Wonderful Coloring - 2 (Codeforces 1551B2)
Tags: Greedy, binary search

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.  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.

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 — $$$3$$$.

Sample Inputs:
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 Outputs:
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

Solution (Python):
import sys
input = sys.stdin.readline

def solve():
    (n, k) = map(int, input().split())
    c = [[] for i in range(n + 1)]
    a = list(map(int, input().split()))
    z = 0
    for i in range(n):
        if len(c[a[i]]) < k:
            c[a[i]].append(i)
            z += 1
    b = z // k
    d = b * k
    r = [0] * n
    j = 0
    for v in c:
        for w in v:
            r[w] = j % k + 1
            j += 1
            if j == d:
                print(' '.join(map(str, r)))
                return
    print(' '.join(map(str, r)))
for i in range(int(input())):
    solve()

Solution (Python):
def solve():
    (n, k) = map(int, input().split())
    c = [[] for i in range(n + 1)]
    a = list(map(int, input().split()))
    z = 0
    for i in range(n):
        if len(c[a[i]]) < k:
            c[a[i]].append(i)
            z += 1
    b = z // k
    d = b * k
    r = [0] * n
    j = 0
    for v in c:
        for w in v:
            r[w] = j % k + 1
            j += 1
            if j == d:
                print(' '.join(map(str, r)))
                return
for i in range(int(input())):
    solve()

Solution (Python):
def solve():
    (n, k) = map(int, input().split())
    c = [[] for i in range(n + 1)]
    a = list(map(int, input().split()))
    z = 0
    for i in range(n):
        if len(c[a[i]]) < k:
            c[a[i]].append(i)
            z += 1
    b = z // k
    d = b * k
    r = [0] * n
    j = 0
    for v in c:
        for w in v:
            r[w] = j % k + 1
            j += 1
            if j == d:
                print(' '.join(map(str, r)))
                return
for i in range(int(input())):
    solve()