TSP

The tree has $10^{18}$ vertices. For every integer $i$ with $2 \le i \le 10^{18}$, there is an edge between vertex $i$ and vertex $\left\lfloor \frac{i}{2} \right\rfloor$. You are given $K$ vertices $v_1, v_2, \cdots, v_K$ in this tree. Find the length of the shortest path that starts at any vertex and visits each of the given $K$ vertices at least once.

The first line contains the number of test cases $T$. $(1 \le T \le 10\,000)$

The first line of each test case contains the number of vertices $K$. $(2 \le K \le 100\,000)$

The second line of each test case contains the vertex numbers $v_1, v_2, \cdots, v_K$, separated by spaces. All $v_i$ are distinct. $(1 \le v_i \le 10^{18})$

All input values are integers.

The sum of $K$ over all test cases does not exceed $100\,000$.

For each test case, print one line containing the length of the shortest path that starts at any vertex and visits each of the given $K$ vertices at least once.

A path of length $L$ in the tree is a sequence of visited vertices $p_0, p_1, \cdots, p_L$ such that for each $1 \le i \le L$, $p_{i-1}$ and $p_i$ are connected by an edge. You may visit the same vertex or edge more than once.