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())
a = [int(x) for x in input().split()]
answers = [0] * n
colours = list(range(1, k + 1))
for i in range(0, n):
    if answers[i] == 0:
        counter = a.count(a[i])
        if counter == 1:
            answers[i] = colours[0]
            colours.remove(colours[0])
            if len(colours) == 0:
                colours = list(range(1, k + 1))
        elif counter > k:
            print("NO")
            break
        else:
            occurrences = [index for index, value in enumerate(a) if value == a[i]]
            while len(occurrences) > 0:
                answers[occurrences[0]] = colours[0]
                colours.remove(colours[0])
                if len(colours) == 0:
                    colours = list(range(1, k + 1))
                occurrences.remove(occurrences[0])
    if i == n-1:
        print("YES")
        print(*answers)