This problem is an extension of the problem "Wonderful Coloring - 1". It has quite many differences, so you should read this statement completely.

Recently, Paul and Mary have found a new favorite sequence of integers a_1, a_2, ..., a_n. They want to paint it using pieces of chalk of k colors. The coloring of a sequence is called wonderful if the following conditions are met:

  1. each element of the sequence is either painted in one of k colors or isn't painted; 
  2. each two elements which are painted in the same color are different (i. e. there's no two equal values painted in the same color); 
  3. let's calculate for each of k colors the number of elements painted in the color — all calculated numbers must be equal; 
  4. the total number of painted elements of the sequence is the maximum among all colorings of the sequence which meet the first three conditions. 



E. g. consider a sequence a=[3, 1, 1, 1, 1, 10, 3, 10, 10, 2] and k=3. One of the wonderful colorings of the sequence is shown in the figure.

<image> The example of a wonderful coloring of the sequence a=[3, 1, 1, 1, 1, 10, 3, 10, 10, 2] and k=3. Note that one of the elements isn't painted.

Help Paul and Mary to find a wonderful coloring of a given sequence a.

Input

The first line contains one integer t (1 ≤ t ≤ 10000) — the number of test cases. Then t test cases follow.

Each test case consists of two lines. The first one contains two integers n and k (1 ≤ n ≤ 2⋅10^5, 1 ≤ k ≤ n) — the length of a given sequence and the number of colors, respectively. The second one contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ n).

It is guaranteed that the sum of n over all test cases doesn't exceed 2 ⋅ 10^5.

Output

Output t lines, each of them must contain a description of a wonderful coloring for the corresponding test case.

Each wonderful coloring must be printed as a sequence of n integers c_1, c_2, ..., c_n (0 ≤ c_i ≤ k) separated by spaces where

  * c_i=0, if i-th element isn't painted; 
  * c_i>0, if i-th element is painted in the c_i-th color. 



Remember that you need to maximize the total count of painted elements for the wonderful coloring. If there are multiple solutions, print any one.

Example

Input


6
10 3
3 1 1 1 1 10 3 10 10 2
4 4
1 1 1 1
1 1
1
13 1
3 1 4 1 5 9 2 6 5 3 5 8 9
13 2
3 1 4 1 5 9 2 6 5 3 5 8 9
13 3
3 1 4 1 5 9 2 6 5 3 5 8 9


Output


1 1 0 2 3 2 2 1 3 3
4 2 1 3
1
0 0 1 1 0 1 1 1 0 1 1 1 0
2 1 2 2 1 1 1 1 2 1 0 2 2
1 1 3 2 1 3 3 1 2 2 3 2 0

Note

In the first test case, the answer is shown in the figure in the statement. The red color has number 1, the blue color — 2, the green — 3.
12
10 3
3 1 1 1 1 10 3 10 10 2
4 4
1 1 1 1
1 1
1
13 1
3 1 4 1 5 9 2 6 5 3 5 8 9
13 2
3 1 4 1 5 9 2 6 5 3 5 8 9
13 3
3 1 4 1 5 9 2 6 5 3 5 8 9
10 3
3 1 1 1 1 10 3 10 10 2
4 4
1 1 1 1
1 1
1
13 1
3 1 4 1 5 9 2 6 5 3 5 8 9
13 2
3 1 4 1 5 9 2 6 5 3 5 8 9
13 3
3 1 4 1 5 9 2 6 5 3 5 8 9
 6
10 3
3 1 1 1 1 10 3 10 10 2
4 4
1 1 1 1
1 1
1
13 1
3 1 4 1 5 9 2 6 5 3 5 8 9
13 2
3 1 4 1 5 9 2 6 5 3 5 8 9
13 3
3 1 4 1 5 9 2 6 5 3 5 8 9

