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.
a,b=map(int,input().split())
l=list(map(int,input().split()))
f=list(set(l))
s=len(f)*[0]
for i in range(len(s)):
    s[i]=[]
h=a*[0]
o=a*[1]
for i in range(b):
    for j in range(len(l)):
        if o[j] and not (i+1) in s[f.index(l[j])]:
            s[f.index(l[j])]+=[i+1]
            h[j]=i+1
            o[j]=0
            break
for i in range(len(l)):
    if not h[i]:
        for j in range(1,b+1):
            if not j in s[f.index(l[i])]:
                s[f.index(l[i])]+=[j]
                h[i]=j
                break
q=1
for i in h:
    if not i:
        q=0
        break
if q:
    print("YES")
    s=''
    for i in h:
        s+=str(i)+' '
    print(s)
else:
    print("NO")
