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;
import java.util.Arrays;
public class Cppp {
  public static void main(String[] args) {
    // put your code here
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int x = sc.nextInt();
    int[] c = new int[n];
    int[] y = new int[n];
    int[] w = new int[n];
    StringBuilder sb = new StringBuilder();
    for(int i = 0; i < n; i++){
      c[i] = sc.nextInt();
      y[i] = c[i];
    }
    Arrays.sort(y);
    int u = 0;
    int p = 0;
    boolean flag = true;
    for(int z : y){
      if (z == p){
        u++;
        if (u>x) {
          flag = false;
          break;
        }
      } else {
        u = 1;
        p = z;
      }
    }
    if (flag){
    int k = 0;
    for(int i = 0;i< n;){
      for(int j = 0; j < n;j++){
        if (i< n && y[i]==c[j]){
          w[j]= k%x + 1;
          k++;
          i++;
        }
      }
    }
    }
    if (flag){
    sb.append("YES\n");
      for(int r : w){
          sb.append(r).append(' ');
      }
    } else {
      sb.append("NO");
    }
    System.out.println(sb);
    sc.close();
    // 1 2 3 4 5 6 7 8 9
  }
}