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.
n, d = input().split()
n = int (n)
d = int (d)
#n = int(input())
a = list(map(int, input().split()))
#g = list(map(int, input().split()))
#x1, y1, x2, y2 =map(int,input().split())
#n = int(input())
# = [""]*n
#f = [0]*n
#t = [0]*n
#f = []

#h = [""] * n
#f1 = sorted(f, key = lambda tup: tup[0])

i = 1
j = 0
w = 0
m = 1
t = []
for i in range (n):
    t.append((a[i], i))
f1 = sorted(t, key = lambda tup: tup[0])
s =[]
c = 0
co = 1
b = True
#print(f1)
for i in range (n):
    s.append((f1[i][1], c % d +1))  
    c += 1
    if (i > 0):
        if(f1[i][0] == f1[i-1][0]):
           co += 1
        else:
            co = 1
    if co > d:
        b = False
#print(s)
s = sorted(s, key = lambda tup: tup[0])
st =""
for i in range (n):
    st += str(s[i][1])+" "
if (b):
    print ("YES")
    print(st)
    
else:
    print("NO")
