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 solve():

    n, k = [int(x) for x in input().split(" ")]

    data = [int(x) for x in input().split(" ")]

    color = {}
    c = 1
    res = []
    for e in data:
        if c > k:
            c = 1
        if e in color and c in color[e]:
            while c in color[e]:
                c += 1
        else:
            if e not in color:
                color[e] = set()

        if c > k:
            c = 1
            if e in color and c in color[e]:
                while c in color[e]:
                    c += 1
            else:
                if e not in color:
                    color[e] = set()

            if c > k:
                print("NO")
                exit()

        color[e].add(c)
        res.append(c)
        c += 1

    print("YES")
    print(" ".join(str(x) for x in res))


if __name__ == '__main__':
    solve()

"""

6 2
1 2 2 3 5 6

3 2
2 2 2

"""