#include <algorithm>
#include <atcoder/all>
#include <bitset>
#include <cassert>
#include <cmath>
#include <ctime>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using namespace atcoder;
typedef long long ll;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define repr(i, n) for (int i = (int)(n) - 1; i >= 0; i--)
#define repk(i, k, n) for (int i = k; i < (int)(n); i++)
#define all(v) v.begin(), v.end()
#define mod1 1000000007
#define mod2 998244353
#define mod3 100000007
#define vi vector<int>
#define vs vector<string>
#define vc vector<char>
#define vl vector<ll>
#define vb vector<bool>
#define vvi vector<vector<int>>
#define vvc vector<vector<char>>
#define vvl vector<vector<ll>>
#define vvb vector<vector<bool>>
#define vvvi vector<vector<vector<int>>>
#define vvvl vector<vector<vector<ll>>>
#define pii pair<int, int>
#define pil pair<int, ll>
#define pli pair<ll, int>
#define pll pair<ll, ll>
#define vpii vector<pair<int, int>>
#define vpll vector<pair<ll, ll>>
#define vvpii vector<vector<pair<int, int>>>
#define vvpll vector<vector<pair<ll, ll>>>

template <typename T>
void debug(T e) {
    cerr << e << endl;
}

template <typename T>
void debug(vector<T> &v) {
    rep(i, v.size()) { cerr << v[i] << " "; }
    cerr << endl;
}

template <typename T>
void debug(vector<vector<T>> &v) {
    rep(i, v.size()) {
        rep(j, v[i].size()) { cerr << v[i][j] << " "; }
        cerr << endl;
    }
}

template <typename T>
void debug(vector<pair<T, T>> &v) {
    rep(i, v.size()) { cerr << v[i].first << " " << v[i].second << endl; }
}

template <typename T>
void debug(set<T> &st) {
    for (auto itr = st.begin(); itr != st.end(); itr++) {
        cerr << *itr << " ";
    }
    cerr << endl;
}

template <typename T>
void debug(multiset<T> &ms) {
    for (auto itr = ms.begin(); itr != ms.end(); itr++) {
        cerr << *itr << " ";
    }
    cerr << endl;
}

template <typename T>
void debug(map<T, T> &mp) {
    for (auto itr = mp.begin(); itr != mp.end(); itr++) {
        cerr << itr->first << " " << itr->second << endl;
    }
}

void debug_out() { cerr << endl; }

template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    cerr << H << " ";
    debug_out(T...);
}

using mint = modint998244353;

void debug_mint1(vector<mint> &vec) {
    for (int i = 0; i < vec.size(); i++) {
        cerr << vec[i].val() << " ";
    }
    cerr << endl;
}

void debug_mint2(vector<vector<mint>> &vec) {
    for (int i = 0; i < vec.size(); i++) {
        for (int j = 0; j < vec[i].size(); j++) {
            cerr << vec[i][j].val() << " ";
        }
        cerr << endl;
    }
}

int main() {
    ll T;
    cin >> T;
    while (T--){
        ll N;
        cin >> N;
        vector<ll> A(N);
        rep(i, N) cin >> A[i];

        if (N == 1){
            cout << A[0] << endl;
            continue;
        }

        ll ok = 1;
        ll ng = N + 2;
        while (ng - ok > 1){
            ll mid = (ok + ng) / 2;
            
            vector<ll> nums(mid, 0);
            rep(i, N){
                if (A[i] < mid) nums[A[i]]++;
            }
            // 作れない値が 20 種類以上ある場合　→　問答無用で答えは No
            ll shorten = 0;
            rep(i, mid){
                if (nums[i] == 0) shorten++;
            }
            
            if (shorten >= 20){
                ng = mid;
            }
            else{
                // 愚直に不足分を補填していく
                ll nes = 0;
                bool pos = true;
                for (ll i = 0; i < mid; i++){
                    if (!pos) break;
                    if (nums[i] >= 1){
                        continue;
                    }
                    else{
                        for (ll j = 0; j < i; j++){
                            if (nums[j] > 1){
                                nums[j]--;
                            }
                            else{
                                if (j >= 30){
                                    pos = false;
                                    break;
                                }
                                else{
                                    if (j == 0) nes++;
                                    else nes += (1LL << (j - 1));
                                }
                            }
                        }
                        nums[i] = 1;
                    }
                }
                // この一連の流れで使われなかったものは何個ある？
                ll rem = 0;
                rep(i, N){
                    if (A[i] >= mid) rem++;
                }
                rep(i, mid){
                    if (nums[i] > 1) rem += (nums[i] - 1);
                }

                if (!pos){
                    ng = mid;
                }
                else if (rem < nes){
                    ng = mid;
                }
                else{
                    ok = mid;
                }
            }
        }
        cout << ok << endl;
    }
}