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 cf {
	static Reader sc = new Reader();
	static PrintWriter out = new PrintWriter(System.out);
	static long mod = (long) 1e9 + 7;

	public static void main(String[] args) {
		int tc = sc.ni();
		while (tc-- > 0) {
			int n = sc.ni(), k = sc.ni();
			int[] arr = sc.nai(n);
			HashMap<Integer, Integer> hm = new HashMap<>();
			for (int e : arr) {
				hm.put(e, hm.getOrDefault(e, 0) + 1);
			}
			HashSet<Integer> all = new HashSet<>();
			int rem = n;
			for (int key : hm.keySet()) {
				if (hm.get(key) >= k) {
					all.add(key);
					rem -= hm.get(key);
				}
			}

			int count = rem / k, curr = 1;
			// out.println("rem " + rem);
			HashMap<Integer, Integer> val = new HashMap<>();
			for (int e : all)
				val.put(e, 1);
			for (int i = 0; i < n; i++) {
				if (all.contains(arr[i])) {
					if (val.get(arr[i]) <= k) {
						out.print(val.get(arr[i]) + " ");
						val.put(arr[i], val.get(arr[i]) + 1);
					} else {
						out.print(0 + " ");
					}
				} else {
					if (curr > k) {
						curr = 1;
						count--;
					}
					if (count > 0) {
						out.print(curr + " ");
						curr++;
					} else {
						out.print(0 + " ");
					}
				}
			}
			out.println();
		}
		out.close();
	}

	static boolean solve(char[] s, char[] t) {
		for (int i = 0; i < s.length; i++) {
			if (s[i] == t[0]) {
				if (check(s, t, i, 0))
					return true;
			}
		}
		return false;
	}

	static boolean check(char[] s, char[] t, int si, int ti) {
		if (ti >= t.length - 1)
			return true;
		if (si == s.length)
			return false;

		ti++;
		for (int j = si + 1; j < s.length; j += 2) {
			if (s[j] == t[ti])
				return check(s, t, j, ti);
		}
		return false;
	}

	public static long pow(long a, long b, long m) {
		if (b == 0) {
			return 1;
		}
		if (b % 2 == 0) {
			return pow((a * a) % m, b / 2, m) % m;
		} else {
			return (a * pow((a * a) % m, b / 2, m)) % m;
		}
	}

	// snippets

	static class Pair implements Comparable<Pair> {
		int x;
		int y;

		Pair(int x, int y) {
			this.x = x;
			this.y = y;

		}

		@Override
		public int compareTo(Pair o) {
			if (this.x > o.x)
				return 1;
			else if (this.x < o.x)
				return -1;
			else {
				if (this.y > o.y)
					return 1;
				else if (this.y < o.y)
					return -1;
				else
					return 0;
			}
		}

		public int hashCode() {
			int ans = 1;
			ans = x * 31 + y * 13;
			return ans;
		}

		@Override
		public boolean equals(Object o) {
			if (this == o) {
				return true;
			}
			if (o == null) {
				return false;
			}
			if (this.getClass() != o.getClass()) {
				return false;
			}
			Pair other = (Pair) o;
			if (this.x == other.x && this.y == other.y) {
				return true;
			}
			return false;
		}

	}

	static void add_map(HashMap<Integer, Integer> map, int v) {
		if (!map.containsKey(v)) {
			map.put(v, 1);
		} else {
			map.put(v, map.get(v) + 1);
		}
	}

	static void remove_map(HashMap<Integer, Integer> map, int v) {
		if (map.containsKey(v)) {
			map.put(v, map.get(v) - 1);
			if (map.get(v) == 0)
				map.remove(v);
		}
	}

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

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

	static void sort(int[] arr) {
		// shuffle
		Random rand = new Random();
		for (int i = 0; i < arr.length; i++) {
			int j = rand.nextInt(i + 1);
			int tmp = arr[i];
			arr[i] = arr[j];
			arr[j] = tmp;
		}
		Arrays.sort(arr);
	}

	static void sort(long[] arr) {
		// shuffle
		Random rand = new Random();
		for (int i = 0; i < arr.length; i++) {
			int j = rand.nextInt(i + 1);
			long tmp = arr[i];
			arr[i] = arr[j];
			arr[j] = tmp;
		}
		Arrays.sort(arr);
	}

	static boolean isPrime(int n) {
		if (n <= 1)
			return false;
		if (n <= 3)
			return true;
		if (n % 2 == 0 || n % 3 == 0)
			return false;
		double sq = Math.sqrt(n);

