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.*;

public class B {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		ArrayList<Integer>[] colored = new ArrayList[5001];
		int[] count = new int[5001];
		for( int i = 0; i < 5001; i++ ) {
			colored[i] = new ArrayList();
		}
		int n = in.nextInt();
		int k = in.nextInt();
		int toColor = 0;
		int toFit = 0;
		boolean poss = true;
		int temp = 0;
		StringBuilder sb = new StringBuilder();		
		for( int i = 0; i < n; i++ ) {
			toColor = in.nextInt();
			toFit = i%k + 1;
			count[toColor]++;
			if( count[toColor] > k ) {
				poss = false;
				break;
			}
			while( colored[toColor].contains(toFit) ) {
				toFit = temp%k + 1;
				temp++;
			}
			colored[toColor].add(toFit);
			sb.append(toFit);
			if( i != n-1 ) sb.append(" ");
			temp = 0;
		}
		if(poss) {
			System.out.println("YES");
			System.out.println(sb.toString());
			
		} else {
			System.out.println("NO");
			
		}
	}
}