2 1 2 3 0 1 3 2 3 1 
1 2 3 4 
1 
1 1 1 0 1 1 1 1 0 0 0 1 0 
2 1 2 2 1 1 1 1 2 1 0 2 2 
1 1 3 2 1 3 3 1 2 2 3 2 0 
2 1 2 3 0 1 3 2 3 1 
1 2 3 4 
1 
1 1 1 0 1 1 1 1 0 0 0 1 0 
2 1 2 2 1 1 1 1 2 1 0 2 2 
1 1 3 2 1 3 3 1 2 2 3 2 0 
 2 1 2 3 0 1 3 2 3 1 
1 2 3 4 
1 
1 1 1 0 1 1 1 1 0 0 0 1 0 
2 1 2 2 1 1 1 1 2 1 0 2 2 
1 1 3 2 1 3 3 1 2 2 3 2 0 

//package com.company;/* package codechef; // don't place package name! */
import java.lang.reflect.Array;
import java.util.*;
import java.lang.*;
import java.io.*;
public class Solution{
//public class Main {
    public static int in =0;
    static class comparator implements Comparator<int[]>{
        public int compare(int[] arr1 ,int[] arr2){
            if(arr1[0]>arr2[0])
                return 1;
            else if(arr1[0]==arr2[0]){
                if(arr1[1]>arr2[1])
                    return 1;
                else
                    return -1;
            }
            return -1;
        }
    }
    static class newcomparator implements Comparator<int[]>{
        public int compare(int[] arr1 ,int[] arr2){
            if(arr1[1]>arr2[1])
                return 1;
            return -1;
        }
    }
    public static void main (String[] args) throws java.lang.Exception {
        FastReader sc = new FastReader();
        int testCase = sc.nextInt();
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
        while (testCase-- > 0) {
            int n= sc.nextInt();
            int k = sc.nextInt();
            int[] intArr =  new int[n];
            for(int i=0; i<n; i++ ){
                intArr[i] = sc.nextInt();
            }
            ArrayList<int[]> al  = new ArrayList();
            for(int i=0;i<n;i++){
                int[] inta = new int[3];
                inta[0] = intArr[i];
                inta[1] = i;
                al.add(inta);
            }
            int[] colorArr = new int[k+1];
            java.util.Collections.sort(al, new comparator());
            int color = 2;
            al.get(0)[2] = 1;
            int at=al.get(0)[0], count=1;
            for(int i=1; i<n; i++){
                if(color==k+1) color=1;
                //System.out.println("yes "+count+" "+color);
                if(al.get(i)[0]==at){
                    count++;
                    if(count<=k){
                       al.get(i)[2] = color;
                       colorArr[color]++;
                       color++;
                    }
                }else{
                    at= al.get(i)[0];
                    al.get(i)[2] = color;
                    colorArr[color]++;
                    count=1;
                    color++;
                }
            }
            colorArr[1]++;
            int min = Integer.MAX_VALUE;
            for(int i=1; i<=k; i++){
                min = Math.min(colorArr[i], min);
            }
            for(int i=1; i<=k; i++){
                colorArr[i]-=min;
                for(int j=n-1; j>=0; j--){
                    if(colorArr[i]==0) break;
                    if(al.get(j)[2]==i) {
                        al.get(j)[2]=0;
                        colorArr[i]--;
                    }
                }
            }
            java.util.Collections.sort(al, new newcomparator());
            for(int[] aa:al){
                out.write(aa+" ");
            }
            out.write("\n");
            out.flush();
        }
    }
    // Fast Reader Class
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;
        public FastReader() { br = new BufferedReader(new InputStreamReader(System.in));}
        String next() { while (st == null || !st.hasMoreElements()) { try { st = new StringTokenizer(br.readLine()); } catch (IOException e) { e.printStackTrace(); } }return st.nextToken(); }
        int nextInt() {
            return Integer.parseInt(next());
        }
        long nextLong() {
            return Long.parseLong(next());
        }
        double nextDouble() {
            return Double.parseDouble(next());
        }
        String nextLine() { String str = ""; try { str = br.readLine(); } catch (IOException e) { e.printStackTrace(); }return str; }
    }
}
