CF2093G Shorten the Array

The beauty of an array $ b $ of length $ m $ is defined as $ \max(b_i \oplus b_j) $ among all possible pairs $ 1 \le i \le j \le m $ , where $ x \oplus y $ is the [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of numbers $ x $ and $ y $ . We denote the beauty value of the array $ b $ as $ f(b) $ . An array $ b $ is called beautiful if $ f(b) \ge k $ . Recently, Kostya bought an array $ a $ of length $ n $ from the store. He considers this array too long, so he plans to cut out some beautiful subarray from it. That is, he wants to choose numbers $ l $ and $ r $ ( $ 1 \le l \le r \le n $ ) such that the array $ a_{l \dots r} $ is beautiful. The length of such a subarray will be the number $ r - l + 1 $ . The entire array $ a $ is also considered a subarray (with $ l = 1 $ and $ r = n $ ). Your task is to find the length of the shortest beautiful subarray in the array $ a $ . If no subarray is beautiful, you should output the number $ -1 $ .

The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^4 $ ). Next, there are $ t $ blocks of two lines: In the first line of the block, there are two integers $ n $ and $ k $ ( $ 1 \le n \le 2 \cdot 10^5 $ , $ 0 \le k \le 10^9 $ ). In the second line of the block, there is the array $ a $ consisting of $ n $ integers ( $ 0 \le a_i \le 10^9 $ ). It is guaranteed that the sum of $ n $ across all tests does not exceed $ 2 \cdot 10^5 $ .

For each test case, you need to output a single integer — the minimum length of the segment $ (l, r) $ for which $ f(a_{l \dots r}) \ge k $ . If such a segment is not found, you should output $ -1 $ .