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.
n,k = map(int,input().split())
walls = list(map(int,input().split()))
wall_color = {}
for wall in walls:
    wall_color[wall] = wall_color.get(wall,0)+1
if max(wall_color.values())<=k and n>=k: 
    print("YES")
    res = sorted(list(wall_color.items()),key=lambda x:x[1],reverse=True)
    colors = [i[1] for i in res]
    start_color = {}
    start_color[res[0][0]] = 1
    cur_sum = 0
    for i in range(n):
        cur_sum +=res[i][1]
        if i>0:
            start_color[res[i][0]] = start_color[res[i-1][0]]+colors[i-1]
        if cur_sum>=k:
            start_color[res[i][0]] = k-res[i][1]+1
            break
    res = []
    for  wall in walls:
        if wall in start_color:
            res.append(str(start_color[wall]))
            start_color[wall] +=1
        else:
            res.append("1")
            start_color[wall] = 2  
    print(' '.join(res))
else:
    print("NO")
	 	     		 	 			 	 	  		 	 		