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.
import sys
def p():
    n,k = map(int,input().split())
    a = list(map(int,input().split()))
    
    a1 = [0]*5001
    res = [0]*n
    
    
    
            
       
    for i in range(0,n):
        res[i] = a1[a[i]]+1
        if res[i] > k:
            print("NO")
            sys.exit()
        a1[a[i]]+=1
    
    k1=[0]*(k+1)
    k1[0]=50007
    for i in range (0,n):
        k1[res[i]]+=1
        #k1[i]=res.count(i)
    kk=k1.count(0)
    
    i=0
    yy=1
    while kk>0:
        if k1[yy]==1:
            i=0
        
            yy+=1
        if res[i]==yy and k1[yy]>1:
            res[i]=k
            k1[yy]-=1
            k1[k]+=1
        
            kk-=1
            k-=1
        i+=1
           
    
    print("YES")
    for i in range(0,n):
        print(res[i], end = " ")

p()