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 

import java.util.*;
import java.io.*;

public class s {
    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()); }
    }
    public static void main(String[] args) throws IOException{
        FastReader fast = new FastReader();
        int t = fast.nextInt();
        while(t-->0){
            int n = fast.nextInt();
            int k = fast.nextInt();
            int[] arr = new int[n];
            for(int i = 0 ; i < n ; i++)
                arr[i] = fast.nextInt();
            int max = 0;
            for(int a:arr) if(max<a) max = a;
            int[] freq = new int[max+1];
            for(int a:arr) freq[a]++;
            int count = 0, temp = 0;
            for(int a:freq)
                if(a>=k) count++;
                else temp += a;
            count += temp/k;
            int[] ans = new int[n];
            for(int i = 1; i<=k ; i++)
            {
                temp = count;
                HashSet<Integer> set = new HashSet<>();
                for(int j = 0 ;j<n ;j++)
                {
                    if(temp>0)
                    {
                        if(ans[j]==0 && !set.contains(arr[j]))
                        {  ans[j] = i;
                            temp--;
                            set.add(arr[j]);
                        }
                    }else{
                        break;
                    }
                }
            }

            for(int a:ans) System.out.print(a+" ");
            System.out.println();


        }
    }
}

//import java.io.*;
//public class s {
//    public static void main(String[] args) throws IOException {
//        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
//        int t = Integer.parseInt(br.readLine());
//        while(t-->0){
//            String str = br.readLine();
//            if(str.length()<=1){
//                System.out.println("0");continue;
//            }
//            int[] arr = new int[26];
//            for(int i = 0 ; i < str.length() ; i++)
//            {
//                arr[str.charAt(i)-'a']++;
//            }
//            int div = 0;
//            int ans = 0;
//            for(int i = 0; i<26 ; i++)
//            {
//                if(arr[i]>=2) ans++;
//                else if(arr[i]==1) div++;
//            }
//            ans += (div/2);
//            System.out.println(ans);
//        }
//    }
//
//}


//    public static void main(String[] args) throws IOException {
//        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
//        int t = Integer.parseInt(br.readLine());
//        while(t-->0){
//            long n = Long.parseLong(br.readLine());
//            long x = n/3;
//            long y = n%3;
//            if(y==0) System.out.println(x+" "+x);
//            else if(y==1) System.out.println((x+1)+" "+x);
//            else System.out.println(x+" "+(x+1));
//        }
//    }