Demonic Subset

Lets not waste your time with long tiring problem statement and just go straight to the point. You are given an array $A$ containing $N$ numbers. You are also given a function. You need to find the result of the function using array $A$ for a specific $K$.

function solveMeIfYouCan(A,K)
    result = 0
    
    subsetList = all the non empty subsets of array A
    
    for all subset s in subsetList
        sortedSubset = sort the elements inside subset from small to large

        size = element count in sortedSubset 
        len = min(size, K)

        for i = 1 to len
             result = result + sortedSubset[i]
        end for
        
    end for

  return result
end function

Note: Array indexing starts from 1.

Since finding the answer for a single $K$ will be too easy, you need to find the answer for all possible $K$ (1 to $N$).

Input

The first line contains an integer, $T$ ($1 ≤ T ≤ 10$), number of tests. The second line contains an integer, $N$ ($1 ≤ N ≤ 10^5$), number of elements in $A$. Next line contains $N$ characters denoting the elements of the array $A$ ($1 ≤ A[i] ≤ 10^9$).

Output

For each test case print a line contains exactly $N$ numbers denoting the answer for all possible $K$ (1 to $N$). The answer may be very large, so you need to print the answer modulo 786433.

Sample

Input	Output
3 3 1 1 1 3 1 2 3 4 1 2 3 4	7 11 12 11 21 24 26 58 76 80