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.
from sys import exit

class CAE:
  def __init__(self, value, pos):
    self.value = value
    self.pos = pos
    self.color = 1

n, k = map(int, input().split())
arr, i = [], 0
for num in map(int, input().split()):
  arr.append(CAE(num,i))
  i += 1

arr.sort(key=lambda x: x.value)
cs = set(range(2,k+1))
for i in range(1,n):
  if arr[i].value == arr[i-1].value:
    arr[i].color = arr[i-1].color+1
    cs.discard(arr[i].color)
    if arr[i].color > k:
      print('NO')
      exit(0)

arr.sort(key=lambda x: x.color)
for i in range(1,n):
  if arr[i].color == arr[i-1].color:
    if len(cs) == 0:
      break
    arr[i-1].color = cs.pop()

print('YES')
arr.sort(key=lambda x: x.pos)
for ele in arr:
  print(ele.color,end=' ')
print()