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, ..., 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.

<image> 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 ≤ t ≤ 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 ≤ n ≤ 2⋅10^5, 1 ≤ k ≤ n) — the length of a given sequence and the number of colors, respectively. The second one contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ n).

It is guaranteed that the sum of n over all test cases doesn't exceed 2 ⋅ 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, ..., c_n (0 ≤ c_i ≤ 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.

Example

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


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.
12
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
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
 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

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

import sys
from math import floor, gcd,factorial
from collections import deque


input = sys.stdin.readline
def printf(x, end='\n'):
    sys.stdout.write(str(x) + end)      
def main():
    T=1
    T=int(input())
    def solve():
        last_stored=0
        value=[0,False]
        rr,tt=0,False
        arr=list(map(int,input().split()))
        n,k=arr[0],arr[1]
        arr=list(map(int,input().split()))
        dict={}
        for i in range(n):
            if(arr[i] in dict.keys()):
                dict[arr[i]].append(i)
            else:
                dict[arr[i]]=[i]

        h=arr.copy()
        h.sort()
        curr_elem=h[0]
        curr_count=0
        count=[]
        for i in range(n):
            if(h[i]==curr_elem):
                curr_count+=1
            else:
                count.append((curr_count,curr_elem))
                curr_count=1
                curr_elem=h[i]
        count.append((curr_count,h[-1]))
        count.sort()
        color=[0]*n
        count.reverse()
        w=len(count)
        x=0
        while(x<w):
            a,b=count[x]
            if(b==value[0]):
                a=last_stored+1
                rr=value[0]
                value[0]=0
                value[1]=False

            if(a>=k):
                for z in range(k):
                    color[dict[b][z]]=z+1
                x+=1    
                continue
            else:
                j=x+1
                stack=deque()
                stack.append((a,b))
                su=a
                while(su!=k and j<w):
                    c,d=count[j]
                    
                    if(su+c>k):
                        x=j
                        stack.append((k-su,d))
                        last_stored=k-su-1
                        value[0]=d
                        
                        

                        su=k
                    elif(su+c==k):
                        x=j+1
                        stack.append((c,d))
                        su=k
                    else:
                        stack.append((c,d)) 
                        su+=c 
                    j+=1      
                if(su==k):
                    sss=k
                    while(stack):
                        e,f=stack.pop()
                        if(f==rr):
                                for g in range(e):
                                    color[dict[f][g+a]]=sss
                                    sss-=1
                        else:
                            for g in range(e):
                                    color[dict[f][g]]=sss
                                    sss-=1            


                else:
                    break
        print(*color)                    


                    








        
               
                








                              

       





                   

            





        
        
                    


       


            
               


        

            
                     
             
        
            




        




            




        


             
                                              


                



                    







                
                      





    for i in range(T):
        solve()
    pass       

        

            
        
        



if __name__ == '__main__':
    main()






