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

public class Main
{

	public static FastIO io = new FastIO();

	public static void main(String[] args)
	{
		int t = io.nextInt();
		while(t-- > 0) solve();
		io.close();
	}

	static class Entity {
		int n;
		Map<Integer, Integer> indices = new HashMap<>();
		int count;
	}
	static class Color {
		int val, freq=0;
		Color(int v) {val = v;}
	}
	private static void solve()
	{
		int n = io.nextInt(), k = io.nextInt();
		int[] a = new int[n];
		for(int i=0; i<n; i++) a[i] = io.nextInt();
		Map<Integer, Entity> map = new HashMap<>();
		for(int i=0; i<n; i++) {
			if(!map.containsKey(a[i])) {
				map.put(a[i], new Entity());

			}
			map.get(a[i]).count += 1;
			map.get(a[i]).indices.put(i, 0);
		}

		PriorityQueue<Color> pq = new PriorityQueue<>(Comparator.comparing(t -> t.freq));
		for(int i=0; i<k; i++) pq.add(new Color(i+1));
		int[] colorCount = new int[k];
		int equalNumber = Integer.MAX_VALUE;

		for(int key : map.keySet()) {
			int count = 0;
			Entity entity = map.get(key);
			List<Color> temp = new ArrayList<>();
			for(int index : entity.indices.keySet()) {
				if(pq.isEmpty()) break;
				Color minColor = pq.poll();
				entity.indices.put(index, minColor.val);
				colorCount[minColor.val - 1] += 1;
				count += 1;
				minColor.freq += 1;
				temp.add(minColor);
				if(count == k) break;
			}
			pq.addAll(temp);
		}

		for(int i=0; i<k; i++) {
			if(colorCount[i] > 0) equalNumber = Math.min(equalNumber, colorCount[i]);
			colorCount[i] = 0;
		}


		int[] solution = new int[n];

		for(int key : map.keySet()) {
			Entity entity = map.get(key);
			for(int index : entity.indices.keySet()) {
				if(entity.indices.get(index) == 0 || colorCount[entity.indices.get(index) - 1] == equalNumber) continue;
				solution[index] = entity.indices.get(index);
				colorCount[entity.indices.get(index) - 1] += 1;
			}
		}

		for(int x : solution) io.print(x + " ");
		io.println();

	}

	static void sort(int[] a)
	{
		ArrayList<Integer> l = new ArrayList<>(a.length);
		for (int i : a) l.add(i);
		Collections.sort(l);
		for (int i = 0; i < a.length; i++) a[i] = l.get(i);
	}

	static class FastIO extends PrintWriter
	{
		private InputStream stream;
		private byte[] buf = new byte[1 << 16];
		private int curChar, numChars;

		public FastIO()
		{
			this(System.in, System.out);
		}

		public FastIO(InputStream i, OutputStream o)
		{
			super(o);
			stream = i;
		}

		public FastIO(String i, String o) throws IOException
		{
			super(new FileWriter(o));
			stream = new FileInputStream(i);
		}

		private int nextByte()
		{
			if (numChars == -1) throw new InputMismatchException();
			if (curChar >= numChars)
			{
				curChar = 0;
				try
				{
					numChars = stream.read(buf);
				}
				catch (IOException e)
				{
					throw new InputMismatchException();
				}
				if (numChars == -1) return -1;
			}
			return buf[curChar++];
		}

		public String next()
		{
			int c;
			do
			{
				c = nextByte();
			} while (c <= ' ');
			StringBuilder res = new StringBuilder();
			do
			{
				res.appendCodePoint(c);
				c = nextByte();
			} while (c > ' ');
			return res.toString();
		}

		public String nextLine()
		{
			int c;
			do
			{
				c = nextByte();
			} while (c < '\n');
			StringBuilder res = new StringBuilder();
			do
			{
				res.appendCodePoint(c);
				c = nextByte();
			} while (c > '\n');
			return res.toString();
		}

		public int nextInt()
		{
			int c;
			do
			{
				c = nextByte();
			} while (c <= ' ');
			int sgn = 1;
			if (c == '-')
			{
				sgn = -1;
				c = nextByte();
			}
			int res = 0;
			do
			{
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = 10 * res + c - '0';
				c = nextByte();
			} while (c > ' ');
			return res * sgn;
		}

		public long nextLong()
		{
			int c;
			do
			{
				c = nextByte();
			} while (c <= ' ');
			int sgn = 1;
			if (c == '-')
			{
				sgn = -1;
				c = nextByte();
			}
			long res = 0;
			do
			{
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = 10 * res + c - '0';
				c = nextByte();
			} while (c > ' ');
			return res * sgn;
		}

		public double nextDouble()
		{
			return Double.parseDouble(next());
		}
	}
}