C. Colorful Table
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You 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.

Input

The 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 $$$10^5$$$.

Output

For 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 $$$k$$$.

Example
Input
5
2 1
1 1
2 2
1 2
3 5
3 2 4
4 2
1 2 1 2
5 3
1 2 3 2 1
Output
4 
4 2 
0 6 6 2 0 
8 6 
10 6 2
Note

In 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:

11
12

One 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:

11111
12221
12321
12221
11111