Super Sort

Given an array of numbers and a non-negative integer $K$ you have to sort the array in such a way so that the absolute difference between every adjacent element is no more than $K$.

For example if you have an array $A = [8, 7, 6, 9]$ and $K = 2$ then one possible solution will be $[8, 9, 7, 6]$ where $|8 - 9| = 1, |9 - 7| = 2, |7 - 6| = 1$ and the absolute difference between every adjacent elements are no more than 2.

If there is many solution you have to print the lexicographically smallest answer. If there are no solution just print $\texttt{No Solution}$.

Input

Input will start with a positive integer $T$ ($0 < T \leq 150$) denoting the number of test cases.

Each test case will have two positive integer $N$ ($2 \leq N \leq 18$) denoting the number elements in the array and $K$ ($0 \leq K \leq 10^3$).

The next line will have $N$ space separated integers representing the array $A$ ($-10^3 \leq A_i \leq 10^3$).

Output

For each test case if there is a solution print the lexicographically smallest sorted array. You have to print $N$ space separated integers without any leading or trailing spaces. If there are no solutions, print $\texttt{No Solution}$.

Sample

Input	Output
2 2 2 3 1 2 1 1 3	1 3 No Solution