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 find_not_in(cols, lis):
    for j in range(1, cols + 1):
        if j not in lis:
            return j


n, k = map(int, input().split())
a = list(map(int, input().split()))
di = {}
for item in a:
    if item in di:
        di[item] += 1
    else:
        di[item] = 1
li = []
for key in di:
    li.append(di[key])
min_colors = max(li)
if min_colors > k:
    print('NO')
else:
    print('YES')
    ans_li = []
    di_cols = {}
    for i in range(len(a)):
        if i < k:
            ans_li.append(i + 1)
            if a[i] not in di_cols:
                di_cols[a[i]] = [i + 1]
            else:
                di_cols[a[i]].append(i + 1)
        else:
            if a[i] not in di_cols:
                color = 1
                di_cols[a[i]] = [color]
            else:
                color = find_not_in(k, di_cols[a[i]])
                di_cols[a[i]].append(color)
            ans_li.append(color)
    print(' '.join(list(map(str, ans_li))))
