Problem Statement

You are given positive integers $v,x$. It is guaranteed that $xv+1$ is prime. Find $1$ sequence of positive integers $a_1,a_2,...,a_x$ satisfying the following conditions.

• $1$ $\le$ $a_1$ $<$ $a_2$ $<$ $...$ $<$ $a_x$ $\le$ $xv$
• For every positive integer $k$ at least $1$ and less than $x$, \( \displaystyle \sum_{i=1}^{x}a_i^k \) is divisible by $xv+1$.
• \( \displaystyle \sum_{i=1}^{x}a_i^x \) leaves a remainder of $x$ when divided by $xv+1$.

Output any valid sequence $a$, separated by spaces. It is guaranteed that a solution always exists.

In this problem, $T$ test cases are given.

Input

$T$
テストケース $1$
テストケース $2$
$.$$.$$.$
テストケース $T$

$v$ $x$

• All inputs are positive integers.
• $1 \le T,v \le 1000$
• $1 \le x \le 100$
• $xv+1$ is prime.

Output

Output $T$ lines. On the $i$-th line, output the answer for test case $i$.

Sample

1
1 2

1 2

3
2 6
2 1
6 7

1 3 4 9 10 12
1
1 4 11 16 21 35 41