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 game_0913 {
	public static void main(String[] args) {
		int flag = 1;
		int mix = 0;
		int mix_index = 0;
		Scanner nScanner = new Scanner(System.in);
		int n = nScanner.nextInt();
		int k = nScanner.nextInt();
		int[] wall = new int[n];
		Map<Integer, Integer> wall_kind_mount = new HashMap<Integer, Integer>();
		for (int i = 0; i < n; i++) {
			wall[i] = nScanner.nextInt();
			wall_kind_mount.put(wall[i], 0);
		}
		if (k>n) {
			System.out.println("NO");
		}else {
			for (int i = 0; i < wall.length; i++) {
				wall_kind_mount.put(wall[i], wall_kind_mount.get(wall[i])+1);
				if (wall_kind_mount.get(wall[i])>mix) {
					mix = wall_kind_mount.get(wall[i]);
					mix_index = wall[i];
				}
				if (mix>k) {
					System.out.println("NO");
					flag = 0;
					break;
				}
			}
			int j=k-mix;
			int x = 0;
			if (flag==1) {
				System.out.println("YES");
				if (k==n) {
					for (int sys = 0; sys < wall.length; sys++) {
						System.out.print(sys+1+" ");
					}
				}else{
					for (int i = 0; i < j; i++) {
						if (wall[i]!=mix_index) {
							System.out.print(k-x+" ");
							x = x+1;
						}else {
							System.out.print(wall_kind_mount.get(wall[i])+" ");
							wall_kind_mount.put(wall[i], wall_kind_mount.get(wall[i])-1);
							j=j+1;
						}
						
					}
					for (int i = j; i < wall.length; i++) {
						System.out.print(wall_kind_mount.get(wall[i])+" ");
						wall_kind_mount.put(wall[i], wall_kind_mount.get(wall[i])-1);
					}
				}	
			}
		}
	}
}

	   		 						  	     		 			 		