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 color_update(c, k):
    if c<k:
        return c+1
    else:
        return 1
s1 = input().split()
n = int(s1[0])
k = int(s1[1])
arr = list(map(int, input().split()))
freq = {}
color = {}
colors = []
for x in arr:
    try:
        freq[x]+=1
    except:
        freq[x]=1
freqs = list(freq.values())
if max(freqs)>k:
    print('NO')
else:
    print('YES')
    for x in arr:
        color[x] = []
    cval = 1
    for x in arr:
        if cval not in color[x]:
            colors.append(cval)
            color[x].append(cval)
            cval = color_update(cval,k)
        else:
            c = color[x][-1]
            cval = color_update(c,k)
            while cval in color[x]:
                cval = color_update(cval,k)
            colors.append(cval)
            color[x].append(cval)
    print(' '.join(list(map(str, colors))))