Powered Addition

题意翻译

一个数列，每个数可以选择一些 $j$，使得这个数加上 $\sum {2^{j-1}}$（$j$ 不一定要连续）。希望加上这些值后的数列成为不降序列。最小化使用到的的 $j$ 的最大值。

题目描述

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.

输入输出格式

输入格式

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} $ ).

输出格式

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

输入输出样例

输入样例 #1

3
4
1 7 6 5
5
1 2 3 4 5
2
0 -4

输出样例 #1

2
0
3

说明

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] $ .