#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
using namespace std;

#include<bits/stdc++.h>
#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp"
namespace noya2 {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p){
    os << p.first << " " << p.second;
    return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p){
    is >> p.first >> p.second;
    return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v){
    int s = (int)v.size();
    for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
    return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v){
    for (auto &x : v) is >> x;
    return is;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u){
    cin >> t;
    in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u){
    cout << t;
    if (sizeof...(u)) cout << sep;
    out(u...);
}

template<typename T>
void out(const vector<vector<T>> &vv){
    int s = (int)vv.size();
    for (int i = 0; i < s; i++) out(vv[i]);
}

struct IoSetup {
    IoSetup(){
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(7);
    }
} iosetup_noya2;

} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"
namespace noya2{

const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 =  998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";

void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }

} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"

#line 6 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"

namespace noya2{

unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
    if (a == 0 || b == 0) return a + b;
    int n = __builtin_ctzll(a); a >>= n;
    int m = __builtin_ctzll(b); b >>= m;
    while (a != b) {
        int mm = __builtin_ctzll(a - b);
        bool f = a > b;
        unsigned long long c = f ? a : b;
        b = f ? b : a;
        a = (c - b) >> mm;
    }
    return a << std::min(n, m);
}

template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }

long long sqrt_fast(long long n) {
    if (n <= 0) return 0;
    long long x = sqrt(n);
    while ((x + 1) * (x + 1) <= n) x++;
    while (x * x > n) x--;
    return x;
}

template<typename T> T floor_div(const T n, const T d) {
    assert(d != 0);
    return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}

template<typename T> T ceil_div(const T n, const T d) {
    assert(d != 0);
    return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}

template<typename T> void uniq(std::vector<T> &v){
    std::sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}

template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }

template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }

template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }

} // namespace noya2
#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"

#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n)-1; i >= 0; i--)
#define all(v) (v).begin(),(v).end()

using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;

namespace noya2{

/*　~ (. _________ . /)　*/

}

using namespace noya2;


#line 2 "c.cpp"

int count0(ll x){
    if (x == 0) return 1;
    return bit_width<uint64_t>(x) - popcount<uint64_t>(x);
}

ll solve_naive(vector<int> a){
    int n = a.size();
    for (ll L = 0; L < 128; L++){
        if ([&]{
            rep(i,n){
                if (count0(L+i) != a[i]){
                    return false;
                }
            }
            return true;
        }()){
            return L;
        }
    }
    return -1;
}

ll solve_fast(vector<int> a){
    int n = a.size();
    const int mx = 62;
    ll ans = 1LL << mx;
    auto say = [&]() -> ll {
        if (ans == (1LL << mx)){
            return -1;
        }
        else {
            return ans;
        }
    };
    auto naive = [&](ll L){
        if (L < 0) return false;
        rep(i,n){
            if (count0(L+i) != a[i]){
                return false;
            }
        }
        return true;
    };
    // 0, 1
    rep(L,2){
        if (naive(L)){
            chmin(ans,L);
        }
    }
    // no change
    repp(w,2,mx+1){
        if ((1LL << (w-1)) < n) continue;
        ll mod = 1, rem = 0;
        bool ok = true;
        auto upd = [&](ll nmod, ll nrem){
            if (mod < nmod){
                swap(mod,nmod);
                swap(rem,nrem);
            }
            ok &= (rem % nmod == nrem);
        };
        rep(i,n-1){
            int add = a[i+1] - a[i];
            if (add < -1){
                return -1;
            }
            if (add == -1){
                // (L+i) % 2 == 0
                upd(2,i%2);
            }
            else {
                // (L+i+1) % 2^{add+2} == 2^{add+1}
                ll irem = 2LL<<add;
                irem -= (i+1) % (4LL<<add);
                if (irem < 0) irem += 4LL<<add;
                upd(4LL<<add,irem);
            }
        }
        if (!ok) continue;
        // L == mod * k + rem
        // 2^{w-1} <= L, L+n-1 < 2^w
        ll kl = ceil_div((1LL<<(w-1))-rem,mod);
        ll kr = ceil_div((1LL<<w)-(n-1)-rem,mod);
        if (kl >= kr) continue;
        // kl <= k < kr, popcount(k) + popcount(rem) == w - a[0]
        int tar = w - a[0] - popcount<uint64_t>(rem);
        if (tar < 0) continue;
        ll k = kl;
        while (k < kr){
            int pc = popcount<uint64_t>(k);
            if (pc == tar) break;
            int lc = countr_zero<uint64_t>(k);
            if (pc < tar){
                if (pc + lc < tar){
                    k += 1LL << lc;
                    continue;
                }
                k += (1LL<<(tar-pc))-1;
                break;
            }
            else {
                k += 1LL << lc;
            }
        }
        if (k < kr){
            ll L = mod * k + rem;
            assert(naive(L));
            chmin(ans,L);
        }
    }
    if (ranges::count(a, 0) > 30){
        return say();
    }
    // change
    rep(i,n-1){
        if (a[i] != 0) continue;
        int w = a[i+1];
        if (w == 0) continue;
        ll val = 1LL << w; // L+i+1
        ll L = val - (i+1);
        if (naive(L)){
            chmin(ans,L);
        }
    }
    return say();
}

void solve(){
    int n; in(n);
    vector<int> a(n); in(a);
    ll ans = solve_fast(a);
    out(ans);
    return ;
    ll nans = solve_naive(a);
    if (ans == nans){
        out(ans);
        return ;
    }
    out(n);
    out(a);
    out(ans,nans);
    exit(1);
}

int main(){
    int t = 1; in(t);
    while (t--) { solve(); }
}