Language: C++

#include <algorithm>
#include <bitset>
#include <cmath>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <numeric>
#include <optional>
#include <set>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// Utility
using std::enable_if_t, std::is_same_v, std::is_array_v, std::is_invocable_v,
    std::declval;
using std::get, std::make_pair, std::make_tuple, std::apply;
using std::iterator_traits, std::random_access_iterator_tag;
using std::make_optional, std::nullopt;
using std::stoll, std::stold, std::operator""s;

// Types
using std::bitset;
using std::deque, std::list, std::multiset, std::unordered_multimap,
    std::unordered_multiset;
using std::nullptr_t, std::pair, std::tuple;
using ll = __int128;
using lf = long double;
using str = std::string;
template <class T> using u_set = std::unordered_set<T>;
template <class T> using vec = std::vector<T>;
using vecl = vec<ll>;
using vecf = vec<lf>;
using vecs = vec<str>;
template <class T> using opt = std::optional<T>;
template <class K, class V> using u_map = std::unordered_map<K, V>;
template <class V> using graph = u_map<V, u_set<V>>;
template <typename _Signature> using fun = std::function<_Signature>;

// Algorithms
using std::accumulate, std::partial_sum, std::inclusive_scan,
    std::exclusive_scan;
using std::all_of, std::any_of, std::none_of, std::count_if, std::count,
    std::find_if, std::for_each, std::max_element, std::min_element,
    std::remove_if, std::replace_if, std::copy, std::copy_if, std::reverse,
    std::transform, std::unique, std::sort, std::next_permutation, std::swap;
using std::back_inserter, std::inserter;
using std::lower_bound, std::upper_bound;
using std::max, std::min, std::clamp, std::lcm, std::gcd;
using std::set_intersection, std::set_difference, std::set_union,
    std::set_symmetric_difference;

namespace utils {
str to_string(__int128 const &x) { return std::to_string((long long)x); }
} // namespace utils
using utils::to_string;

namespace io {
// Input
using IS = std::istream;
IS &in(IS &);
IS &in(IS &i) { return i; }
template <class T, class... Ts> IS &in(IS &i, T &a, Ts &... as) {
  return in(i >> a, as...);
}
IS &operator>>(IS &i, __int128 &x) {
  long long int xx;
  i >> xx;
  x = xx;
  return i;
}
template <class V> IS &operator>>(IS &i, vec<V> &a) {
  for (auto &ai : a)
    i >> ai;
  return i;
}
template <class F, class S> IS &operator>>(IS &i, pair<F, S> &p) {
  return in(i, p.first, p.second);
}
template <class... Ts> IS &operator>>(IS &i, tuple<Ts...> &t) {
  return apply([&](auto &... ts) -> IS & { return in(i, ts...); }, t);
}
// Output
using OS = std::ostream;

