A12303. Array K-Coloring

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 $c_1, c_2, \dots c_n$ , where $1 \le c_i \le k$ 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.

The first line of the input contains two integers $n$ and $k$ ( $1 \le k \le n \le 5000$ ) — the length of the array $a$ and the number of colors, respectively.

The second line of the input contains $n$ integers $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le 5000$ ) — elements of the array $a$ .

If there is no answer, print "NO". Otherwise print "YES" and any coloring (i.e. numbers $c_1, c_2, \dots c_n$ , where $1 \le c_i \le k$ 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.

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.