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 random, math
from copy import deepcopy as dc
from bisect import bisect_left, bisect_right


# Function to call the actual solution
def solution(li, k):
	ma = {}
	for i in li:
		ma[i] = ma.get(i, 0) + 1
		if ma[i] > k:
			return [False, []]
	o = []
	for i in range(len(li)):
		o.append([li[i], i])
	o.sort(key = lambda x: x[0])
	for i in range(len(li)):
		o[i].append((i%k) + 1)

	out = [0]*len(li)
	for i in range(len(li)):
		out[o[i][1]] = o[i][2]
	return [True, out]

# Function to take input
def input_test():
	# for _ in range(int(input())):
		# n = int(input())
		n, k = map(int, input().strip().split(" "))
		# a, b, c = map(int, input().strip().split(" "))
		li = list(map(int, input().strip().split(" ")))
		out = solution(li, k)
		if not out[0]:
			print("NO")
		else:
			print("YES")
			print(*out[1])

# Function to check test my code
def test():
	pass


input_test()
# test()