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 paint(array, n, colors_sum):
    if colors_sum > n:
        print("NO")
        return
    duplicates = defaultdict(int)
    for elem in array:
        duplicates[elem] += 1
        if duplicates[elem] > colors_sum:
            print("NO")
            return
    paints = []
    curr_color = 1
    for duplicate_value, duplicates_count in duplicates.items():
        for position, value in enumerate(array):
            if value == duplicate_value:
                color = curr_color
                paints.append((position, color))
                curr_color = 1 if curr_color == colors_sum else curr_color + 1
    sorted_by_position = sorted(paints, key=lambda tup: tup[0])
    result = ''
    for elem in sorted_by_position:
        result += str(elem[1]) + ' '
    print("YES")
    print(result)
    return
        
         
def main():
    n, k = [int(x) for x in input().split()]
    a = [int(x) for x in input().split()]
    paint(a, n, k)


if __name__ == "__main__":
    main()