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.HashSet;
import java.util.Map;
import java.util.Scanner;
import java.util.Set;

public class ArrayKColoring {

  public static void main(String[] args) {
    Scanner input = new Scanner(System.in);
    int n = input.nextInt();
    int k = input.nextInt();

    int[] a = new int[n];
    int[] colors = new int[n];
    for (int i = 0; i < n; ++i) {
      a[i] = input.nextInt();
    }

    if (k > n) {
      System.out.println("NO");
      return;
    }

    Map<Integer, Set<Integer>> elements = new HashMap<>(k);
    for (int i = 1; i <= k; ++i) {
      elements.put(i, new HashSet<>());
    }

    int initialColor = 1;
    for (int i = 0; i < n; ++i) {
      int element = a[i];

      int color = initialColor;

      while (elements.get(color).contains(element)) {
        ++color;
        if (color > k) {
          color = 1;
        }
        if (color == initialColor) {
          System.out.println("NO");
          return;
        }
      }

      elements.get(color).add(element);
      colors[i] = color;

      ++initialColor;
      if (initialColor > k) {
        initialColor = 1;
      }
    }

    System.out.println("YES");
    for (int i = 0; i < n; ++i) {
      System.out.print((i > 0 ? " " : "") + colors[i]);
    }
    System.out.println();
  }
}
