p);
for (T b = next_prime; b * b <= n; b += period) {
for (int offset : s) f(b + offset);
}
if (n != 1) res.emplace_back(n, 1);
return res;
}
/**
* O(sigma(n))
* Returns a vector that contains all divisors of `n`.
* It is NOT guaranteed that the vector is sorted.
*/
template <typename T>
std::vector<T> divisors(const std::vector<std::pair<T, int>>& factorized) {
std::vector<T> res{ 1 };
for (auto [p, c] : factorized) {
for (int i = 0, sz = res.size(); i < sz; ++i) {
T d = res[i];
for (int j = 0; j < c; ++j) res.push_back(d *= p);
}
}
return res;
}
/**
* O(sqrt(n))
* Returns a vector that contains all divisors of `n`.
* It is NOT guaranteed that the vector is sorted.
*/
template <typename T, constraints_t<std::is_integral<T>> = nullptr>
std::vector<T> divisors(T n) {
return divisors(factorize(n));
}
template <typename T>
T totient(T n) {
for (const auto& [p, _] : factorize(n)) n /= p, n *= p - 1;
return n;
}
std::vector<int> totient_table(int n) {
std::vector<int> res(n + 1);
for (int i = 0; i <= n; ++i) res[i] = (i & 1) == 0 ? i >> 1 : i;
for (int p = 3; p * p <= n; p += 2) {
if (res[p] != p) continue;
for (int q = p; q <= n; q += p) res[q] /= p, res[q] *= p - 1;
}
return res;
}
// Returns { l, r } := min_max { x>0 | fld(n,x)=q }.
template <typename T, constraints_t<std::is_integral<T>> = nullptr>
std::optional<std::pair<T, T>> same_fld_denominators_positive(T n, T q, T max_val = std::numeric_limits<T>::max()) {
T l, r;
if (q >= 0) {
if (n < 0) return std::nullopt;
// cld(n + 1, q + 1) <= x <= fld(n, q)
l = (n + 1 + q) / (q + 1), r = q == 0 ? max_val : std::min(max_val, n / q);
} else {
if (n >= 0) return std::nullopt;
// cld(n, q) <= x <= fld(n + 1, q + 1)
l = (n + q + 1) / q, r = q == -1 ? max_val : std::min(max_val, (n + 1) / (q + 1));
}
if (l <= r) return std::make_pair(l, r);
else return std::nullopt;
}
// Returns { l, r } := min_max { x<0 | fld(n,x)=q }.
template <typename T, constraints_t<std::is_integral<T>> = nullptr>
std::optional<std::pair<T, T>> same_fld_denominators_negative(T n, T q, T min_val = std::numeric_limits<T>::min()) {
T l, r;
if (q >= 0) {
if (n > 0) return std::nullopt;
// cld(n, q) <= x <= fld(n - 1, q + 1)
l = q == 0 ? min_val : std::max(min_val, n / q), r = (n - 1 - q) / (q + 1);
} else {
if (n <= 0) return std::nullopt;
// cld(n - 1, q + 1) <= x <= fld(n, q)
l = q == -1 ? min_val : std::max(min_val, (n - 1) / (q + 1)), r = (n - q - 1) / q;
}
if (l <= r) return std::make_pair(l, r);
else return std::nullopt;
}
// Returns { l, r } := min_max { x>0 | cld(n,x)=q }.
template <typename T, constraints_t<std::is_integral<T>> = nullptr>
std::optional<std::pair<T, T>> same_cld_denominators_positive(T n, T q, T max_val = std::numeric_limits<T>::max()) {
T l, r;
if (q > 0) {
if (n <= 0) return std::nullopt;
l = (n + q - 1) / q, r = q == 1 ? max_val : std::min(max_val, (n - 1) / (q - 1));
} else {
if (n > 0) return std::nullopt;
l = (n - 1 + q) / (q - 1), r = q == 0 ? max_val : std::min(max_val, n / q);
}
if (l <= r) return std::make_pair(l, r);
else return std::nullopt;
}
// Returns { l, r } := min_max { x<0 | cld(n,x)=q }.
template <typename T, constraints_t<std::is_integral<T>> = nullptr>
std::optional<std::pair<T, T>> same_cld_denominators_negative(T n, T q, T min_val = std::numeric_limits<T>::min()) {
T l, r;
if (q > 0) {
if (n >= 0) return std::nullopt;
l = q == 1 ? min_val : std::max(min_val, (n + 1) / (q - 1)), r = (n - q + 1) / q;
} else {
if (n < 0) return std::nullopt;
l = q == 0 ? min_val : std::max(min_val, n / q), r = (n + 1 - q) / (q - 1);
}
if (l <= r) return std::make_pair(l, r);
else return std::nullopt;
}
/**
* O(sqrt(n)).