template <class... Ts> OS &out_join(OS &o, str const &, Ts const &...);
OS &out_join(OS &o, str const &) { return o; }
template <class... Ts> OS &out_join(OS &o, str const &sep, Ts const &... as) {
  auto f = [&](auto const &head, auto const &... tails) -> OS & {
    using swallow = std::initializer_list<int>;
    o << head;
    (void)swallow{(void(o << sep << tails), 0)...};
    return o;
  };
  return f(as...);
}
OS &operator<<(OS &o, __int128 const &x) { return o << (long long int)x; }
template <class F, class S> OS &operator<<(OS &o, pair<F, S> const &p) {
  return o << p.first << ":" << p.second;
}
template <class T> OS &operator<<(OS &o, opt<T> const &opt) {
  return opt.has_value() ? (o << "Some(" << opt.value() << ")") : (o << "None");
}
template <class... Ts> OS &operator<<(OS &o, tuple<Ts...> const &t) {
  auto f = [&](auto const &... ts) -> OS & {
    return out_join(o << "(", ",", ts...);
  };
  return apply(f, t) << ")";
}
template <class T> struct Joiner {
  str const pre;
  str const post;
  str const sep;
  vec<T> const container;
  template <class Itr>
  Joiner(Itr begin, Itr end, str const &sep, str const &pre, str const &post)
      : pre(pre), post(post), sep(sep), container(begin, end) {}
};
template <class T> OS &operator<<(OS &o, Joiner<T> const &joiner) {
  auto itr = joiner.container.begin();
  auto end = joiner.container.end();
  o << joiner.pre;
  if (itr != end)
    o << *(itr++);
  while (itr != end)
    o << joiner.sep << *(itr++);
  return o << joiner.post;
}
template <class Itr>
auto join(Itr b, Itr e, str const &sep = ""s, str const &pre = ""s,
          str const &post = ""s) {
  using T = typename iterator_traits<Itr>::value_type;
  return Joiner<T>(b, e, sep, pre, post);
}
template <class C, enable_if_t<!is_same_v<C, str> && !is_array_v<C> &&
                                   !std::is_pointer_v<C>,
                               nullptr_t> = nullptr>
OS &operator<<(OS &o, C const &a) {
  return o << join(a.begin(), a.end(), ",", "[", "]");
}
} // namespace io
using std::cerr, std::cin, std::cout;
auto init_io = []() {
  std::ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  cout << std::fixed << std::setprecision(15);
};
template <class... Ts> void input(Ts &... a) { io::in(cin, a...); };
template <class... Ts> void print(Ts const &... a) {
  io::out_join(cout, " "s, a...) << "\n";
};
#ifdef JUMPAKU_DEBUG
auto dump = [](auto const &... a) { io::out_join(cerr, " "s, a...) << "\n"; };
#else
auto dump = [](auto const &...) {};
#endif
using io::join;

// Hash
namespace hashcode {
template <class... Ts> ll hash_args(ll h, Ts const &... ts) {
  using swallow = std::initializer_list<int>;
  auto f = [](auto const &a) {
    using T = std::remove_const_t<std::remove_reference_t<decltype(a)>>;
    return std::hash<T>{}(a);
  };
  (void)swallow{(void(h = ((h << 19) - h) ^ f(ts)), 0)...};
  return h ^ (h >> 32);
}
} // namespace hashcode
namespace std {
#ifndef __clang__
template <> struct hash<__int128> {
  size_t operator()(__int128 const &t) const {
    return hash<long long>{}((long long)((t >> 64) ^ t) & 0xffffffff);
  }
};
#endif
template <class... Ts> struct hash<tuple<Ts...>> {
  size_t operator()(tuple<Ts...> const &t) const {
    auto f = [&](auto &... ts) { return hashcode::hash_args(17, ts...); };
    return apply(f, t);
  }
};
template <class T> struct hash<u_set<T>> {
  size_t operator()(u_set<T> const &t) const {
    auto hasher = std::hash<T>{};
    return accumulate(
        t.begin(), t.end(), (size_t)0,
        [&](auto acc, auto const &ti) { return acc + hasher(ti); });
  }
};
} // namespace std

// Range
namespace ranges {
template <class T, class Itr> struct iterator_base {
  using difference_type = ll;
  using value_type = T;
  using pointer = T *;
  using reference = T &;
  using iterator_category = random_access_iterator_tag;
  ll i;
  iterator_base(ll const &i) : i(i) {}
  bool operator==(Itr const &itr) const { return i == itr.i; }
  bool operator!=(Itr const &itr) const { return i != itr.i; }
  ll operator-(Itr const &itr) const { return i - itr.i; }
  Itr operator++(int) { return with(i++); }
  Itr operator--(int) { return with(i--); }
  Itr operator+(ll const &n) const { return with(i + n); }
  Itr operator-(ll const &n) const { return with(i - n); }
  Itr &operator+=(ll const &n) {
    i += n;
    return self();
  }
  Itr &operator-=(ll const &n) { return self() += (-n); }
  Itr &operator++() { return self() += 1; }
  Itr &operator--() { return self() -= 1; }

