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 main():
    n, k = map(int, input().split())
    a = list(map(int, input().split()))

    c = [0] * 5001
    res = [0] * n
    imposs = False

    for i, v in enumerate(a):
        c[v] += 1
        if c[v] > k:
            imposs = True
            break
        else:
            res[i] = c[v]

    if imposs:
        print('NO')
    else:
        all_used = set(res)
        unused = list(set([x for x in range(1, k+1)]) - all_used)
        pos = 0

        used = set()
        for i, v in enumerate(res):
            if not v in used:
                used.add(v)
            else:
                if pos < len(unused):
                    res[i] = unused[pos]
                    pos += 1

        print('YES')
        print(' '.join(map(str, res)))


if __name__ == '__main__':
    main()
