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 CodeForces {
    static HashMap<String, Boolean> hs;
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);


        int n = Integer.parseInt(scan.next());
        int k = Integer.parseInt(scan.next());

        int[] arr = new int[n];
        int[] ans = new int[n];
        for(int i = 0; i < arr.length; i++){
            arr[i] = Integer.parseInt(scan.next());
        }

        if(arr.length < k){
            System.out.println("NO");
            System.exit(0);
        }

        HashMap<Integer, HashSet<Integer>> paints = new HashMap<>();
        for(int i = 0; i < k; i++){
            paints.put(i, new HashSet<>());
        }

        HashMap<Integer, Integer> hs = new HashMap<>();

        for(int i : arr){
            if(!hs.containsKey(i)){
                hs.put(i, 0);
            }

        }

        for(int i = 0; i < arr.length; i++){
            int val = arr[i];
            int id  = hs.get(arr[i]);

            if(paints.get(id).contains(val)){
                System.out.println("NO");
                System.exit(0);
            }else{
                paints.get(id).add(val);
                hs.put(val, (id + 1) % k);
                ans[i] = id + 1;
            }
        }

        Stack<Integer> unused = new Stack<>();
        for(int i : paints.keySet()){
            if(paints.get(i).size() == 0)
                unused.push(i);
        }

        for(int i = 0; i < ans.length && !unused.isEmpty(); i++){

            if(paints.get(ans[i] - 1).size() > 1) {
                int original = arr[i];

                paints.get(ans[i] - 1).remove(original);
                ans[i] = unused.pop() + 1;
            }
        }


        if(!unused.isEmpty()){
            System.out.println("NO");
        }else {
            System.out.println("YES");
            for (int i : ans) {
                System.out.print(i + " ");
            }
        }
    }
}