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.Scanner;

public class Ask6 {
	public static void main(String args[]) {
		Scanner sc = new Scanner(System.in);
		String temp[] = sc.nextLine().split(" ");
		int n = Integer.parseInt(temp[0]);
		int k = Integer.parseInt(temp[1]);
		int colors[] = new int[n];
		temp = sc.nextLine().split(" ");
		int values[] = new int[n];
		
		if(n<k) {
			System.out.println("NO");
			sc.close();
			return;
		}
		for(int i=0;i<n;i++) {
			values[i]=Integer.parseInt(temp[i]);
		}
		int currentColor = 1;
		for(int i=0;i<n;i++) {
			if(colors[i]!=0) {
				continue;
			}
			int currentVal = values[i];
			int seriesColor = currentColor;//the color that we started with
			colors[i]=currentColor;
			currentColor=currentColor%k+1;
			for(int j=i+1;j<n;j++) {
				if(currentVal==values[j]) {
					if(currentColor==seriesColor) {
						System.out.println("NO");
						sc.close();
						return;
					}
					colors[j]=currentColor;
					currentColor=currentColor%k+1;
				}
			}
		}
		System.out.println("YES");
		for(int i=0;i<n;i++) {
			System.out.print(colors[i]+" ");
		}
		sc.close();
	}
}
