You are given an array a consisting of n integer numbers.

You have to color this array in k colors in such a way that: 

  * Each element of the array should be colored in some color; 
  * For each i from 1 to k there should be at least one element colored in the i-th color in the array; 
  * For each i from 1 to k all elements colored in the i-th color should be distinct. 



Obviously, such coloring might be impossible. In this case, print "NO". Otherwise print "YES" and any coloring (i.e. numbers c_1, c_2, ... c_n, where 1 ≤ c_i ≤ k and c_i is the color of the i-th element of the given array) satisfying the conditions above. If there are multiple answers, you can print any.

Input

The first line of the input contains two integers n and k (1 ≤ k ≤ n ≤ 5000) — the length of the array a and the number of colors, respectively.

The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 5000) — elements of the array a.

Output

If there is no answer, print "NO". Otherwise print "YES" and any coloring (i.e. numbers c_1, c_2, ... c_n, where 1 ≤ c_i ≤ k and c_i is the color of the i-th element of the given array) satisfying the conditions described in the problem statement. If there are multiple answers, you can print any.

Examples

Input


4 2
1 2 2 3


Output


YES
1 1 2 2


Input


5 2
3 2 1 2 3


Output


YES
2 1 1 2 1


Input


5 2
2 1 1 2 1


Output


NO

Note

In the first example the answer 2~ 1~ 2~ 1 is also acceptable.

In the second example the answer 1~ 1~ 1~ 2~ 2 is also acceptable.

There exist other acceptable answers for both examples.
import java.util.ArrayList;
import java.util.HashMap;
import java.util.Scanner;
import java.util.Set;

public class ArrayKcoloring1102_B {

	public static void main(String[] args) {
		Scanner s=new  Scanner (System.in);
		int n=s.nextInt();
		int k=s.nextInt();
		int[] array=new int[n];
		HashMap<Integer,ArrayList<Integer>> map=new HashMap<>();
		for (int i=0;i<n;i++)
			{
				array[i]=s.nextInt();
				if (map.containsKey(array[i]))
				{
					map.get(array[i]).add(i);
				}
				else
				{
					ArrayList<Integer> temp=new ArrayList<>();
					temp.add(i);
					map.put(array[i],temp);
				}
			}
		s.close();
		Set<Integer> keys=map.keySet();
		int c=1;
		for (int i : keys)
		{
			if (map.get(i).size()>k)
			{
				System.out.println("NO");
				return;
			}
			
			for (int j=0;j<map.get(i).size();j++)
			{
			    if (c>k)
					c=1;
				array[map.get(i).get(j)]=c;
				c++;
				
			}
		}
		System.out.println("YES");
		for (int i:array)
			System.out.print(i+" ");
	}
}