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.Collections;
import java.util.Comparator;
import java.util.Scanner;

public class main {
	
	public static void swap(int arr[][], int a, int b) {
		int temp[] = new int [3];
		for(int i = 0; i < 3; i++) temp[i] = arr[a][i];
		for(int i = 0; i < 3; i++) arr[a][i] = arr[b][i];
		for(int i = 0; i < 3; i++) arr[b][i] = temp[i];
	}
	
    public static int partition(int arr[][], int low, int high, int idx) 
    { 
        int pivot = arr[high][idx];  
        int i = (low-1); 
        for (int j=low; j<high; j++) 
        { 
            if (arr[j][idx] <= pivot) 
            { 
                i++; 
                swap(arr,i,j);
            } 
        } 
 
        swap(arr,i+1,high);
        return i+1; 
    } 

    public static void sort(int arr[][], int low, int high, int idx) 
    { 
        if (low < high) 
        { 
            int pi = partition(arr, low, high, idx); 
            sort(arr, low, pi-1, idx); 
            sort(arr, pi+1, high, idx); 
        } 
    } 
    
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int k = in.nextInt();
		int arr[][] = new int [n][3];
		
		for(int i = 0; i < n; i++) {
			arr[i][0] = in.nextInt();
			arr[i][1] = i;
			arr[i][2] = -1;
		} 
		sort(arr, 0, n-1, 0);
		boolean flag = false;
		for(int i = 0; i < n; i++) {
			arr[i][2] = 1 + (i)%(k);
			if (i >= k && arr[i][0] == arr[i-k][0]) {
				flag = true;
			}
		}
		if (flag) { System.out.println("NO");	}
		else {
			sort(arr, 0, n-1, 1);
			System.out.println("YES");
			for (int i = 0; i < n; i++) System.out.print(arr[i][2]+" ");
			System.out.println();
		}
		
	}
}
