fn run<W: Write>(sc: &mut scanner::Scanner, out: &mut std::io::BufWriter<W>) {
    let t: u32 = sc.next();
    for _ in 0..t {
        let n: usize = sc.next();
        let a: Vec<u32> = sc.next_vec(n);
        if let Some(x) = solve(a) {
            writeln!(out, "{}", x).ok();
        } else {
            writeln!(out, "-1").ok();
        }
    }
}

fn solve(a: Vec<u32>) -> Option<usize> {
    let check = |v: usize| -> bool {
        for (i, a) in a.iter().enumerate() {
            let v = v + i;
            if v == 0 {
                if *a != 1 {
                    return false;
                }
            } else {
                let k = (v + 1).next_power_of_two() / 2;
                if ((k - 1) & !v).count_ones() != *a {
                    return false;
                }
            }
        }
        true
    };
    if check(0) {
        return Some(0);
    }
    let min = *a.iter().min().unwrap();
    let pos = a.iter().rposition(|a| *a == min).unwrap();
    let n = a.len();
    if n == 1 {
        return Some(1 << a[0]);
    }
    let k = (n + 1).next_power_of_two() / 2;
    let v = (k - 1) & !pos;
    for j in 0..8 {
        let v = j * k + ((k - 1) & !pos);
        if check(v) {
            return Some(v);
        }
    }
    let t = k * 4;
    let mut ans = std::usize::MAX;
    'outer: for m in 0..4 {
        let fix = m * k + ((k - 1) & !pos);
        let mut b = a.clone();
        let mut carry = vec![0; n];
        for (i, b) in b.iter_mut().enumerate() {
            let v = fix + i;
            let z = ((t - 1) & !v).count_ones();
            if z > *b {
                continue 'outer;
            }
            *b -= z;
            carry[i] = if v >= t {1} else {0};
        }
        let x = carry.iter().position(|c| *c > 0).unwrap_or(n);
        if b[..x].iter().all(|b| *b == 0) && b[x..].windows(2).all(|b| b[0] == b[1]) && (x == n || b[x] > 0) {
            let val = fix + ((1 << b[x]) - 1) * t;
            ans = ans.min(val);
        }
    }
    if ans == std::usize::MAX {
        None
    } else {
        assert!(check(ans));
        Some(ans)
    }
}

/*

A_i = k という値の時、どういうLが条件満たすのか
k=0の時
L+i=2^j-1 という形のj>=1しか無理
全探索できる
以降k>0
A_iの最小値を考えると下位floor(log_2 N)桁は全部1という形じゃないといけない?

*/

// ---------- begin scannner ----------
#[allow(dead_code)]
mod scanner {
    use std::str::FromStr;
    pub struct Scanner<'a> {
        it: std::str::SplitWhitespace<'a>,
    }
    impl<'a> Scanner<'a> {
        pub fn new(s: &'a String) -> Scanner<'a> {
            Scanner {
                it: s.split_whitespace(),
            }
        }
        pub fn next<T: FromStr>(&mut self) -> T {
            self.it.next().unwrap().parse::<T>().ok().unwrap()
        }
        pub fn next_bytes(&mut self) -> Vec<u8> {
            self.it.next().unwrap().bytes().collect()
        }
        pub fn next_chars(&mut self) -> Vec<char> {
            self.it.next().unwrap().chars().collect()
        }
        pub fn next_vec<T: FromStr>(&mut self, len: usize) -> Vec<T> {
            (0..len).map(|_| self.next()).collect()
        }
    }
}
// ---------- end scannner ----------

use std::io::Write;
use std::collections::*;

type Map<K, V> = BTreeMap<K, V>;
type Set<T> = BTreeSet<T>;
type Deque<T> = VecDeque<T>;

fn main() {
    use std::io::Read;
    let mut s = String::new();
    std::io::stdin().read_to_string(&mut s).unwrap();
    let mut sc = scanner::Scanner::new(&s);
    let out = std::io::stdout();
    let mut out = std::io::BufWriter::new(out.lock());
    run(&mut sc, &mut out);
}