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.
from collections import defaultdict

def func():
    m = input()
    k = int(m.split(" ")[1])
    m = int(m.split(" ")[0])
    if k > m:
        print("NO")
        return
    k_l = [str(i) for i in range(1,k+1)]
    n = input()
    n = n.split(" ")

    dict_n = defaultdict(int)
    for val in n:
        dict_n[val] += 1
    result = []
    start = 0
    dict_c = {}
    for key in dict_n:
        if dict_n[key] > k:
            print("NO")
            return

        end = start+dict_n[key]
        if end % k <= start % k:
            dict_c[key] = k_l[start%k:k]+k_l[0:end%k]
        else:
            dict_c[key] = k_l[start%k:end%k]
        start = end
    for val in n:
        result.append(dict_c[val].pop())
    print("YES")
    print(" ".join(result))



func()
	 	  			     	 			  				 						