* Returns vector of { l : T, r : T, q : T } s.t. let S be { d | n / d = q }, l = min S and r = max S.
* It is guaranteed that `l`, `r` is ascending (i.e. `q` is descending).
*/
template <typename T, constraints_t<std::is_integral<T>> = nullptr>
auto enumerate_quotients(T n) {
assert(0 <= n);
std::vector<std::tuple<T, T, T>> res;
for (T l = 1, r = 1; l <= n; l = r + 1) {
T q = n / l;
res.emplace_back(l, r = n / q, q);
}
return res;
}
/**
* Template Parameter:
* - vector<T> or array<T, N>
*
* Time Complexity: O(|vs| * Sum_{v in vs} sqrt(v))
*
* Returns vector of { l : T, r : T, qs : Container } s.t. let S be { d | vs[i] / d = qs[i] (for all i) }, l = min S and r = max S
* It is guaranteed that `l`, `r` is ascending (i.e. for all `i`, `q[i]` is descending).
*/
template <typename Container>
std::vector<std::tuple<typename Container::value_type, typename Container::value_type, Container>>
enumerate_multiple_quotients(const Container& vs) {
using T = typename Container::value_type;
static_assert(std::is_integral_v<T>);
int n = vs.size();
T max_val = *std::max_element(vs.begin(), vs.end());
assert(*std::min_element(vs.begin(), vs.end()) >= 0);
std::vector<std::tuple<T, T, Container>> res;
for (T l = 1, r = 1; l <= max_val; l = r + 1) {
Container qs{};
if constexpr (std::is_same_v<Container, std::vector<T>>) qs.resize(n);
r = std::numeric_limits<T>::max();
for (int i = 0; i < n; ++i) {
qs[i] = vs[i] / l;
r = std::min(r, qs[i] == 0 ? std::numeric_limits<T>::max() : vs[i] / qs[i]);
}
res.emplace_back(l, r, std::move(qs));
}
return res;
}
template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
T floor_kth_root(T x, int k) {
if (k == 1 or x == 0 or x == 1) return x;
if (k >= 64) return 1;
if (k == 2) return sqrtl(x);
// if (k == 3) return cbrtl(x);
T res = powl(x, nextafterl(1 / (long double) k, 0));
while (powl(res + 1, k) <= x) ++res;
return res;
}
} // namespace suisen
#include <queue>
namespace suisen {
template<typename Cost>
class dijkstra {
public:
template <typename Transition>
dijkstra(unsigned int n, Transition transition, unsigned int src) : _src(src) {
_par.resize(n);
_dist.assign(n, UNREACHABLE);
_dist[src] = 0;
using state = std::pair<Cost, unsigned int>;
std::priority_queue<state, std::vector<state>, std::greater<state>> pq;
pq.emplace(0, src);
auto g = [&](unsigned int u) {
return [&, u](unsigned int v, Cost new_cost) {
if (new_cost < _dist[v]) pq.emplace(_dist[v] = new_cost, v), _par[v] = u;
};
};
while (pq.size()) {
auto [du, u] = pq.top(); pq.pop();
if (du == _dist[u]) transition(u, du, g(u));
}
}
dijkstra(const std::vector<std::vector<std::pair<int, Cost>>> &g, unsigned int src) :
dijkstra(g.size(), [&](int u, Cost du, auto f) { for (auto [v, c] : g[u]) f(v, du + c); }, src) {}
std::vector<unsigned int> path_to(unsigned int t) const {
assert(is_reachale(t));
std::vector<unsigned int> path = {t};
while (t != _src) path.push_back(t = _par[t]);
std::reverse(path.begin(), path.end());
return path;
}
Cost operator[](unsigned int t) const { return _dist[t]; }
bool is_reachale (unsigned int t) const { return _dist[t] != UNREACHABLE; }
bool is_unreachable(unsigned int t) const { return _dist[t] == UNREACHABLE; }
private:
const Cost UNREACHABLE = std::numeric_limits<Cost>::max();
const unsigned int _src;
std::vector<Cost> _dist;
std::vector<unsigned int> _par;
};
} // namespace suisen
int main() {
input(int, n, m);
input(long long, a, b);
vector<int> c(m);
read(c);
auto div = divisors(n);
sort(all(div));
const int k = div.size();
vector<vector<pair<int, long long>>> g(k);
rep(i, k) {
int ng = numeric_limits<int>::max();
for (int v : c) if (v % div[i] == 0) {
chmin(ng, v);
}
rep(j, i + 1, k) {
if (div[j] >= ng) break;
if (div[j] % div[i]) continue;
long long t = div[j] / div[i];
g[i].emplace_back(j, (t - 1) * a + b);
}
}
dijkstra<long long> dij(g, 0);
if (dij.is_unreachable(k - 1)) {
print(-1);
} else {
print(dij[k - 1] - b);
}
return 0;
}