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 game3 {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        while (sc.hasNext()) {
            int n = sc.nextInt();//n面墙
            int k = sc.nextInt();//k种颜料
            int[] shuzu = new int[n];
            Map<Integer, ArrayList<Integer>> map = new HashMap<>();
            for (int i = 0; i < n; i++) {
                int temp = sc.nextInt();
                if (map.get(temp) == null) {
                    ArrayList<Integer> list = new ArrayList<>();
                    list.add(i);
                    map.put(temp, list);
                } else {
                    map.get(temp).add(i);
                }
            }
            Set<Integer> set = map.keySet();
            int color = 1;
            boolean flag = true;
            for (int i : set) {
                if (map.get(i).size() > k) {
                    flag = false;
                }
                for (int j : map.get(i)) {
                    shuzu[j] = color;
                    color++;
                    if (color > k) {
                        color = 1;
                    }
                }
            }
            if (flag) {
                System.out.println("YES");
                for (int i = 0; i < n; i++) {
                    if(i==n-1){
                        System.out.println(shuzu[i]);
                    }else{
                        System.out.print(shuzu[i]+" ");
                    }
                }
            } else {
                System.out.println("NO");
            }
        }
    }
}

					 	   	 				 	  			  	 	