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 ArrayKColoring {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int k = scanner.nextInt();
        Map<Integer, Vector> arr = new HashMap<>();
        int[] nums = new int[n];
        for (int i = 0; i < n; i++) {
            int x = scanner.nextInt();
            nums[i] = x;
            if (!arr.containsKey(x)) {
                Vector<Integer> v = new Vector<>();
                v.add(i);
                arr.put(x, v);
            } else {
                Vector v = arr.get(x);
                v.add(i);
                arr.put(x, v);
            }
            if (arr.get(x).size() > k) {
                System.out.println("NO");
                return;
            }
        }

        int color =  0;
        int[] ans = new int[n];
        for (int i = 0; i < n; i++) {
            if (ans[i] == 0) {
                Vector v = arr.get(nums[i]);
                for (int j = 0; j < v.size(); j++) {
                    ans[(int) v.get(j)] = color + 1;
                    color++;
                    color %= k;
                }
            }
        }

//        System.out.println(Arrays.toString(ans));
        System.out.println("YES");
        for (int i = 0; i < n; i++)
            System.out.print(ans[i] + " ");
    }
}
