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.
//package codeforces.div2;

import java.util.*;

public class ArrayKColoring {

    static public void print(int arr[], int k) {

        HashMap<Integer, Integer> map = new HashMap<>();
        int max = 0;
        int va = 0;
        for(int i = 0; i < arr.length; i++) {
            map.put(arr[i], map.getOrDefault(arr[i], 0) + 1);
            if(map.get(arr[i]) > max) {
                max = Math.max(max, map.get(arr[i]));
                va = arr[i];
            }
        }
        if(max > k || arr.length < k) {
            System.out.println("NO");
        } else {



            System.out.println("YES");
            int res[] = new int[arr.length];
            int col = 1;
            if(arr.length==k) {
                for(int i = 0; i < arr.length; i++) {
                    res[i] = col++;
                }
            } else {
                map = new HashMap<>();

                for (int i = 0; i < arr.length; i++) {
                    int val = arr[i];
                    res[i] = map.getOrDefault(val, 0) + 1;
                    map.put(val, res[i]);
                }
                int rem = k - max;
                if(rem > 0 && k > 0) {
                    HashSet<Integer> set = new HashSet<>();
                    for (int i = arr.length-1; i >= 0; i--) {
                        if(set.contains(res[i]) && rem > 0) {
                            res[i] = k;
                            k--;
                            rem--;
                        }
                       set.add(res[i]);
                    }
                }
            }

            for(int i : res) {
                System.out.print(i + " ");
            }

        }
    }

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