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.
c = 1


def coloring(k, a):
    global c
    frequency, d, color = [0] * 5001, [[] for x in range(5002)], [0] * 5001
    for i in range(len(a)):
        frequency[a[i]] += 1
        m = a[i]
        d[m].append(i)
    for i in range(len(frequency)):
        if frequency[i] > k:
            return "NO",
    for elem in d:
        for i in elem:
            color[i] = (c % k) + 1
            c += 1
    return "YES", color[0:len(a)]


N, K = [int(i) for i in input().split()]
b = [int(x) for x in input().split()]
if len(coloring(K, b)) == 1:
    print(*coloring(K, b))
else:
    print(coloring(K, b)[0])
    print(*coloring(K, b)[1])
