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 

/*
                       _oo0oo_
                      o8888888o
                      88" . "88
                      (| -_- |)
                      0\  =  /0
                    ___/`---'\___
                  .' \\|     |// '.
                 / \\|||  :  |||// \
                / _||||| -:- |||||- \
               |   | \\\  -  /// |   |
               | \_|  ''\---/''  |_/ |
               \  .-\__  '-'  ___/-. /
             ___'. .'  /--.--\  `. .'___
          ."" '<  `.___\_<|>_/___.' >' "".
         | | :  `- \`.;`\ _ /`;.`/ - ` : | |
         \  \ `_.   \_ __\ /__ _/   .-` /  /
     =====`-.____`.___ \_____/___.-`___.-'=====
                       `=---='
 
*/
import java.util.function.Consumer;
import java.util.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.text.DecimalFormat;
import java.io.*;
import java.lang.Math.*;
 public class KickStart2020{
	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());}
        float nextFloat() {return Float.parseFloat(next());}
        String nextLine() {
            String str = "";
            try {str = br.readLine();}
            catch (IOException e) { e.printStackTrace();}
            return str; }}
	static boolean isBracketSequence(String s, int a, int b) {
		Stack<Character> ss = new Stack<>();
		boolean hachu = true;
		for(int i = a; i <= b; i++) {
			if(s.charAt(i) == ')' && ss.isEmpty()) {hachu = false; break;}
			if(s.charAt(i) == '(') ss.add('(');
			else ss.pop();
		}
		return ss.empty() && hachu;
	}
	static String reverseOfString(String a) {
		StringBuilder ssd = new StringBuilder();
		for(int i = a.length() - 1; i >= 0; i--) {
			ssd.append(a.charAt(i));
		}
		return ssd.toString();
	}
	static char[] reverseOfChar(char a[]) {
		char b[] = new char[a.length];
		int j = 0;
		for(int i = a.length - 1; i >= 0; i--) {
			b[i] = a[j];
			j++;
		}
		return b;
	}
	static boolean isPalindrome(char a[]) {
		boolean hachu = true;
		for(int i = 0; i <= a.length / 2; i++) {
			if(a[i] != a[a.length - 1 - i]) {
				hachu = false;
				break;
			}
		}
		return hachu;
	} 
	static long gcd(long a, long b)
	{
	    if (b == 0)
	        return a;
	    return gcd(b, a % b);
	     
	}
	static long powermod(long x, long y, long mod){
	    long ans = 1;
	    x = x % mod; 
	    if (x == 0)
	      return 0; 
	    int i = 1;
	    while (y > 0){
	      if ((y & 1) != 0)
	        ans = (ans * x) % mod;
	      y = y >> 1; 
	      x = (x * x) % mod;
	    }
	    return ans;
	  }
	static long power(long x, long y){
	    long ans = 1;
	    if (x == 0)
	      return 0; 
	    int i = 1;
	    while (y > 0){
	      if ((y & 1) != 0)
	        ans = (ans * x);
	      y = y >> 1; 
	      x = (x * x);
	    }
	    return ans;
	  }
	static boolean check(String a) {
		boolean hachu = true;
		for(int i = 0; i < a.length(); i++) {
			if(a.charAt(0) != a.charAt(i)) {hachu = false; break;}
		}
		return hachu;
	}
	 public static class Pair implements Comparable<Pair> {
	        public  int index;
	        public  int value;
	 
	        public Pair(int index, int value) {
	            this.index = index;
	            this.value = value;
	        }
	        @Override
	        public int compareTo(Pair other) {
	            //multiplied to -1 as the author need descending sort order
	            return   -1 * Integer.valueOf(this.value).compareTo(other.value);
	        }
	 }
	 static boolean equalString(int i, int j, int arr[], String b) {
		 int brr[] = new int[26];
		 for(int k = i; k <= j; k++) brr[b.charAt(k) - 'a']++;
		 for(int k = 0; k < 26; k++) {
			 if(arr[k] != brr[k]) return false;
		 }
		 return true;
	 }
	 static boolean cequalArray(String a, String b) {
		  int count[] = new int[26];
		  int count1[] = new int[26];
		  for(int i = 0; i < a.length(); i++) count[a.charAt(i) - 'a']++;
		  for(int i = 0; i < a.length(); i++) count1[b.charAt(i) - 'a']++;
		  for(int i = 0; i < 26; i++) if(count[i] != count1[i]) return false;
		  return true;
	 }
	 static boolean isPrime(long d) {
		 if(d == 1) return true;
		 for(int i = 2; i <= (long)Math.sqrt(d); i++) {
			 if(d % i == 0) return false;
		 }
		 return true;
	 }
		public static void main(String[] args) throws Exception{
			FastReader sc = new FastReader();
			PrintWriter out = new PrintWriter(System.out);
              int t = sc.nextInt();
              outerloop:
           while(t-- > 0) {
                int n = sc.nextInt();
                int k = sc.nextInt();
                Pair arr[] = new Pair[n];
                int crr[] = new int[n];
                for(int i = 0; i < n; i++) arr[i] = new Pair(i + 1, 0);
                for(int i = 0; i < n; i++) {
                	int a = sc.nextInt();
                	crr[i] = a;
                	arr[a - 1].value++;
                }
                Arrays.sort(arr);
                int sum = 0;
                for(int i = 0; i < n; i++) {
                	if(arr[i].value > k) sum += arr[i].value - k;
                	else break;
                }
                int n1 = (n - sum) / k;
                int brr[] = new int[k];
                for(int i = 0; i < k; i++) brr[i] = n1;
                HashMap<Integer, LinkedList<Integer>> ss = new HashMap<>();
                int j = 0;
                for(int i = 0; i < n; i++) {
                	if(arr[i].value == 0) break;
                	LinkedList<Integer> ssd = new LinkedList<>();
                	while(j < k && brr[j] == 0) j++;
                	if(j == k) break;
                	for(int l = 0; l < Math.min(k - j, arr[i].value); l++) {ssd.add(j + 1 + l); brr[j + l]--;}
                	ss.put(arr[i].index, ssd);
                }
                for(int i = 0; i < n; i++) {
                	if(ss.containsKey(crr[i])) {
                		if(ss.get(crr[i]).size() == 0) out.print(0 + " ");
                		else out.print(ss.get(crr[i]).poll() + " ");
                	}
                	else out.print(0 + " ");
                }
                out.println();
                
                
                 }
                 out.close();
			}
		}