A13434. Powered Addition

You have an array $a$ of length $n$ . For every positive integer $x$ you are going to perform the following operation during the $x$ -th second:

- Select some distinct indices $i_{1}, i_{2}, \ldots, i_{k}$ which are between $1$ and $n$ inclusive, and add $2^{x-1}$ to each corresponding position of $a$ . Formally, $a_{i_{j}} := a_{i_{j}} + 2^{x-1}$ for $j = 1, 2, \ldots, k$ . Note that you are allowed to not select any indices at all.

You have to make $a$ nondecreasing as fast as possible. Find the smallest number $T$ such that you can make the array nondecreasing after at most $T$ seconds.

Array $a$ is nondecreasing if and only if $a_{1} \le a_{2} \le \ldots \le a_{n}$ .

You have to answer $t$ independent test cases.

The first line contains a single integer $t$ ( $1 \le t \le 10^{4}$ ) — the number of test cases.

The first line of each test case contains single integer $n$ ( $1 \le n \le 10^{5}$ ) — the length of array $a$ . It is guaranteed that the sum of values of $n$ over all test cases in the input does not exceed $10^{5}$ .

The second line of each test case contains $n$ integers $a_{1}, a_{2}, \ldots, a_{n}$ ( $-10^{9} \le a_{i} \le 10^{9}$ ).

For each test case, print the minimum number of seconds in which you can make $a$ nondecreasing.

In the first test case, if you select indices $3, 4$ at the $1$ -st second and $4$ at the $2$ -nd second, then $a$ will become $[1, 7, 7, 8]$ . There are some other possible ways to make $a$ nondecreasing in $2$ seconds, but you can't do it faster.

In the second test case, $a$ is already nondecreasing, so answer is $0$ .

In the third test case, if you do nothing at first $2$ seconds and select index $2$ at the $3$ -rd second, $a$ will become $[0, 0]$ .