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.
n,k=map(int,input().split())
l=[int(n) for n in input().split(" ")]
temp=sorted(l)
a=0
ans=[]
flag=0
for i in range(n):
    if temp[i]!=a:
        ct=1
        a=temp[i]
    else:
        ct+=1
    if ct>k:
        print("NO")
        flag=1
        break
a=0
for i in range(n):
    if temp[i]!=a:
        ans.append(1)
        a=temp[i]
    else:
        ans.append(ans[i-1]+1)
a=[]
for i in range(n):
    index=temp.index(l[i])
    a.append(ans[index])
    temp[index]=-temp[index]
b=1
q=max(a)
w=[]
for i in range(n):
    w.append(0)
for i in range(n):
    w[a[i]-1]+=1
for i in range(k,q,-1):
    a[a.index(b)]=i
    w[b-1]-=1
    if w[b-1]==1:
        b+=1
if flag==0:
    print("YES")
    for i in a:
        print(i,end=' ')