protected:
  virtual Itr with(ll i) const = 0;
  virtual Itr &self() = 0;
};
template <class T> struct seq_base {
  ll const b;
  ll const e;
  seq_base(ll b, ll e) : b(b), e(max(b, e)) {}
  ll size() const { return e - b; }
  bool empty() const { return size() == 0; }
};
template <class T> struct seq : seq_base<T> {
  struct iterator : iterator_base<T, iterator> {
    seq<T> const &s;
    iterator(seq<T> const &s, ll const &i)
        : iterator_base<T, iterator>(i), s(s) {}
    iterator with(ll i) const override { return iterator(s, i); }
    iterator &self() override { return *this; }
    T operator*() const { return s[this->i]; }
    iterator &operator=(iterator const &itr) {
      this->i = itr.i;
      return *this;
    }
  };
  fun<T(ll)> const f;
  seq(ll b, ll e, fun<T(ll)> const &f) : seq_base<T>(b, e), f(f) {}
  iterator begin() const { return iterator(*this, 0); }
  iterator end() const { return iterator(*this, this->size()); }
  T operator[](ll i) const { return f(i + this->b); }
};
template <class F>
seq(ll b, ll e, F const &f)->seq<typename std::invoke_result<F, ll>::type>;

struct range : seq_base<ll> {
  struct iterator : iterator_base<ll, iterator> {
    iterator(ll const &i) : iterator_base<ll, iterator>(i) {}
    iterator with(ll i) const override { return iterator(i); }
    iterator &self() override { return *this; }
    ll operator*() const { return i; }
  };
  range(ll n) : range(0, n) {}
  range(ll b, ll e) : seq_base<ll>(b, e) {}
  iterator begin() const { return iterator(b); }
  iterator end() const { return iterator(e); }
  bool has(ll x) const { return b <= x && x < e; }
  ll operator[](ll i) const { return i + b; }
};
} // namespace ranges
using range = ranges::range;
range::iterator end(ll i) { return range::iterator(i); }
range::iterator begin(ll i = 0) { return range::iterator(i); }
template <class F> auto seq(ll n, F const &f) { return ranges::seq(0LL, n, f); }

bool odd(ll n) { return n & 1; }
bool even(ll n) { return !odd(n); }

bool imply(bool p, bool q) { return !p || q; }
bool iff(bool p, bool q) { return p == q; }

constexpr lf PI = 3.141592653589793238462643383279502884L;
constexpr ll MOD = 1e9 + 7;

void solve();
int main() {
  init_io();
  ll t = 1;
  /**/ input(t); /**/
  while (t--)
    solve();
  cout.flush();
}

ll f(ll const n, ll const A, ll const B, ll const C, ll const D,
     u_map<ll, ll> &dp) {
  if (n == 0)
    return 0;
  if (n == 1)
    return D;
  if (n == 2) {
    return min(D + f(n - 1, A, B, C, D, dp), A + f(n / 2, A, B, C, D, dp));
  }
  if (n < 0)
    return 1e18;
  if (dp.find(n) != dp.end())
    return dp.at(n);
  ll r2 = n % 2;
  ll r3 = n % 3;
  ll r5 = n % 5;
  return dp[n] = min({
             D * n,
             r2 * D + A + f(n / 2, A, B, C, D, dp),
             (2 - r2) * D + A + f((n + 2) / 2, A, B, C, D, dp),
             r3 * D + B + f(n / 3, A, B, C, D, dp),
             (3 - r3) * D + B + f((n + 3) / 3, A, B, C, D, dp),
             r5 * D + C + f(n / 5, A, B, C, D, dp),
             (5 - r5) * D + C + f((n + 5) / 5, A, B, C, D, dp),
         });
}

void solve() {
  ll N, A, B, C, D;
  input(N, A, B, C, D);
  u_map<ll, ll> dp;
  print(f(N, A, B, C, D, dp));
}


