Colorful Table
Description
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.
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 $10^5$.
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 $k$.
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 $k$.
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
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:
| 1 | 1 |
| 1 | 2 |
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:
| 1 | 1 | 1 | 1 | 1 |
| 1 | 2 | 2 | 2 | 1 |
| 1 | 2 | 3 | 2 | 1 |
| 1 | 2 | 2 | 2 | 1 |
| 1 | 1 | 1 | 1 | 1 |