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.
global s
s = 0
inp = input().split()
n = int(inp[0])
k = int(inp[1])
st = [int(g) for g in input().split()]
bag = [[] for g in range(0,k)]
res = []
fl = 0
def ss():
    global s
    global k
    if (s == k-1):
        s = 0
    else:
        s = s + 1
    return s
s = -1
for i in st:
    fl = 0
    for j in range(ss(),2*k):
        if not(i in bag[j%k]):
             bag[j%k].append(i)
             fl = 1
             res.append(str(j%k+1))
             break
    if (fl == 0):
        break
for i in bag:
    if len(i) == 0:
        fl = 0
if fl == 0:
    print("NO")
else:
    print("YES\n")
    print(" ".join(res))
            