Compiler output:
a.cc:182:20: error: redefinition of 'struct std::hash<__int128>'
  182 | template <> struct hash<__int128> {
      |                    ^~~~~~~~~~~~~~
In file included from /usr/include/c++/14/string_view:50,
                 from /usr/include/c++/14/bits/basic_string.h:47,
                 from /usr/include/c++/14/string:54,
                 from /usr/include/c++/14/bitset:52,
                 from a.cc:2:
/usr/include/c++/14/bits/functional_hash.h:176:3: note: previous definition of 'struct std::hash<__int128>'
  176 |   _Cxx_hashtable_define_trivial_hash(__GLIBCXX_TYPE_INT_N_0)
      |   ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
a.cc: In instantiation of 'io::IS& io::in(IS&, T&, Ts& ...) [with T = __int128; Ts = {}; IS = std::basic_istream<char>]':
a.cc:157:54:   required from 'void input(Ts& ...) [with Ts = {__int128}]'
  157 | template <class... Ts> void input(Ts &... a) { io::in(cin, a...); };
      |                                                ~~~~~~^~~~~~~~~~~
a.cc:295:13:   required from here
  295 |   /**/ input(t); /**/
      |        ~~~~~^~~
a.cc:72:15: error: no match for 'operator>>' (operand types are 'io::IS' {aka 'std::basic_istream<char>'} and '__int128')
   72 |   return in(i >> a, as...);
      |             ~~^~~~
In file included from /usr/include/c++/14/sstream:40,
                 from /usr/include/c++/14/bits/quoted_string.h:38,
                 from /usr/include/c++/14/iomanip:50,
                 from a.cc:6:
/usr/include/c++/14/istream:170:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(bool&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  170 |       operator>>(bool& __n)
      |       ^~~~~~~~
/usr/include/c++/14/istream:170:7: note:   conversion of argument 1 would be ill-formed:
/usr/include/c++/14/istream:170:7: error: cannot bind non-const lvalue reference of type 'bool&' to a value of type '__int128'
/usr/include/c++/14/istream:174:7: note: candidate: 'std::basic_istream<_CharT, _Traits>& std::basic_istream<_CharT, _Traits>::operator>>(short int&) [with _CharT = char; _Traits = std::char_traits<char>]' (near match)
  174 |       operator>>(short& __n);
      |       ^~~~~~~~
/usr/include/c++/14/istream:174:7: note:   conversion of argument 1 would be ill-formed:
/usr/include/c++/14/istream:174:7: error: cannot bind non-const lvalue reference of type 'short int&' to a value of type '__int128'
/usr/include/c++/14/istream:177:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(short unsigned int&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  177 |       operator>>(unsigned short& __n)
      |       ^~~~~~~~
/usr/include/c++/14/istream:177:7: note:   conversion of argument 1 would be ill-formed:
/usr/include/c++/14/istream:177:7: error: cannot bind non-const lvalue reference of type 'short unsigned int&' to a value of type '__int128'
/usr/include/c++/14/istream:181:7: note: candidate: 'std::basic_istream<_CharT, _Traits>& std::basic_istream<_CharT, _Traits>::operator>>(int&) [with _CharT = char; _Traits = std::char_traits<char>]' (near match)
  181 |       operator>>(int& __n);
      |       ^~~~~~~~
/usr/include/c++/14/istream:181:7: note:   conversion of argument 1 would be ill-formed:
/usr/include/c++/14/istream:181:7: error: cannot bind non-const lvalue reference of type 'int&' to a value of type '__int128'
/usr/include/c++/14/istream:184:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(unsigned int&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  184 |       operator>>(unsigned int& __n)
      |       ^~~~~~~~
/usr/include/c++/14/istream:184:7: note:   conversion of argument 1 would be ill-formed:
/usr/include/c++/14/istream:184:7: error: cannot bind non-const lvalue reference of type 'unsigned int&' to a value of type '__int128'
/usr/include/c++/14/istream:188:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(long int&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  188 |       operator>>(long& __n)
      |       ^~~~~~~~
/usr/include/c++/14/istream:188:7: note:   conversion of argument 1 would be ill-formed:
/usr/include/c++/14/istream:188:7: error: cannot bind non-const lvalue reference of type 'long int&' to a value of type '__int128'
