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 Test4{
	
	public static void main(String[] args) {
		int n,k,i,j;
		Scanner sc = new Scanner(System.in);
		n = sc.nextInt();
		k = sc.nextInt();
		int a[] = new int[n];
		int res[] = new int[n];
		Map<Integer,Integer> walls = new HashMap<Integer,Integer>();
		int color_use_max = 1;
		for(i=0;i<n;i++) {
			a[i] = sc.nextInt();
			if(walls.get(a[i]) == null) {
				walls.put(a[i], 1);
				res[i] = 1;
			}
			else {
				int value = walls.get(a[i]);
				value++;
				walls.put(a[i], value);
				res[i] = value;
				color_use_max = Math.max(color_use_max, value);
			}
		}
		if(color_use_max > k) {
			System.out.println("NO");
		}
		else {
			System.out.println("YES");
			int curColor = color_use_max + 1;
			boolean is_first = true;
			for(j=1;j<=k;j++) {
				if(curColor > k) {
					break;
				}
				is_first = true;
				for(i=0;i<n;i++) {
					if(res[i] == j) {
						if(is_first) {
							is_first = false;
							continue;
						}
						walls.put(a[i], curColor);
						res[i] = curColor;
						curColor++;
					}
					if(curColor > k) {
						break;
					}
				}
			}
			for(i=0;i<n;i++) {
				System.out.print(res[i]+" ");
			}
		}
	}
}
 				  	       			 	 	     	 	