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 VJ0907 {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int k = in.nextInt();
        List<Integer> a = new ArrayList<>(n);
        for (int i=0;i<n;i++){
            a.add(in.nextInt());
        }
        Map<Boolean, List<Integer>> an = calAn(n, k, a);
        if((boolean)an.keySet().toArray()[0]){
            System.out.println("YES");
            for(int i:an.get(true)){
                System.out.printf("%d ", i);
            }
        }else{
            System.out.println("NO");
        }
    }

    public static Map<Boolean, List<Integer>> calAn(int n, int k, List<Integer> a){
        Map<Boolean, List<Integer>> r = new HashMap<>(1);
        if(k>n){
            r.put(false, a);
            return r;
        }else if(k == n){
            List<Integer> l = new ArrayList<>(k);
            for (int i=1;i<=k;i++){
                l.add(i);
            }
            r.put(true, l);
            return r;
        }else{
            Set<Integer> set = new HashSet();
            a.forEach(i->set.add((Integer) i));
            int[] tuSe = new int[n];
            int sz = 1;
            int f = 1;
            for (Integer integer : set) {
                int x = integer;
                for (int i = 0; i < n; i++) {
                    if ((int) a.get(i) == x) {
                        if(f > k){
                            r.put(false, Collections.emptyList());
                            return r;
                        }
                        tuSe[i] = sz;
                        if(sz == k){
                            sz = 1;
                        }else {
                            sz++;
                        }
                        f++;
                    }
                }
                f = 1;
            }
            List<Integer> tt = new ArrayList<>();
            for (int i:tuSe){
                tt.add(i);
            }
            r.put(true, tt);
            return r;
        }
    }
}

  	 		 		 	 	 	 	   				     	