P10306 "Cfz Round 2" How to Prove

Given a positive integer $n$. We define that for a set $S$, $\Omega(S)$ is the set consisting of the **sums of elements of all non-empty subsets** of $S$. Formally, $\Omega(S)=\{x\mid x=\sum\limits_{i\in T}i,T\subseteq S,T\neq \varnothing\}$. For example, when $S=\{2,0,-3,5\}$, $\Omega(S)=\{-3,-1,0,2,4,5,7\}$. You need to construct a set $S$ of size $n$ such that: - All elements in $S$ are integers not greater than $10^9$ and not less than $-10^9$. - $|\Omega(S)|$ is minimized, i.e., $\Omega(S)$ contains as few elements as possible.

**This problem has multiple test cases.** The first line contains an integer $T$, representing the number of test cases. Then each test case is given as follows. For each test case, one line contains a positive integer $n$.

For each test case, output one line with $n$ integers, representing all elements in the set $S$ you constructed. **Any output that satisfies the requirements will be accepted.**

#### "Sample Explanation #1" For the $1$st test case, $S=\{3\}$, $\Omega(S)=\{3\}$. Of course, $\{0\}$, $\{-2\}$, etc. are also valid sets $S$. For the $2$nd test case, $S=\{0,5\}$, $\Omega(S)=\{0,5\}$. For the $3$rd test case, $S=\{2,0,-2,4\}$, $\Omega(S)=\{-2,0,2,4,6\}$. It can be proven that the above constructions all satisfy the requirements. #### Constraints Let $\sum n$ denote the sum of $n$ within a single test case file. For all testdata, $1 \le T \le 100$, $1 \le n \le 10^6$, $\sum n \le 10^6$. **You can get the score for this problem only if you pass all test cases.** Translated by ChatGPT 5