Different Sums

Problem Description

A subsum of the sequence is sum of one or more consecutive integers of it. You are given an integer $N$($1\leq N \leq 2000$ ). Your task is to make a sequence of integers which are less than $3(N+ 6)$, such that its all subsums ($N (N +1) / 2$ in total) are different from each other.

Input

There are several test cases. The first line of the input contains an integer $T(1\leq T\leq 200 )$, the number of test cases. Each of the next $T$ lines contains an integer ,$N$ the length of the sequence.

Output

For each test case, print one line with $N$ space separated integers representing your sequence. If multiple solutions exist, any of them will be accepted.

Sample Input

2
2
5

Sample Output

1 2
1 2 4 8 16

Author

金策工业综合大学（DPRK）

Source

2016 Multi-University Training Contest 9