for _ in range(int(input())):
    N = int(input())
    def count(x: int):
        x = bin(x)[2:]
        return x.count("0")
    A = list(map(int, input().split()))


    def check(L: int):
        B = [count(L + i) for i in range(N)]
        return A == B

    if N == 1:
        print(1 << A[0])
        continue
    if min(A) == 0:
        it = A.index(0)

        ok = False
        for i in range(61):
            x = 1 << i
            if check(x - 1 - it):
                print(x - 1 - it)
                ok = True
                break
        if not ok:
            print(-1)
    else:
        G = [A[i + 1] - A[i] + 1 for i in range(N - 1)]
        it = G.index(max(G))
        x = int("1" + "0" * A[it] + "1" * G[it], 2)
        if check(x - it):
            print(x - it)
        else:
            print(-1)