Problem Statement

You are given positive integers $N$ and $K$.

Find one length-$N$ sequence of positive integers $A=(A_1,A_2,\ldots,A_N)$ with the minimum value of $A_N$ among the ones that satisfy all of the following conditions.

• $A$ is non-decreasing. That is, $A_i \le A_{i+1}$ for $1\le i\le N-1$.
• $\displaystyle \sum_{i=1}^{N-1} (A_{i+1} \bmod A_i)=K$.

You are given $T$ test cases; solve each of them.

Constraints

• $1\le T \le 10^5$
• $2\le N \le 2\times 10^5$
• The sum of $N$ over all test cases is at most $2\times 10^5$.
• $1\le K\le 10^9$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

T
\text{case}_1
\text{case}_2
\vdots
\text{case}_T

Each test case is given in the following format:

N K

Output

Output the answers for each test case in order, separated by newlines.

For each test case, print $A$ that satisfies all conditions and has the minimum value of $A_N$ in the following format:

A_1 A_2 \ldots A_N

If there are multiple $A$ that satisfy all conditions and have the minimum value of $A_N$, any of them will be accepted.