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.
#!/usr/bin/python2.7
figures_colors = raw_input()
arrays = raw_input()
fc_s = figures_colors.split(' ')
ar_s = arrays.split(' ')
fc = [ int(x) for x in fc_s]
ar = [ int(x) for x in ar_s]
ar_s = [[i, j] for i, j in zip(range(0, len(ar)), ar)]
ar_s = sorted(ar_s, key=lambda x : x[1])

if len(ar_s) < fc[1]:
    print("NO")
    exit()

count = 1
value = ar_s[0][1]
for x in ar_s[1:]:
    if x[1] == value:
        count = count + 1
    else:
        count = 1
        value = x[1]
    if count > fc[1]:
        print("NO")
        exit()
color = 1
for x in ar_s:
    x.append(color)
    color = color + 1
    if color > fc[1]:
        color = 1
ar_s = sorted(ar_s, key=lambda x : x[0])
res = ""
for x in ar_s:
    res = res + str(x[2]) + " "
print("YES")
print(res.strip())
