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.Scanner;
import java.util.Map;
import java.util.HashMap;
import java.util.TreeMap;
import java.lang.Math;
import java.util.Arrays;
import java.util.LinkedHashMap;
import java.util.List;
import java.util.ArrayList;

public class ArrKColorEditorial {
    private static void colorArr (int[] arr, int size, int k) {
        Map<Integer, Integer> counts = new HashMap<>();
        int[] color = new int[size];

        for (int elem : arr) {
            if (!counts.containsKey(elem)) {
                 counts.put(elem, 1);       
            }        
            else {
                counts.put(elem, counts.get(elem) + 1);
            }
        }
        
        int flag = 0;
        for (Map.Entry<Integer, Integer> entry : counts.entrySet()) {
           int key = entry.getKey();
           int value = entry.getValue();
           if (value > k) {
                flag = 1;
                break;            
            } 
        }            
        
        if (flag == 1) {
            System.out.println("NO");        
        }   
        else {
            
           Map <Integer, Integer> map = new HashMap<>();
           Map<Integer, Integer> sortMap = new TreeMap<>();            

           for (int i = 0; i < size; i++) {
                map.put(i,arr[i]);
            }    
            
            map = sortByValue(map);
            
           /* 
            for (Map.Entry<Integer, Integer> hm : map.entrySet()) {            
                System.out.println(hm.getKey() + " " + hm.getValue());
            }
            */
            
            for (int i = 0; i < size; i++) {
                color[i] = i%k + 1;
            }
            
            int c = 0;
            for (Map.Entry<Integer, Integer> hm: map.entrySet()) {
                int key = hm.getKey();
                sortMap.put(key,color[c]);
                c++;            
            }
            
            System.out.println("YES");    
            for (Map.Entry<Integer, Integer> hm: sortMap.entrySet()) {
                System.out.print(hm.getValue() + " ");            
            }

        }
    }
    
    private static Map<Integer, Integer> sortByValue (Map<Integer, Integer> map) {
        List<Map.Entry<Integer, Integer>> list = new ArrayList<>(map.entrySet());
        list.sort(Map.Entry.comparingByValue());
        
        Map<Integer, Integer> result = new LinkedHashMap<>();
        for (Map.Entry<Integer, Integer> entry : list) {
            result.put(entry.getKey(), entry.getValue());        
        }
       return result;
    }

    public static void main (String[] args) {
        try (Scanner sc = new Scanner(System.in)) {
            int size = sc.nextInt();
            int k = sc.nextInt();
            int[] arr = new int[size];
            for (int i = 0; i < size; i++) {
                arr[i] = sc.nextInt();        
            }        
            colorArr(arr,size,k);
        }
    }


}
                
