P11172 "CMOI R1" mex2

Little U is very interested in functions that map a set to a number, and $\text{mex}$ is a good example. $\text{mex}(S)$ is the smallest non-negative integer that does not appear in the set $S$.

Multiple test cases. For each test case, given $c$, you need to construct a sequence $a_1,a_2,\ldots,a_n \in [0,2\times 10^9]$ such that $$\sum\limits_{1\le l\le r\le n}\text{mex}(a_l,a_{l+1},\ldots,a_r)=c$$ where it is required that $1 \le n \le 3000$. It can be proven that within the constraints of this problem, if a solution exists, then a solution must exist with $1 \le n \le 3000$.

The first line contains an integer $T$, the number of test cases. Then $T$ lines follow, each containing one non-negative integer $c$.

For each test case: If there is no solution, output only one line containing an integer $-1$. Otherwise, output a positive integer $n$ on the first line. Output $n$ non-negative integers $a_1,a_2,\ldots,a_n$ on the second line.

### Sample Explanation For sample #1: only $\text{mex}(a_7)=1$, and for all $1\le i\le6$, we have $\text{mex}(a_i,a_{i+1},\ldots,a_7)=2$, so the total sum is $13$. ### Constraints $id$ is the $\text{subtask}$ index. |$id$|Special Property|Score|$id$|Special Property|Score| |-:|-:|-:|-:|-:|-:| |$1$|$c\le3\times10^3$|$3$|$5$|$c\le8\times 10^6$|$10$| |$2$|$c\le6\times 10^3$|$7$|$6$|$c\le1\times 10^8$|$10$| |$3$|$c\le8\times10^4$|$10$|$7$|$c\le1\times 10^9$|$25$| |$4$|$c\le4\times 10^6$|$15$|$8$|$c\le2\times 10^9$|$20$| For $100\%$ of the testdata, $T\le 310$, $0\le c\le 2\times 10^9$. Translated by ChatGPT 5