Array K-Coloring

2000ms

262144K

Description:

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.

Input:

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 $$$a$$$.

Output:

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.

Sample Input:

4 2
1 2 2 3

Sample Output:

YES
1 1 2 2

Sample Input:

5 2
3 2 1 2 3

Sample Output:

YES
2 1 1 2 1

Sample Input:

5 2
2 1 1 2 1

Sample 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.

Informação

Provedor Codeforces

Código CF1102B