Language: C++

#include <bits/stdc++.h>
using namespace std;

namespace {
    #define DUMPOUT cerr
    #ifndef DEBUG_
    #define dump(...)
    #else
    #define dump(...)                                                                       \
        DUMPOUT << "  ";                                                                    \
        DUMPOUT << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << endl; \
        DUMPOUT << "    ";                                                                  \
        dump_func(__VA_ARGS__)
    #endif
    void dump_func()
    {
        DUMPOUT << endl;
    }
    template <class Head, class... Tail>
    void dump_func(Head &&head, Tail &&... tail)
    {
        DUMPOUT << head;
        if (sizeof...(Tail) == 0)
        {
            DUMPOUT << " ";
        }
        else
        {
            DUMPOUT << ", ";
        }
        dump_func(std::move(tail)...);
    }
    template <class T>
    ostream &operator<<(ostream &os, const vector<T> &v)
    {
        for (auto i = begin(v); i != end(v); ++i)
            os << *i << (i == end(v) - 1 ? "" : " ");
        return os;
    }
    template <class T>
    void out2Dvector(vector<T> v)
    {
        for (const auto &vv : v)
            cout << vv << endl;
    }
    template <class T>
    istream &operator>>(istream &is, vector<T> &v)
    {
        for (auto i = begin(v); i != end(v); ++i)
            is >> *i;
        return is;
    }
    template <typename T, typename U>
    ostream &operator<<(ostream &os, pair<T, U> &pair_var)
    {
        os << "(" << pair_var.first << ", " << pair_var.second << ")";
        return os;
    }
    template <typename T, typename U>
    ostream &operator<<(ostream &os, map<T, U> &map_var)
    {
        os << "{";
        for (auto itr = map_var.begin(); itr != map_var.end(); itr++)
        {
            os << "(" << itr->first << ", " << itr->second << ")";
            itr++;
            if (itr != map_var.end())
                os << ", ";
            itr--;
        }
        os << "}";
        return os;
    }
    template <typename T>
    ostream &operator<<(ostream &os, set<T> &set_var)
    {
        os << "{";
        for (auto itr = set_var.begin(); itr != set_var.end(); itr++)
        {
            os << *itr;
            ++itr;
            if (itr != set_var.end())
                os << ", ";
            itr--;
        }
        os << "}";
        return os;
    }
} // namespace

namespace {
    using ull = unsigned long long;
    using ll = long long;
    #define endl "\n"

    #define REP(i, n) for (ll i = 0; i < n; i++)
    #define REPR(i, n) for (ll i = n; i >= 0; i--)
    #define FOR(i, m, n) for (ll i = m; i < n; i++)
    #define even(x) (x) % 2 == 0
    #define odd(x) (x) % 2 != 0
    #define all(x) (x).begin(), (x).end()
    #define rall(x) (x).rbegin(), (x).rend()
    #define pcnt __builtin_popcount
    #define buli(x) __builtin_popcountll(x)
    #define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end());
    #define inp(t, x) \
        t x;          \
        cin >> x;
    #define ithBit(n, i) ((n) >> (i)&1)
    #define INIT()               \
        cin.tie(0);              \
        ios::sync_with_stdio(0); \
        cout << fixed << setprecision(20)

    // these functions return the position of result of Binary Search.
    #define LB(s, t, x) (int)(lower_bound(s, t, x) - s)
    #define UB(s, t, x) (int)(upper_bound(s, t, x) - s)

