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.lang.*;
import java.util.*;
public class there{
	public static void main(String args[]){
	Scanner sc= new Scanner(System.in);
	int n = sc.nextInt();
		int k = sc.nextInt();
	int col[] = new int[n];
		int counts[] = new int[5001];
		int[]  arr = new int[n];
		boolean flag = true;
		for(int i=0; i<n; i++) {
			int c = sc.nextInt();
			counts[c]++;
			col[i] = counts[c];
			arr[i] = c;
			if(counts[c] > k)
				flag = false;
		}
		int mask[] = new int[5001];
		for(int i=1; i<5001; i++) {
			mask[i] = counts[i-1] + mask[i-1];
		}
		for(int i=0; i<n; i++) {
			col[i] = (col[i] + mask[arr[i]])% k;
			col[i] = col[i] == 0? k : col[i];
		}
		if(!flag || k > n) {
			System.out.println("NO");
		} else {
			System.out.println("YES");
			for(int x: col) 
				System.out.print(x+" ");
		}
	}
}