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.HashMap;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt();
        int []a = new int[n];
        StringBuffer s = new StringBuffer();
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
            s.append(" ");
        }
        String str = s.toString();
        if ( func(k , a) ) {
            System.out.println("YES");
            for (int i = 0; i < a.length; i++) {
                System.out.print(a[i] + str);
            }
        }
        else{
            System.out.println("NO");
        }
    }

    private static Boolean func(int k, int[] a) {
        HashMap<Integer,Integer> map = new HashMap<>();
        int max = 1;
        for (int i = 0; i < a.length ; i++) {
            if (map.containsKey(a[i])) {
                max = max >= map.get(a[i])? max:map.get(a[i]);
            }
            if ((k - max) < (a.length - i)  ) {
                if (map.containsKey(a[i])) {
                    map.put(a[i], map.get(a[i]) + 1);
                    if (map.get(a[i]) > k){
                        return false;
                    }
                } else {
                    map.put(a[i], 1);
                }
                a[i] = map.get(a[i]);
            }
            else{
                a[i] = ++max;
                if (max > k){
                    return false;
                }
            }
        }
        return true;
    }

}

			 		 	 	 	 					 		 		  					