B2. Wonderful Coloring - 2time limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThis 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.  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.InputThe 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.OutputOutput 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.ExampleInput
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
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
NoteIn 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.
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

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 
['binary search', 'constructive algorithms', 'data structures', 'greedy', '*1400']