#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } const std::vector> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}}; int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); } template std::pair operator+(const std::pair &l, const std::pair &r) { return std::make_pair(l.first + r.first, l.second + r.second); } template std::pair operator-(const std::pair &l, const std::pair &r) { return std::make_pair(l.first - r.first, l.second - r.second); } template std::vector sort_unique(std::vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template IStream &operator>>(IStream &is, std::vector &vec) { for (auto &v : vec) is >> v; return is; } template OStream &operator<<(OStream &os, const std::vector &vec); template OStream &operator<<(OStream &os, const std::array &arr); template OStream &operator<<(OStream &os, const std::unordered_set &vec); template OStream &operator<<(OStream &os, const pair &pa); template OStream &operator<<(OStream &os, const std::deque &vec); template OStream &operator<<(OStream &os, const std::set &vec); template OStream &operator<<(OStream &os, const std::multiset &vec); template OStream &operator<<(OStream &os, const std::unordered_multiset &vec); template OStream &operator<<(OStream &os, const std::pair &pa); template OStream &operator<<(OStream &os, const std::map &mp); template OStream &operator<<(OStream &os, const std::unordered_map &mp); template OStream &operator<<(OStream &os, const std::tuple &tpl); template OStream &operator<<(OStream &os, const std::vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } template std::istream &operator>>(std::istream &is, std::tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template OStream &operator<<(OStream &os, const std::tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } template OStream &operator<<(OStream &os, const std::unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::pair &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; } template OStream &operator<<(OStream &os, const std::map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl #define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr) #else #define dbg(x) ((void)0) #define dbgif(cond, x) ((void)0) #endif void Yes(const vector &A) { cout << "Yes\n"; REP(i, A.size()) cout << A.at(i) << (i + 1 < (int)A.size() ? ' ' : '\n'); exit(0); } bool validate(int K, const vector &A, int X, int Y) { if (A.front() != X) return false; if (A.back() != Y) return false; const int N = A.size(); vector cs(N + 1); REP(i, N) cs.at(i + 1) = cs.at(i) ^ A.at(i); FOR(i, K, N) { auto prv = cs.at(i) ^ cs.at(i - K); if (prv >= A.at(i)) { dbg(make_tuple(i, prv, A)); return false; } } return true; } vector greedy_build(int n, int k) { vector ret(k, 0); vector csret(k + 1, 0); while ((int)ret.size() < n) { // int cs = 0; // REP(i, k) cs ^= ret.at(ret.size() - 1 - i); const int cs = csret.at(csret.size() - 1) ^ csret.at(csret.size() - 1 - k); // int nxt_cs = 0; // REP(i, k - 1) nxt_cs ^= ret.at(ret.size() - 1 - i); const int nxt_cs = csret.at(csret.size() - 1) ^ csret.at(csret.size() - 1 - k + 1); int best_eval = 1 << 30; int best = -1; FOR(v, cs + 1, (cs + 100) * 4) { if (chmin(best_eval, nxt_cs ^ v)) { best = v; } } ret.push_back(best); csret.push_back(csret.back() ^ best); } return ret; } vector solve(int N, int K, int X, int Y) { if (Y == 0) return {}; if (K == 1) { vector ret(N); REP(i, N) ret.at(i) = X + i; if (ret.back() <= Y) { ret.back() = Y; return ret; } else { return {}; } } assert(K >= 2); if (X) { if (K % 2 == 0) { vector ret(N, X); ret.back() = Y; return ret; } else { assert(K >= 3); const int n0 = X; const int n1 = (n0 == 1 ? 2 : 1); vector C(K, n1); C.at(0) = n0; C.back() = n0 ^ n1; vector ret(N); REP(i, N) { ret.at(i) = C.at(i % C.size()); } ret.back() = Y; return ret; } } else { if (K == N - 1) { vector ret(N); ret.back() = Y; return ret; } if (K == N - 2) { if (Y == 1) return {}; vector ret(N); ret.at(N - 3) = 2; ret.at(N - 2) = 3; ret.back() = Y; return ret; } if (K % 2 == 0) { vector ret(N); FOR(i, K, N) { ret.at(i) = ((i - K) % (K + 1) == 0) ? 2 : 3; } ret.back() = Y; return ret; } if (Y >= 3) { auto gri = greedy_build(N + K - 1, K); gri.erase(gri.begin(), gri.begin() + K - 1); gri.back() = Y; return gri; // vector ret(N); // FOR(i, K, N) ret.at(i) = ((i - K) % (K + 1) == 0 ? 1 : 3); // ret.back() = Y; // return ret; } return {}; // ret.back() = 0; // reverse(ALL(ret)); // return ret; } } #include #include struct rand_int_ { using lint = long long; std::mt19937 mt; rand_int_() : mt(std::chrono::steady_clock::now().time_since_epoch().count()) {} lint operator()(lint x) { return this->operator()(0, x); } // [0, x) lint operator()(lint l, lint r) { std::uniform_int_distribution d(l, r - 1); return d(mt); } } rnd; int main() { dbg(greedy_build(100, 8)); while (true) { break; int n = rnd(2, 10); int k = rnd(1, n); int x = rnd(0, 16); int y = rnd(0, 16); auto ret = solve(n, k, x, y); if (ret.size() and !validate(k, ret, x, y)) { cerr << "Invalid output for n=" << n << ", k=" << k << ", x=" << x << ", y=" << y << ": " << ret << endl; exit(1); } } int N, K, X, Y; cin >> N >> K >> X >> Y; const auto ret = solve(N, K, X, Y); if (ret.empty()) { puts("No"); } else { Yes(ret); } }