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 Counter
n, k = map(int, input().split())
a = list(map(int, input().split()))
s = set(a)

c = Counter(a)
groups = []
while c:
    t = []
    for item in s:
        if item in c:
            t.append(item)
            if c[item] == 1:
                del c[item]
            else:
                c[item] -= 1
    groups.append(t)

if len(groups) > k:
    print('NO')
else:
    diff = k-len(groups)

    final_groups = []
    for group in groups:
        l = len(group)
        if diff >= l-1:
            diff -= l -1
            for x in group:
                final_groups.append([x])
        else:

            for i in range(diff):
                final_groups.append([group.pop()])
            final_groups.append(group)
            diff = 0

    d = dict(zip(range(1, k+1), final_groups))

    indexes = {}
    for i in range(n):
        if a[i] in indexes:
            indexes[a[i]] += [i]
        else:
            indexes[a[i]] = [i]

    colors = [0]*n
    for color in d:
        for val in d[color]:
            colors[indexes[val].pop()] = color
    print('YES')
    print(*colors)