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 Test1 {

    static int x = 1;

    public static void main(String[] args){
        Scanner in = new Scanner(System.in);
        int n = in.nextInt(), k = in.nextInt(), c[] = new int[n], a[] = new int[n];
        HashMap<Integer, ArrayList<Integer>> hm = new HashMap<>();
        TreeSet<Integer> set;
        for(int i = 0; i<n; i++){
            a[i] = in.nextInt();
            if(hm.get(a[i])==null){
                ArrayList<Integer> h = new ArrayList<>();
                h.add(i);
                hm.put(a[i], h);
            }
            else{
                ArrayList<Integer> h = hm.get(a[i]);
                h.add(i);
                hm.put(a[i], h);
            }
        }

        Iterator<Map.Entry<Integer, ArrayList<Integer>>> itr = hm.entrySet().iterator();
        while(itr.hasNext()){
            Map.Entry<Integer, ArrayList<Integer>> now = itr.next();
            ArrayList<Integer> nowList = now.getValue();
            set = new TreeSet<>();
            for(int y:nowList){
                if(set.contains(x)){
                    System.out.println("NO");
                    return;
                }
                set.add(x);
                c[y] = x;
                inc(k);
            }
        }

        for(int i = 0; i<n; i++){
            if(c[i]!=0) continue;
            c[i] = x;
            inc(k);
        }
        System.out.println("YES");
        for(int y:c) System.out.print(y+" ");

    }

    static void inc(int k){
        x++;
        if(x>k) x = 1;
    }
}