Colorful Table

TA. Colorful Table

You are given two integers $n$ and $k$. You are also given an array of integers $a_1,a_2,\dots ,a_n$ of size $n$. It is known that for all $1\le i\le n$, $1\le a_i\le k$.

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 $t$ ($1\le t\le 10^4$) — 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 $k$ ($1\le n,k\le 10^5$) — the size of array $a$ and the number of colors.

The second line of each test case contains $n$ integers $a_1,a_2,\dots ,a_n$ ($1\le a_i\le k$) — 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:

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

code

#include<bits/stdc++.h>
#define int long long
#define endl '\n'
 
using namespace std;


const int N = 2e5+10,INF=0x3f3f3f3f,mod=1e9+7;
 
typedef pair<int,int> PII;

int T=1;

void solve(){
	int n,k;
	int a;
	cin >> n >> k;
    vector<int> mx(k+1, -1), mn(k+1, n);

    for (int i = 0; i < n; i++) {
        cin >> a;
        mn[a] = min(mn[a], i);
        mx[a] = max(mx[a], i);
    }

    int mn2 = mn[k], mx2 = mx[k];
    for (int i = k - 1; i > 0; i--) {
        mn2 = min(mn2, mn[i]);
        mx2 = max(mx2, mx[i]);

        if (mn[i] < n) mn[i] = mn2;
        if (mx[i] > -1) mx[i] = mx2;
    }

    for (int i = 1; i <= k; i++) {
         int t=max((int)0,(int)mx[i]-mn[i]+1)*2;
         cout<<t<<" ";
    }
    cout << endl;
}

signed main(){
	cin>>T; 
    while(T--){
        solve();
    }
    return 0;
}