Wonderful Coloring - 2

题意翻译

给定一个数列 $a_1,a_2\cdots a_n $ ($n \le 2\times 10^5$) ，将其用 $k$ 种颜色染色 ($k \le n$)，满足 * 每个点或被用 $k$ 种染色中的一个被染，或不被染色 * 同色的任两个字母不相同 * 每一种颜色染的字母的数量全部相等 在满足上面三个条件的情况下，构造一种染色方案，使得每个颜色染的字母的数量最大。 如下图就是在 $a=[3,1,1,1,1,10,3,10,10,2]$，$k=3$ 时，最佳染色方案之一。  输出方案时，颜色从 $1$ 到 $k$ 编号，某个数若不染色，则这个数答案为 $0$。 __多组数据__

题目描述

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: 1. each element of the sequence is either painted in one of $ k $ colors or isn't painted; 2. 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); 3. let's calculate for each of $ k $ colors the number of elements painted in the color — all calculated numbers must be equal; 4. 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. 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 $ .

输入输出格式

输入格式

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 $ .

输出格式

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.

输入输出样例

输入样例 #1

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

输出样例 #1

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

说明

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 $ .