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.Map;
import java.util.Scanner;

public class Solution {


    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        int k = scan.nextInt();
        String word = "YES";
        int[] array = new int[n];
        int[] newArray = new int[n];
        HashMap <Integer,Integer> map = new HashMap<>();

            for (int i = 0; i < n; i++) {
                array[i] = scan.nextInt();
                if (!map.containsKey(array [i])) map.put(array[i], 1);
                else {
                    map.replace(array[i], map.get(array[i])+1);
                    if (map.get(array [i]) > k) word = "NO";
                }
            }
        int copy = k;
        for (Map.Entry <Integer,Integer> pair : map.entrySet()) {
            for (int i = 0; i < n; i++) {
                if ( copy == 0) copy = k;

                if ( array [i] == pair.getKey()){
                newArray [i] = copy;
                copy--;
                }
            }

        }
        System.out.println(word);
        if (word.length() > 2) {
            for (int i = 0; i < n; i++) {
                System.out.print(newArray[i] + " ");
            }
        }
    }
}