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
import math

sys.setrecursionlimit(10**9)

n, k = map(int, sys.stdin.readline().split())
array = list(map(int, sys.stdin.readline().split()))
color =  [[0]*k for i in range(5005)]
done = [0]*k
end = True
for i in range(n):
    first = 0
    for a in range(k):
        if 0 == done[a]:
            first = a
            break
    if color[array[i]][first] == 0:
        color[array[i]][first] = 1
        done[first]=1
        array[i] = first+1
        #print(i, first)
    else:
        #print(i)
        possible = False
        for a in range(k):
            if color[array[i]][a] == 0:
                done[a]=1
                color[array[i]][a] = 1
                array[i] = a+1
                possible = True
                break

        if not possible:
            #print("hello", i)
            end = False
    #print(array[i], color[1], color[2], color[3])

for a in range(k):
    if 0 == done[a]:
        end = False
        break

if end:
    print("YES")
    print(*array)
else:
    print("NO")



    
