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.
def solve(n, k, values):
    values_count = {}
    colors_set = []
    colors = [0] * n
    for index in range(n):
        value = values[index]
        if len(colors_set) < k:
            colors_set.append(set())
            colors_set[-1].add(value)
            colors[index] = str(len(colors_set))
        else:
            found = False
            for j in range(k):
                if value not in colors_set[j]:
                    found = True
                    colors_set[j].add(value)
                    colors[index] = str(j + 1)
                    break
            if found == False:
                return (False, None)
    return (True, colors)

n, k = map(int, input().strip().split(' '))
values = list(map(int, input().strip().split(' ')))

can_color, colors = solve(n, k, values)

if can_color == True:
    print('YES')
    print(' '.join(colors))
else:
    print('NO')
