C. Colorful Tabletime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given two integers n and k. You are also given an array of integers a_1, a_2, \ldots, a_n of size n. It is known that for all 1 \leq i \leq n, 1 \leq a_i \leq k.Define a two-dimensional array b of size n \times n as follows: b_{i, j} = \min(a_i, a_j). Represent array b as a square, where the upper left cell is b_{1, 1}, rows are numbered from top to bottom from 1 to n, and columns are numbered from left to right from 1 to n. Let the color of a cell be the number written in it (for a cell with coordinates (i, j), this is b_{i, j}).For each color from 1 to k, find the smallest rectangle in the array b containing all cells of this color. Output the sum of width and height of this rectangle.InputThe first line contains a single integer t (1 \leq t \leq 10^4) — the number of test cases. Then follows the description of the test cases.The first line of each test case contains two integers n and k (1 \leq n, k \leq 10^5) — the size of array a and the number of colors.The second line of each test case contains n integers a_1, a_2, \ldots, a_n (1 \leq a_i \leq k) — the array a.It is guaranteed that the sum of the values of n and k over all test cases does not exceed 10^5.OutputFor each test case, output k numbers: the sums of width and height of the smallest rectangle containing all cells of a color, for each color from 1 to k.ExampleInput
52 11 12 21 23 53 2 44 21 2 1 25 31 2 3 2 1Output
4 
4 2 
0 6 6 2 0 
8 6 
10 6 2 
NoteIn the first test case, the entire array b consists of color 1, so the smallest rectangle for color 1 has a size of 2 \times 2, and the sum of its sides is 4.In the second test case, the array b looks like this:1112One of the corner cells has color 2, and the other three cells have color 1. Therefore, the smallest rectangle for color 1 has a size of 2 \times 2, and for color 2 it is 1 \times 1.In the last test case, the array b looks like this:1111112221123211222111111
52 11 12 21 23 53 2 44 21 2 1 25 31 2 3 2 1
4  4 2  0 6 6 2 0  8 6  10 6 2  
['binary search', 'data structures', 'dp', 'implementation', 'math', 'two pointers', '*1300']