Rikka with Subset

Problem Description

As we know, Rikka is poor at math. Yuta is worrying about this situation, so he gives Rikka some math tasks to practice. There is one of them: Yuta has $n$ positive $A_1-A_n$ and their sum is $m$. Then for each subset $S$ of $A$, Yuta calculates the sum of $S$. Now, Yuta has got $2^n$ numbers between $[0,m]$. For each $i \in [0,m]$, he counts the number of $i$s he got as $B_i$. Yuta shows Rikka the array $B_i$ and he wants Rikka to restore $A_1-A_n$. It is too difficult for Rikka. Can you help her?

Input

The first line contains a number $t(1 \leq t \leq 70)$, the number of the testcases. For each testcase, the first line contains two numbers $n,m(1 \leq n \leq 50,1 \leq m \leq 10^4)$. The second line contains $m+1$ numbers $B_0-B_m(0 \leq B_i \leq 2^n)$.

Output

For each testcase, print a single line with $n$ numbers $A_1-A_n$. It is guaranteed that there exists at least one solution. And if there are different solutions, print the lexicographic minimum one.

Sample Input

2
2 3
1 1 1 1
3 3
1 3 3 1

Sample Output

1 2
1 1 1

Hint

In the first sample, $A$ is $[1,2]$. $A$ has four subsets $[],[1],[2],[1,2]$ and the sums of each subset are $0,1,2,3$. So $B=[1,1,1,1]$

Source

2017 Multi-University Training Contest - Team 5

https://acm.hdu.edu.cn/showproblem.php?pid=6092