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

s = input().split(' ')
n = int(s[0])
k = int(s[1])

count_ = [0 for l in range(5001)]
rask = [0 for l in range(k)]
if n < k:
    print('NO')
    sys.exit(0)
l = 0
m = []
raskraska = [0 for l in range(n)]
for index, v in enumerate(input().split(' ')):

    i = int(v)
    m.append(i)
    count_[i] += 1
    if count_[i] > k:
        print('NO')
        sys.exit(0)
    raskraska[index] = count_[i] % k
    rask[count_[i] % k] += 1

rask2 = [i for i, v in enumerate(rask) if v == 0]
print('YES')
l = 0

for i1, v in enumerate(m):
    if rask[raskraska[i1]] > 1 and l < len(rask2):
        rask[raskraska[i1]] -= 1
        raskraska[i1] = rask2[l]
        l += 1
    print(raskraska[i1] + 1, end=' ')

if __name__ == "__main__":
    pass
