/* #region Head */ // #define _GLIBCXX_DEBUG #include using namespace std; using ll = long long; using ull = unsigned long long; using ld = long double; using pll = pair; template using vc = vector; template using vvc = vc>; using vll = vc; using vvll = vvc; using vld = vc; using vvld = vvc; using vs = vc; using vvs = vvc; template using um = unordered_map; template using pq = priority_queue; template using pqa = priority_queue, greater>; template using us = unordered_set; #define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i)) #define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i)) #define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i)) #define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d)) #define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d)) #define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++) #define ALL(x) begin(x), end(x) #define SIZE(x) ((ll)(x).size()) #define PERM(c) \ sort(ALL(c)); \ for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c))) #define UNIQ(v) v.erase(unique(ALL(v)), v.end()); #define endl '\n' #define sqrt sqrtl #define floor floorl #define log2 log2l constexpr ll INF = 1'010'000'000'000'000'017LL; constexpr int IINF = 1'000'000'007LL; constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7 constexpr ld EPS = 1e-12; constexpr ld PI = 3.14159265358979323846; template istream &operator>>(istream &is, vc &vec) { // vector 入力 for (T &x : vec) is >> x; return is; } template ostream &operator<<(ostream &os, vc &vec) { // vector 出力 (for dump) os << "{"; REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", "); os << "}"; return os; } template ostream &operator>>(ostream &os, vc &vec) { // vector 出力 (inline) REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " "); return os; } template istream &operator>>(istream &is, pair &pair_var) { // pair 入力 is >> pair_var.first >> pair_var.second; return is; } template ostream &operator<<(ostream &os, pair &pair_var) { // pair 出力 os << "(" << pair_var.first << ", " << pair_var.second << ")"; return os; } // map, um, set, us 出力 template ostream &out_iter(ostream &os, T &map_var) { os << "{"; REPI(itr, map_var) { os << *itr; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } return os << "}"; } template ostream &operator<<(ostream &os, map &map_var) { return out_iter(os, map_var); } template ostream &operator<<(ostream &os, um &map_var) { os << "{"; REPI(itr, map_var) { auto [key, value] = *itr; os << "(" << key << ", " << value << ")"; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } os << "}"; return os; } template ostream &operator<<(ostream &os, set &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, us &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, pq &pq_var) { pq pq_cp(pq_var); os << "{"; if (!pq_cp.empty()) { os << pq_cp.top(), pq_cp.pop(); while (!pq_cp.empty()) os << ", " << pq_cp.top(), pq_cp.pop(); } return os << "}"; } // dump #define DUMPOUT cerr void dump_func() { DUMPOUT << endl; } template void dump_func(Head &&head, Tail &&... tail) { DUMPOUT << head; if (sizeof...(Tail) > 0) DUMPOUT << ", "; dump_func(move(tail)...); } // chmax (更新「される」かもしれない値が前) template > bool chmax(T &xmax, const U &x, Comp comp = {}) { if (comp(xmax, x)) { xmax = x; return true; } return false; } // chmin (更新「される」かもしれない値が前) template > bool chmin(T &xmin, const U &x, Comp comp = {}) { if (comp(x, xmin)) { xmin = x; return true; } return false; } // ローカル用 #define DEBUG_ #ifdef DEBUG_ #define DEB #define dump(...) \ DUMPOUT << " " << string(#__VA_ARGS__) << ": " \ << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl \ << " ", \ dump_func(__VA_ARGS__) #else #define DEB if (false) #define dump(...) #endif #define VAR(type, ...) \ type __VA_ARGS__; \ cin >> __VA_ARGS__; template istream &operator,(istream &is, T &rhs) { return is >> rhs; } template ostream &operator,(ostream &os, const T &rhs) { return os << ' ' << rhs; } struct AtCoderInitialize { static constexpr int IOS_PREC = 15; static constexpr bool AUTOFLUSH = false; AtCoderInitialize() { ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr); cout << fixed << setprecision(IOS_PREC); if (AUTOFLUSH) cout << unitbuf; } } ATCODER_INITIALIZE; void Yn(bool p) { cout << (p ? "Yes" : "No") << endl; } void YN(bool p) { cout << (p ? "YES" : "NO") << endl; } /* #endregion */ /* #region rand */ // [lb, ub] の値を等確率で発生させる class Rand { std::random_device rd; // Will be used to obtain a seed for the random number engine std::mt19937 gen; // Standard mersenne_twister_engine seeded with rd() std::uniform_int_distribution<> dis; public: Rand(ll lb, ll ub) : rd(), gen(rd()), dis(lb, ub) {} inline int operator()() noexcept { return dis(gen); } }; // [lb, ub) の値を等確率で発生させる class RandDouble { std::random_device seed_gen; std::default_random_engine engine; std::uniform_real_distribution<> dist; public: RandDouble(double lb, double ub) : seed_gen(), engine(seed_gen()), dist(lb, ub) {} inline double operator()() noexcept { return dist(engine); } }; /* #endregion */ // 誰でもできる焼きなまし法 - gasin’s blog http://gasin.hatenadiary.jp/entry/2019/09/03/162613 struct Anneal { using clk = chrono::system_clock; double timespan_ms; // 焼きなます時間 double start_temp; // 開始温度 (一回の遷移で動きうるスコア幅の最大値程度) double end_temp; // 終了温度 (一回の遷移で動きうるスコア幅の最小値程度) RandDouble rd; clk::time_point start_time; double ms_elapsed; // コンストラクタ Anneal(double timespan_ms, double start_temp, double end_temp) : timespan_ms(timespan_ms), start_temp(start_temp), end_temp(end_temp), rd(0, 1), start_time(clk::now()), ms_elapsed(0) {} // スコアの差分から,遷移するかどうかを確率的に決定して返す bool transit(double dif) noexcept { clk::time_point cur_time = clk::now(); ms_elapsed = static_cast(chrono::duration_cast(cur_time - start_time).count() / 1000.0); // 温度関数 double temperature = start_temp + (end_temp - start_temp) * (ms_elapsed / timespan_ms); // 遷移確率関数(最大化の場合) double prob = exp((double)dif / temperature); // cout << dif, prob, '\n'; return prob > rd(); } // 時間切れかどうかを返す bool runnable() noexcept { return ms_elapsed < timespan_ms; } }; // Problem void solve() { int n, m; cin >> n, m; vc a(n); cin >> a; // 初期解生成 vc ans(m), trash(n - m); int ans_xor = 0; REP(i, 0, m) ans_xor ^= (ans[i] = a[i]); REP(i, 0, n - m) trash[i] = a[m + i]; // dump(ans_xor, ans, trash); Rand r_ans(0, m - 1); Rand r_trash(0, n - m - 1); double timespan_ms = 1450.0; // 焼きなます時間 double start_temp = (double)(*max_element(ALL(a))); // 開始温度 (一回の遷移で動きうるスコア幅の最大値程度); double end_temp = 1; // 終了温度 (一回の遷移で動きうるスコア幅の最小値程度); Anneal anneal(timespan_ms, start_temp, end_temp); while (anneal.runnable()) { int idx_ans = r_ans(); int idx_trash = r_trash(); int new_ans_xor = ans_xor ^ ans[idx_ans] ^ trash[idx_trash]; int dif = new_ans_xor - ans_xor; // スコアの差分 if (anneal.transit(dif)) { swap(ans[idx_ans], trash[idx_trash]); // ans_xor = new_ans_xor; } } // dump(ans_xor); cout >> ans; } // entry point int main() { solve(); return 0; }