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.
def givemin(a):
	a=list(set(a))
	a.sort()
	for i in range(len(a)):
		if a[i]!=i+1:
			return i+1
	return a[-1]+1

n,k=map(int,input().split())
a=list(map(int,input().split()))
if n<k:
	print("NO")
	exit()
d={}
for i in a:
	if i in d:
		d[i]+=1
	else:
		d[i]=1
f=0
for i in d:
	if d[i]>k:
		print("NO")
		exit()
	elif d[i]==k:
		f=1

print("YES")
h={}
c=[]
if f==1:
	for i in range(n):
		if a[i] in h:
			h[a[i]]+=1
		else:
			h[a[i]]=1
		c.append(h[a[i]])
	print(*c)
else:
	j=1
	for i in a:
		if i in h:
			if j<=k:
				h[i].append(j)
				j+=1
			else:
				#print(h,i,h[i],givemin(h[i]))
				h[i].append(givemin(h[i]))
		else:
			if j<=k:
				h[i]=[j]
				j+=1
			else:
				h[i]=[1]
		c.append(h[i][-1])
	print(*c)
