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
I = lambda : map(int,sys.stdin.readline().split())
n,m = I()
li = list(I())
p=[0]*n
c=0
d={}
for i in range(len(li)) :
    p[i]=[(li[i],i)]
    d[li[i]]=d.get(li[i],0)+1

p.sort()
li.sort()
#print(p,li,d)
if max(d.values()) > m  :
    exit(print("NO"))
c=1
j=1
l=[1]
for i in range(1,n) :
    if m-j == n-i :
        k=m-j
        for i in range(k) :
            #print(l)
            j+=1
            l.append(j)
        break
    if li[i]==li[i-1] :
        c=c+1
        l.append(c)
    else :
        c=1
        l.append(c)
    j=max(c,j)
#print(l)
ans=[0]*n
for i in range (n) :
    x,y=p[i][0]
    ans[y]=l[i]
print("YES")
print(*ans)