    #define M_PI 3.14159265358979323846
    ll qp(ll a, ll b, int mo)
    {
        ll ans = 1;
        do
        {
            if (b & 1)
                ans = 1ll * ans * a % mo;
            a = 1ll * a * a % mo;
        } while (b >>= 1);
        return ans;
    }
    ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
    ll lcm(ll a, ll b)
    {
        ll temp = gcd(a, b);
        return temp ? (a / temp * b) : 0;
    }
    int mDays[] = {31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
    int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
    int dx8[] = {1, -1, 0, 0, 1, 1, -1, -1}, dy8[] = {0, 0, -1, 1, -1, 1, -1, 1};

    template <typename F>
    class
    #if defined(__has_cpp_attribute) && __has_cpp_attribute(nodiscard)
        [[nodiscard]]
    #elif defined(__GNUC__) && __GNUC_PREREQ(3, 4)
        __attribute__((warn_unused_result))
    #endif // defined(__has_cpp_attribute) && __has_cpp_attribute(nodiscard)
        FixPoint : F {
            public :
                explicit constexpr FixPoint(F &&f) noexcept : F(std::forward<F>(f)) {}

            template <typename... Args>
            constexpr decltype(auto)
            operator()(Args &&... args) const {
                return F::operator()(*this, std::forward<Args>(args)...);
    } // namespace
    }
    ; // class FixPoint
    template <typename F>
    static inline constexpr decltype(auto)
    makeFixPoint(F &&f) noexcept
    {
        return FixPoint<F>{std::forward<F>(f)};
    }

    template <typename T>
    vector<T> make_v(size_t a) { return vector<T>(a); }
    template <typename T, typename... Ts>
    auto make_v(size_t a, size_t b, Ts... ts) { return vector<decltype(make_v<T>(b, ts...))>(a, make_v<T>(b, ts...)); }
    template <typename T, typename U, typename... V>
    typename enable_if<is_same<T, U>::value != 0>::type
    fill_v(U &u, const V... v) { u = U(v...); }
    template <typename T, typename U, typename... V>
    typename enable_if<is_same<T, U>::value == 0>::type
    fill_v(U &u, const V... v)
    {
        for (auto &e : u)
            fill_v<T>(e, v...);
    }

    template <class T>
    bool chmax(T &a, const T &b)
    {
        if (a < b)
        {
            a = b;
            return 1;
        }
        return 0;
    }
    template <class T>
    bool chmin(T &a, const T &b)
    {
        if (b < a)
        {
            a = b;
            return 1;
        }
        return 0;
    }

    inline bool rangeCheck2D(int nx, int ny, int Width, int Height) { return nx >= 0 and nx < Width and ny >= 0 and ny < Height; }

    int i_query(int a, int b)
    {
        cout << "? " << a << " " << b << endl;
        fflush(stdout);
        ll ret;
        cin >> ret;
        return ret;
    }

    void i_answer(vector<ll> ans)
    {
        cout << "! " << ans << endl;
        fflush(stdout);
    }
} // namespace

/*
    tuple binding
    auto [x, y] = make_tuple(0, 0);
    for pair
    auto [a, b] = pair<int, int>({v1, v2});

    bitset<N> bs(ini_val); // N must be constant
    bs.reset(); // reset all
*/


using ld = long double;

int main(void)
{
    INIT(); // comment out for Interective Problem

    inp(ll, N);
    inp(ll, K);
    deque<int> dq(N); REP(i, N) cin >> dq[i];

    map<deque<int>, int> dp;

    auto rec = makeFixPoint([&](auto rec, deque<int> &dq, int sum, multiset<int> &h) -> int {
        if (dp.count(dq))
            return dp[dq];
        int ret = 0;
        int v = *dq.begin();
        dq.pop_front();
        h.insert(v);
        chmax(ret, rec(dq, sum + v, h));
        dq.push_front(v);
        h.erase(h.find(v));
        
        v = *dq.back();
        dq.pop_back();
        h.insert(v);
        chmax(ret, rec(dq, sum + v, h));
        dq.push_back(v);
        h.erase(h.find(v));

        int m = *h.begin();
        dq.push_front();
        h.erase(h.find(m));
        chmax(ret, rec(dq, sum - m, h));
        dq.pop_front();

        dq.push_back();
        chmax(ret, rec(dq, sum - m, h));
        dq.pop_front();

        return dp[dq] = ret;
    });

    cout << rec(dq, 0, multiset<int>()) << endl;

