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.*;

import java.lang.Math;

public class B2_Wonderful_Coloring_2{

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;
    }

    int[] readintarray(int n) {
        int res [] = new int[n];
        for(int i = 0; i<n; i++)
        res[i] = nextInt();
        return res;
    }

    long[] readlongarray(int n) {
        long res [] = new long[n];
        for(int i = 0; i<n; i++)
        res[i] = nextLong();
        return res;
    }

}

    static int gcd(int a, int b) {
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }

    static int lcm(int a, int b) {
         return (a / gcd(a, b)) * b;
    }

    public static void main(String args[]) throws IOException {
        FastReader s=new FastReader();
        int t;
        t =s.nextInt();
        while (t-- > 0) {

            int n=s.nextInt();
            int k=s.nextInt();
            int[] a=s.readintarray(n);
           
            HashMap<Integer,Integer> freq=new HashMap<Integer,Integer>();
            HashMap<Integer,Vector<Integer>> indexmap=new HashMap<Integer,Vector<Integer>>();

            for(int i=0;i<n;i++){
                if(freq.containsKey(a[i])){
                  if(freq.get(a[i])<k){
                        freq.put(a[i],freq.get(a[i])+1);
                        Vector<Integer> indices=indexmap.get(a[i]);
                        indices.add(i);
                        indexmap.put(a[i],indices);

                    }  
                }
                else{
                    freq.put(a[i],1);
                    Vector<Integer> indices=new Vector<Integer>();
                    indices.add(i);
                    indexmap.put(a[i],indices);

                }
            }
            // ans[10] = {0};
            // color = 1;

            // 3 -> 0 6
            //      1 2
            // 1 -> 1 2 3
            //      3 1 2    
            // 10-> 5 7 8 
            //      3 1 2
            // 2 -> 9
            //      3

                 

            //      ans =  [1,3,1,2,0,3,2,1,2,3]
            int color=1;
            int[] ans=new int[n];
            Arrays.fill(ans,0);

            for(Map.Entry<Integer,Vector<Integer>> m: indexmap.entrySet()){
                Vector<Integer> index=(Vector<Integer>)m.getValue();
                for(int i=0;i<index.size();i++){
                    ans[index.get(i)]=color;
                    color++;
                    if(color>k)
                    color=1;
                }

            }
            
            // System.out.println(color);
            for(int i=1;i<=color-1;i++){
                for(int j=0;j<n;j++){
                    if(ans[j]==i){
                        ans[j]=0;
                        break;
                    }
                }
            }

            for(int i=0;i<n;i++){
                System.out.print(ans[i]+" ");
            }
            System.out.println();
        }
    }
}