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문제

A subsum of a sequence is a sum of one or more consecutive elements of this sequence.

You are given an integer $N$. Your task is to make a sequence of positive integers which are not greater than $3 \cdot (N + 6)$ such that all its $N \cdot (N + 1) / 2$ subsums are different from each other.

입력

There are several test cases.

The first line of input contains an integer $T$, the number of test cases ($1 \leq T \leq 200$).

Each of the next $T$ lines contains an integer $N$, the length of the sequence ($1 \le N \le 2000$).

출력

For each test case, print one line with $N$ space-separated positive integers representing your sequence.

If multiple solutions exist, any of them will be accepted.

예제 입력 1

2
2
5

예제 출력 1

1 2
1 2 4 8 16