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 = input().split(' ')
n = int(n)
k = int(k)
m = input().split(' ')
colors = []
used = []
used_colors = []
max_k = 1
if n < k:
    print('NO')
else:
    for i in range (0,len(m)):
        if m[i] not in used:
            colors.append(1)
            used.append(m[i])
        else:
            j = i - 1
            while m[i] != m[j]:
                j = j - 1
            colors.append(colors[j] + 1)
            if colors[j] + 1 > max_k:
                max_k = colors[j] + 1
    if max_k > k:
        print('NO')
    else:
        if max_k < k:
            j = 0
            i = max_k + 1
            while i <= k:
                if colors[j] in used_colors:
                    colors[j] = i
                    i = i+1
                else:
                    used_colors.append(colors[j])
                j = j + 1
        print('YES')
        print(*colors, sep=' ')
            