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
from functools import reduce
import bisect


def getN():
    return int(input())


def getNM():
    return map(int, input().split())


def getList():
    return list(map(int, input().split()))


def input():
    return sys.stdin.readline().rstrip()


# input = sys.stdin.buffer.readline

def index(a, x):
    i = bisect.bisect_left(a, x)
    if i != len(a) and a[i] == x:
        return -1
    return i


#############
# MAIN CODE #
#############

n, k = getNM()
arr = getList()

colors = [0] * n

z = sorted(zip(arr, [i for i in range(n)]))

values = [x[0] for x in z]
inds = [x[1] for x in z]

c = 0
nums = [0] * 5047
for i in range(n):
    if c == k:
        c = 0
    colors[i] = c
    c += 1
    nums[values[i]] += 1

if max(nums) > k:
    print("NO")
else:
    print("YES")
    for x in sorted(zip(inds, colors)):
        print(x[1] + 1, end=" ")
