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 ia():
    n=input().split()
    return list(map(int,n))
def ic():
    return input().split()
def ii():
    return int(input())

n,k=ia()
a=ia()

b=[0]*k

d={}
for i in a:
    d[i]=0
m=[0]*n
flag=1
if(k>n):
    print("NO")
else:
    for i in range(n):
        m[i]=d[a[i]]+1
        
        if(m[i]>k):
            flag=0
            break
        b[m[i]-1]+=1
        d[a[i]]+=1
    if(max(d.values())<k):
        j=0
        p=max(d.values())+1
        while(j<n and p<k+1):
            if(b[m[j]-1]>1):
                b[m[j]-1]-=1
                m[j]=p
                b[p-1]=1
                p+=1
            j+=1


            
    if(flag==1):
        print("YES")
        print(*m)
    else:
        print("NO")
