XOR Operator () is used to perform a XOR operation on the individual bits of two operands. The XOR operator returns  if the corresponding bits in the two operands are different, and returns  if they are the same.

We define a non-decreasing non-negative array of size  to be great only if  is a factor of , where  is the xor sum of the array , which is equal to .

Given an integer , can you come up with a great array of size ?

输入描述:

The first line of the input contains a single integer  () which is the number of test cases. 

The first line of each test case contains a single integer  () — the size of array.

It is also guarenteed that the sum of  over all test cases does not exceed .

输出描述:

Output  lines. for each test case, output  non-decreasing non-negative integers as one possible great array  () of size . If it is impossible, output one integer .

3
1
2
3

1
1 3
2 2 3

For the first test case, xor sum  is a factor of .
For the third test case, xor sum  is a factor of .

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