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.*;
import java.io.*;
public class ArrayKColoring {

	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		HashMap<Integer,Integer> map = new HashMap<>();
		String[] input= br.readLine().split(" ");
		int n= Integer.parseInt(input[0]);
		int k= Integer.parseInt(input[1]);
		String[] values = br.readLine().split(" ");
		int[] array = new int[n];
		int[] output = new int[n];
		for(int i=0;i<n;i++){
			array[i] = Integer.parseInt(values[i]);
			if(map.containsKey(array[i]))
			{
				map.put(array[i], map.get(array[i])+1);
			}else map.put(array[i], 1);
			output[i]=map.get(array[i]);
		}
		int max=0;
		for(int i=0;i<n;i++)
		{
			if(output[i]>max)max=output[i];
		}
		if(max>k)
		{
			System.out.println("NO");
		}else if(max==k)
		{
			System.out.println("YES");
			for(int i=0;i<n;i++)
			{
				System.out.printf("%d ",output[i]);
			}
		}else if(max<k)
		{
			int flag=0;
			for(int i=0;i<n;i++)
			{
				if(output[i]==max)
				{
					flag=array[i];
					break;
				}
			}
			for(int i=n-1;i>=0;i--)
			{
				if(array[i]!=flag && k>max)
				{
					output[i]=k--;
				}
			}
			if(k>max)
			{
				System.out.println("NO");
			}else
			{
				System.out.println("YES");
				for(int i=0;i<n;i++)
				{
					System.out.printf("%d ",output[i]);
				}
			}
		}
	}

}
