#include <bits/stdc++.h>
#ifdef LOCAL
#include <debug.hpp>
#else
#define debug(...) void(0)
#endif

template <class T> std::istream& operator>>(std::istream& is, std::vector<T>& v) {
    for (auto& e : v) {
        is >> e;
    }
    return is;
}

template <class T> std::ostream& operator<<(std::ostream& os, const std::vector<T>& v) {
    for (std::string_view sep = ""; const auto& e : v) {
        os << std::exchange(sep, " ") << e;
    }
    return os;
}

template <class T, class U = T> bool chmin(T& x, U&& y) {
    return y < x and (x = std::forward<U>(y), true);
}

template <class T, class U = T> bool chmax(T& x, U&& y) {
    return x < y and (x = std::forward<U>(y), true);
}

template <class T> void mkuni(std::vector<T>& v) {
    std::ranges::sort(v);
    auto result = std::ranges::unique(v);
    v.erase(result.begin(), result.end());
}

template <class T> int lwb(const std::vector<T>& v, const T& x) {
    return std::distance(v.begin(), std::ranges::lower_bound(v, x));
}

using namespace std;

using ll = long long;

vector<int> Solve(int n, vector<int> a) {
    vector<int> b;
    auto res = a;
    for (int _ = 0; _ < 2; _++) {
        for (int i = 0; i < n; i++) {
            b.emplace_back(a[i]);
        }
    }
    vector<vector<pair<int, int>>> cand(n);
    {
        map<int, int> mp, nmp;
        for (int i = 2 * n - 1; i >= 0; i--) {
            for (auto [val, len] : mp) {
                if (len + 1 >= n) continue;
                int nval = (val + b[i + 1]) / 2;
                if (not nmp.count(nval)) {
                    nmp[nval] = len + 1;
                } else {
                    chmin(nmp[nval], len + 1);
                }
            }
            swap(mp, nmp);
            mp[0] = 0;
            nmp.clear();
            if (i < n) {
                for (auto [val, len] : mp) {
                    cand[i].emplace_back(val, len);
                }
            }
        }
    }
    {
        map<int, int> mp, nmp;
        for (int i = 0; i < 2 * n; i++) {
            for (auto [val, len] : mp) {
                int nval = (val + b[i - 1]) / 2;
                if (not nmp.count(nval)) {
                    nmp[nval] = len + 1;
                } else {
                    chmin(nmp[nval], len + 1);
                }
            }
            swap(mp, nmp);
            mp[0] = 0;
            nmp.clear();
            if (i >= n) {
                int maxi = 0;
                for (auto itr = mp.begin(); auto [val1, len1] : cand[i - n] | views::reverse) {
                    for (; itr != mp.end(); itr++) {
                        auto [val2, len2] = *itr;
                        if (len1 + len2 <= n - 1) {
                            chmax(maxi, val2);
                        } else {
                            break;
                        }
                    }
                    chmax(res[i - n], a[i - n] + maxi + val1);
                }
            }
        }
    }

    return res;
}

void solve() {
    int n;
    cin >> n;
    vector<int> a(n);
    cin >> a;

    auto ans = a;
    for (int _ = 0; _ < 2; _++) {
        auto res = Solve(n, a);
        if (_) ranges::reverse(res);
        for (int i = 0; i < n; i++) chmax(ans[i], res[i]);
        ranges::reverse(a);
    }

    cout << ans << "\n";
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(15);

    int T;
    cin >> T;
    for (; T--;) solve();
    return 0;
}