		for (int i = 5; i <= sq; i = i + 6)
			if (n % i == 0 || n % (i + 2) == 0)
				return false;
		return true;
	}

	static boolean isPrime(long n) {
		if (n <= 1)
			return false;
		if (n <= 3)
			return true;
		if (n % 2 == 0 || n % 3 == 0)
			return false;
		double sq = Math.sqrt(n);

		for (int i = 5; i <= sq; i = i + 6)
			if (n % i == 0 || n % (i + 2) == 0)
				return false;
		return true;
	}

	static void print_arr(int A[]) {
		for (int i : A) {
			System.out.print(i + " ");
		}
		System.out.println();
	}

	static void print_arr(long A[]) {
		for (long i : A) {
			System.out.print(i + " ");
		}
		System.out.println();
	}

	static void print_arr(char A[]) {
		for (char i : A) {
			System.out.print(i + " ");
		}
		System.out.println();
	}

	static int min(int a, int b) {
		return Math.min(a, b);
	}

	static int min(int a, int b, int c) {
		return Math.min(a, Math.min(b, c));
	}

	static int min(int a, int b, int c, int d) {
		return Math.min(a, Math.min(b, Math.min(c, d)));
	}

	static int max(int a, int b) {
		return Math.max(a, b);
	}

	static int max(int a, int b, int c) {
		return Math.max(a, Math.max(b, c));
	}

	static int max(int a, int b, int c, int d) {
		return Math.max(a, Math.max(b, Math.max(c, d)));
	}

	static long min(long a, long b) {
		return Math.min(a, b);
	}

	static long min(long a, long b, long c) {
		return Math.min(a, Math.min(b, c));
	}

	static long min(long a, long b, long c, long d) {
		return Math.min(a, Math.min(b, Math.min(c, d)));
	}

	static long max(long a, long b) {
		return Math.max(a, b);
	}

	static long max(long a, long b, long c) {
		return Math.max(a, Math.max(b, c));
	}

	static long max(long a, long b, long c, long d) {
		return Math.max(a, Math.max(b, Math.max(c, d)));
	}

	static int max(int A[]) {
		int max = Integer.MIN_VALUE;
		for (int i = 0; i < A.length; i++) {
			max = Math.max(max, A[i]);
		}
		return max;
	}

	static int min(int A[]) {
		int min = Integer.MAX_VALUE;
		for (int i = 0; i < A.length; i++) {
			min = Math.min(min, A[i]);
		}
		return min;
	}

	static long max(long A[]) {
		long max = Long.MIN_VALUE;
		for (int i = 0; i < A.length; i++) {
			max = Math.max(max, A[i]);
		}
		return max;
	}

	static long min(long A[]) {
		long min = Long.MAX_VALUE;
		for (int i = 0; i < A.length; i++) {
			min = Math.min(min, A[i]);
		}
		return min;
	}

	static long sum(int A[]) {
		long sum = 0;
		for (int i : A) {
			sum += i;
		}
		return sum;
	}

	static long sum(long A[]) {
		long sum = 0;
		for (long i : A) {
			sum += i;
		}
		return sum;
	}

	static ArrayList<Integer> sieve(int n) {
		ArrayList<Integer> primes = new ArrayList<>();
		boolean[] isPrime = new boolean[n];
		Arrays.fill(isPrime, true);
		isPrime[0] = isPrime[1] = false;
		for (int i = 2; i * i <= n; i++) {
			if (isPrime[i]) {
				for (int j = i * i; j < n; j += i) {
					isPrime[j] = false;
				}
			}
		}
		for (int i = 2; i < n; i++) {
			if (isPrime[i])
				primes.add(i);
		}
		return primes;
	}

	static class Reader {
		BufferedReader br;
		StringTokenizer st;

		Reader() {
			br = new BufferedReader(new InputStreamReader(System.in));
			st = new StringTokenizer("");
		}

		Reader(File f) throws FileNotFoundException {
			br = new BufferedReader(new FileReader(f));
			st = new StringTokenizer("");
		}

		String next() {
			while (!st.hasMoreTokens())
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
				}
			return st.nextToken();
		}

		int ni() {
			return Integer.parseInt(next());
		}

		long nl() {
			return Long.parseLong(next());
		}

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

		int[] nai(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = ni();
			return a;
		}

		long[] nal(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nl();
			return a;
		}
	}

}