/usr/include/c++/14/istream:192:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(long unsigned int&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  192 |       operator>>(unsigned long& __n)
      |       ^~~~~~~~
/usr/include/c++/14/istream:192:7: note:   conversion of argument 1 would be ill-formed:
/usr/include/c++/14/istream:192:7: error: cannot bind non-const lvalue reference of type 'long unsigned int&' to a value of type '__int128'
/usr/include/c++/14/istream:199:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(long long int&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  199 |       operator>>(long long& __n)
      |       ^~~~~~~~
/usr/include/c++/14/istream:199:7: note:   conversion of argument 1 would be ill-formed:
/usr/include/c++/14/istream:199:7: error: cannot bind non-const lvalue reference of type 'long long int&' to a value of type '__int128'
/usr/include/c++/14/istream:203:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(long long unsigned int&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  203 |       operator>>(unsigned long long& __n)
      |       ^~~~~~~~
/usr/include/c++/14/istream:203:7: note:   conversion of argument 1 would be ill-formed:
/usr/include/c++/14/istream:203:7: error: cannot bind non-const lvalue reference of type 'long long unsigned int&' to a value of type '__int128'
/usr/include/c++/14/istream:219:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(float&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  219 |       operator>>(float& __f)
      |       ^~~~~~~~
/usr/include/c++/14/istream:219:7: note:   conversion of argument 1 would be ill-formed:
/usr/include/c++/14/istream:219:7: error: cannot bind non-const lvalue reference of type 'float&' to a value of type '__int128'
/usr/include/c++/14/istream:223:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(double&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  223 |       operator>>(double& __f)
      |       ^~~~~~~~
/usr/include/c++/14/istream:223:7: note:   conversion of argument 1 would be ill-formed:
/usr/include/c++/14/istream:223:7: error: cannot bind non-const lvalue reference of type 'double&' to a value of type '__int128'
/usr/include/c++/14/istream:227:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(long double&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  227 |       operator>>(long double& __f)
      |       ^~~~~~~~
/usr/include/c++/14/istream:227:7: note:   conversion of argument 1 would be ill-formed:
/usr/include/c++/14/istream:227:7: error: cannot bind non-const lvalue reference of type 'long double&' to a value of type '__int128'
/usr/include/c++/14/istream:328:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(void*&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  328 |       operator>>(void*& __p)
      |       ^~~~~~~~
/usr/include/c++/14/istream:328:7: note:   conversion of argument 1 would be ill-formed:
/usr/include/c++/14/istream:328:7: error: invalid conversion from '__int128' to 'void*' [-fpermissive]
  328 |       operator>>(void*& __p)
      |       ^~~~~~~~
      |       |
      |       __int128
/usr/include/c++/14/istream:328:7: error: cannot bind rvalue '(void*)((long int)a)' to 'void*&'
/usr/include/c++/14/istream:122:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(__istream_type& (*)(__istream_type&)) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  122 |       operator>>(__istream_type& (*__pf)(__istream_type&))
      |       ^~~~~~~~
/usr/include/c++/14/istream:122:7: note:   conversion of argument 1 would be ill-formed:
/usr/include/c++/14/istream:122:7: error: invalid conversion from '__int128' to 'std::basic_istream<char>::__istream_type& (*)(std::basic_istream<char>::__istream_type&)' {aka 'std::basic_istream<char>& (*)(std::basic_istream<char>&)'} [-fpermissive]
  122 |       operator>>(__istream_type& (*__pf)(__istream_type&))
      |       ^~~~~~~~
      |       |
      |       __int128
/usr/include/c++/14/istream:126:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(__ios_type& (*)(__ios_type&)) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>; __ios_type = std::basic_ios<char>]' (near match)
  126 |       operator>>(__ios_type& (*__pf)(__ios_type&))
      |       ^~~~~~~~
/usr/include/c++/14/istream:126:7: note:   conversion of argument 1 would be ill-formed:
/usr/include/c++/14/is