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.io.*;
import java.util.*;
public class Main {
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int n=scan.nextInt();
        int k=scan.nextInt();
        HashSet<Integer> set=new HashSet<>();
        int[] a=new int[n];
        int[] b=new int[5001];
        ArrayList<Integer>[] arr=new ArrayList[5001];
        int j=1;
        for(int i=0;i<n;i++){
            a[i]=scan.nextInt();

            b[a[i]]++;
            set.add(a[i]);
        }
        for(int i=1;i<=5000;i++){
            arr[i]=new ArrayList<>();
            if(b[i]>k){
                System.out.print("NO");
                return;
            }
        }
        for(int i=0;i<5001;i++){
            while(b[i]--!=0){
                arr[i].add(j++);
                if(j>k)
                    j=1;
            }
        }
        System.out.println("YES");
        for(int i=0;i<n;i++){
            int curr=a[i];
            System.out.print(arr[curr].remove(0)+" ");
        }









    }
}