Wonderful Coloring - 2

2000ms

262144K

Description:

This problem is an extension of the problem "Wonderful Coloring - 1". It has quite many differences, so you should read this statement completely.

Recently, Paul and Mary have found a new favorite sequence of integers $$$a_1, a_2, \dots, a_n$$$. They want to paint it using pieces of chalk of $$$k$$$ colors. The coloring of a sequence is called wonderful if the following conditions are met:

each element of the sequence is either painted in one of $$$k$$$ colors or isn't painted;
each two elements which are painted in the same color are different (i. e. there's no two equal values painted in the same color);
let's calculate for each of $$$k$$$ colors the number of elements painted in the color — all calculated numbers must be equal;
the total number of painted elements of the sequence is the maximum among all colorings of the sequence which meet the first three conditions.

E. g. consider a sequence $$$a=[3, 1, 1, 1, 1, 10, 3, 10, 10, 2]$$$ and $$$k=3$$$. One of the wonderful colorings of the sequence is shown in the figure.

$\text{[math]}$ The example of a wonderful coloring of the sequence $$$a=[3, 1, 1, 1, 1, 10, 3, 10, 10, 2]$$$ and $$$k=3$$$. Note that one of the elements isn't painted.

Help Paul and Mary to find a wonderful coloring of a given sequence $$$a$$$.

Input:

The first line contains one integer $$$t$$$ ($$$1 \le t \le 10000$$$) — the number of test cases. Then $$$t$$$ test cases follow.

Each test case consists of two lines. The first one contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n \le 2\cdot10^5$$$, $$$1 \le k \le n$$$) — the length of a given sequence and the number of colors, respectively. The second one contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le n$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases doesn't exceed $$$2 \cdot 10^5$$$.

Output:

Output $$$t$$$ lines, each of them must contain a description of a wonderful coloring for the corresponding test case.

Each wonderful coloring must be printed as a sequence of $$$n$$$ integers $$$c_1, c_2, \dots, c_n$$$ ($$$0 \le c_i \le k$$$) separated by spaces where

$$$c_i=0$$$, if $$$i$$$-th element isn't painted;
$$$c_i>0$$$, if $$$i$$$-th element is painted in the $$$c_i$$$-th color.

Remember that you need to maximize the total count of painted elements for the wonderful coloring. If there are multiple solutions, print any one.

Sample Input:

6
10 3
3 1 1 1 1 10 3 10 10 2
4 4
1 1 1 1
1 1
1
13 1
3 1 4 1 5 9 2 6 5 3 5 8 9
13 2
3 1 4 1 5 9 2 6 5 3 5 8 9
13 3
3 1 4 1 5 9 2 6 5 3 5 8 9

Sample Output:

1 1 0 2 3 2 2 1 3 3
4 2 1 3
1
0 0 1 1 0 1 1 1 0 1 1 1 0
2 1 2 2 1 1 1 1 2 1 0 2 2
1 1 3 2 1 3 3 1 2 2 3 2 0

Note:

In the first test case, the answer is shown in the figure in the statement. The red color has number $$$1$$$, the blue color — $$$2$$$, the green — $$$3$$$.

Informação

Provedor Codeforces

Código CF1551B2