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 collections

if __name__ == "__main__":

    line1 = input()
    n, k = [int(x) for x in line1.split()]
    line2 = input()
    arr = [int(x) for x in line2.split()]
    element_index = [[] for _ in range(max(arr))]
    for idx, x in enumerate(arr):
        element_index[x-1].append(idx)
    arr_count = collections.Counter(arr)

    max_element_len = arr_count.most_common(1)[0][1]

    res = [0 for _ in range(n)]

    if len(arr) < k or max_element_len > k:
        print("NO")
    else:
        c = 1
        for indexs in element_index:
                for idx in indexs:
                    res[idx] = c
                    c += 1
                    if c > k:
                        c = 1
        print("YES")
        print(*res, sep=" ")
	   				 	 			  				 	 	  		 	