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 calc(n, k, arr):
    not_used = set(range(1, k+1))
    all = set(range(1, k+1))
    d = [set() for i in range(5001)]
    res = []
    for a in arr:
        if len(d[a]) <= k:
            c = not_used - d[a]
            if c:
                res.append(list(c)[0])
                not_used -= {list(c)[0]}
                d[a] |= {list(c)[0]}
            else:
                c1 = all - d[a]
                if c1:
                    res.append(list(c1)[0])
                    d[a] |= {list(c1)[0]}
                else:
                    return []

        else:
            return []

    return res


if __name__ == '__main__':
    n, k = map(int, input().split())
    arr = map(int, input().split())
    r = calc(n, k, arr)
    if r:
        print("YES")
        print(" ".join(list(map(str, r))))
    else:
        print("NO")