    return 0;
}
//*/


Compiler output:
a.cc: In lambda function:
a.cc:254:13: error: invalid type argument of unary '*' (have '__gnu_cxx::__alloc_traits<std::allocator<int>, int>::value_type' {aka 'int'})
  254 |         v = *dq.back();
      |             ^~~~~~~~~~
a.cc:262:22: error: no matching function for call to 'std::deque<int>::push_front()'
  262 |         dq.push_front();
      |         ~~~~~~~~~~~~~^~
In file included from /usr/include/c++/14/deque:66,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:139,
                 from a.cc:1:
/usr/include/c++/14/bits/stl_deque.h:1501:7: note: candidate: 'void std::deque<_Tp, _Alloc>::push_front(const value_type&) [with _Tp = int; _Alloc = std::allocator<int>; value_type = int]'
 1501 |       push_front(const value_type& __x)
      |       ^~~~~~~~~~
/usr/include/c++/14/bits/stl_deque.h:1501:7: note:   candidate expects 1 argument, 0 provided
/usr/include/c++/14/bits/stl_deque.h:1516:7: note: candidate: 'void std::deque<_Tp, _Alloc>::push_front(value_type&&) [with _Tp = int; _Alloc = std::allocator<int>; value_type = int]'
 1516 |       push_front(value_type&& __x)
      |       ^~~~~~~~~~
/usr/include/c++/14/bits/stl_deque.h:1516:7: note:   candidate expects 1 argument, 0 provided
a.cc:267:21: error: no matching function for call to 'std::deque<int>::push_back()'
  267 |         dq.push_back();
      |         ~~~~~~~~~~~~^~
/usr/include/c++/14/bits/stl_deque.h:1538:7: note: candidate: 'void std::deque<_Tp, _Alloc>::push_back(const value_type&) [with _Tp = int; _Alloc = std::allocator<int>; value_type = int]'
 1538 |       push_back(const value_type& __x)
      |       ^~~~~~~~~
/usr/include/c++/14/bits/stl_deque.h:1538:7: note:   candidate expects 1 argument, 0 provided
/usr/include/c++/14/bits/stl_deque.h:1553:7: note: candidate: 'void std::deque<_Tp, _Alloc>::push_back(value_type&&) [with _Tp = int; _Alloc = std::allocator<int>; value_type = int]'
 1553 |       push_back(value_type&& __x)
      |       ^~~~~~~~~
/usr/include/c++/14/bits/stl_deque.h:1553:7: note:   candidate expects 1 argument, 0 provided
a.cc: In instantiation of 'constexpr decltype(auto) {anonymous}::FixPoint<F>::operator()(Args&& ...) const [with Args = {std::deque<int, std::allocator<int> >&, int, std::multiset<int, std::less<int>, std::allocator<int> >}; F = main()::<lambda(auto:28, std::deque<int>&, int, std::multiset<int>&)>]':
a.cc:274:16:   required from here
  274 |     cout << rec(dq, 0, multiset<int>()) << endl;
      |             ~~~^~~~~~~~~~~~~~~~~~~~~~~~
a.cc:155:37: error: no matching function for call to '{anonymous}::FixPoint<main()::<lambda(auto:28, std::deque<int>&, int, std::multiset<int>&)> >::operator()(const {anonymous}::FixPoint<main()::<lambda(auto:28, std::deque<int>&, int, std::multiset<int>&)> >&, std::deque<int>&, int, std::multiset<int>) const'
  155 |                 return F::operator()(*this, std::forward<Args>(args)...);
      |                        ~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
a.cc:243:29: note: candidate: 'template<class auto:28> main()::<lambda(auto:28, std::deque<int>&, int, std::multiset<int>&)>'
  243 |     auto rec = makeFixPoint([&](auto rec, deque<int> &dq, int sum, multiset<int> &h) -> int {
      |                             ^
a.cc:243:29: note:   template argument deduction/substitution failed:
a.cc:155:37: note:   cannot convert 'std::forward<multiset<int> >((* & args#2))' (type 'std::multiset<int>') to type 'std::multiset<int>&'
  155 |                 return F::operator()(*this, std::forward<Args>(args)...);
      |                        ~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~