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.*;

public class Solution {
    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt(), k=sc.nextInt();
        HashMap<Integer, List<Integer>> paintIndexs=new HashMap<>();
        int temp=0;
        for (int i=0; i<n; i++) {
            temp=sc.nextInt();
            if (paintIndexs.containsKey(temp)) {
                paintIndexs.get(temp).add(i);
            } else {
                paintIndexs.put(temp, new ArrayList<Integer>());
                paintIndexs.get(temp).add(i);
            }
        }

        int maxCount=0;
        for (int key : paintIndexs.keySet()) {
            maxCount=Math.max(paintIndexs.get(key).size(), maxCount);
        }
        if (k<maxCount) {
            System.out.println("NO");
            return;
        }

        int[] colors=new int[n];
        int curIndex=1;
        for (int key : paintIndexs.keySet()) {
            for (int wallIndex : paintIndexs.get(key)) {
                colors[wallIndex]=curIndex++;
                if (curIndex == k+1) curIndex=1;
            }
        }

        System.out.println("YES");
        System.out.print(colors[0]);
        for (int i=1; i<n; i++) {
            System.out.print(" "+colors[i]);
        }
        System.out.println();

    }

}

   	 	    	 					 		 		 		