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.LinkedList;
import java.util.Scanner;

public class no20200907 {

	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int k=sc.nextInt();
		int[] wallArray=new int[n];
		for(int i=0;i<n;i++)
			wallArray[i]=sc.nextInt();
		sc.close();
		if(n<k) {
			System.out.println("NO");
		}else {
			HashMap<Integer,LinkedList<Integer>> resMap=new HashMap<Integer,LinkedList<Integer>>();
			boolean sign=true;
			for(int i=0;i<n;i++) {
				if(resMap.keySet().contains(wallArray[i])) {
					LinkedList<Integer> ll=resMap.get(wallArray[i]);
					if(ll.size()>=k) {
						sign=false;
						break;
					}else {
						ll.add(i);
						resMap.put(wallArray[i],ll);
					}
				}else {
					LinkedList<Integer> ll=new LinkedList<Integer>();
					ll.add(i);
					resMap.put(wallArray[i], ll);
				}
			}
			if(!sign) {
				System.out.println("NO");
			}else {
				System.out.println("YES");
				int[] resArray=new int[n];
				int curUsed=1;
				for(Integer i:resMap.keySet()) {
					LinkedList<Integer> ll=resMap.get(i);
					for(Integer index:ll) {
						resArray[index]=curUsed++;
						if(curUsed>k)curUsed=1;
					}
				}
				for(int res:resArray)
					System.out.print(res+" ");
			}
		}
	}
	

}


			  	 			  		  	 	 	      	 	