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 re, math, decimal, bisect, collections
def read(): return input().strip()
def iread(): return int(input().strip())
def viread(): return [int(_) for _ in input().strip().split()]

# code goes here
n, k = viread()
lst = viread()
freq = collections.defaultdict(int)
color = [0] * n
cused = [[a, b] for a, b in zip([0] * k, range(1, k+1))]
for i, l in enumerate(lst):
	freq[l] += 1
	color[i] = freq[l]
	if (color[i] > k):
		print("NO")
		exit()
	cused[freq[l] - 1][0] += 1
cused.sort()
# print(freq)
# print(cused)
# print(color)
for c in [x[1] for x in cused if x[0] == 0]:
	steal = -1
	while cused[steal][0] <= 1:
		steal -= 1
	color[color.index(cused[steal][1])] = c
	cused[steal][0] -= 1

print("YES")
print(*color)
