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 f(l, k):
    if len(l)==1:
        return True, [1]
    output = [0]*len(l)
    i=0
    ktoosmall = False
    hitallvaluesk = False
    for value in range(1,max(l)+1):
        loc = [i for i, el in enumerate(l) if el==value]
        if len(loc)>k:
            ktoosmall = True
        for el in loc:
            output[el] = (i%k)+1
            if i==k-1:
                hitallvaluesk = True
            i += 1
    return (not ktoosmall) and (hitallvaluesk), output

row1 = input().split(' ')
n = int(row1[0])
k = int(row1[1])
l = input().split(' ')
l = [int(el) for el in l]

works, output = f(l, k)

if works:
    print('YES')
    outputstring = ' '.join([str(el) for el in output])
    print(outputstring)
else:
    print('NO')



