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, k = map(int, input().split())
c, r, i, d = [], [], 0, 0
for _ in map(int, input().split()):
    i += 1
    c.append([_, i])
c.sort(key=lambda x: x[0])
r.append([1, c[0][1]])
l, t = 1, 1
for j in range(1, n ):
    l += 1
    if c[j][0] == c[j-1][0]:
        t += 1
        if t == k + 1:
            d = -1
            break
    else:
        t = 1
    s = l % k
    if s == 0:
        s = k
    r.append([s, c[j][1]])
if d == -1:
    print('NO')
else:
    r.sort(key=lambda x: x[1])
    print('YES')
    for p in range (n):
        print(r[p][0], sep=' ',  end = ' ')

