You are given three integers $x$, $y$, and $n$.

Your task is to construct an array $a$ consisting of $n$ integers which satisfies the following conditions:

1. $a_1=x$, $a_n=y$;
2. $a$ is strictly increasing (i.e. $a_1 < a_2 < \ldots < a_n$);
3. if we denote $b_i=a_{i+1}-a_{i}$ for $1 \leq i \leq n-1$, then $b$ is strictly decreasing (i.e. $b_1 > b_2 > \ldots > b_{n-1}$).

If there is no such array $a$, print a single integer $-1$.

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 1000$). The description of the test cases follows.

The only line of each test case contains three integers $x$, $y$, $n$ ($1 \le x < y \le 1000,3 \le n \le 1000$).

For each test case, output $n$ integers $a_1,a_2,\ldots,a_n$. If there are multiple solutions, print any of them.

If there is no solution, print a single integer $-1$.