F1. Min Cost Permutation (Easy Version)time limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThe only difference between this problem and the hard version is the constraints on t and n.You are given an array of n positive integers a_1,\dots,a_n, and a (possibly negative) integer c.Across all permutations b_1,\dots,b_n of the array a_1,\dots,a_n, consider the minimum possible value of \sum_{i=1}^{n-1} |b_{i+1}-b_i-c|. Find the lexicographically smallest permutation b of the array a that achieves this minimum.A sequence x is lexicographically smaller than a sequence y if and only if one of the following holds: x is a prefix of y, but x \ne y; in the first position where x and y differ, the sequence x has a smaller element than the corresponding element in y.InputEach test contains multiple test cases. The first line contains the number of test cases t (1 \le t \le 10^3). The description of the test cases follows.The first line of each test case contains two integers n and c (1 \le n \le 5 \cdot 10^3, -10^9 \le c \le 10^9).The second line of each test case contains n integers a_1,\dots,a_n (1 \le a_i \le 10^9).It is guaranteed that the sum of n over all test cases does not exceed 5 \cdot 10^3.OutputFor each test case, output n integers b_1,\dots,b_n, the lexicographically smallest permutation of a that achieves the minimum \sum\limits_{i=1}^{n-1} |b_{i+1}-b_i-c|.ExampleInput
36 -73 1 4 1 5 93 21 3 51 27182818Output
9 3 1 4 5 1
1 3 5
2818
NoteIn the first test case, it can be proven that the minimum possible value of \sum\limits_{i=1}^{n-1} |b_{i+1}-b_i-c| is 27, and the permutation b = [9,3,1,4,5,1] is the lexicographically smallest permutation of a that achieves this minimum: |3-9-(-7)|+|1-3-(-7)|+|4-1-(-7)|+|5-4-(-7)|+|1-5-(-7)| = 1+5+10+8+3 = 27.In the second test case, the minimum possible value of \sum\limits_{i=1}^{n-1} |b_{i+1}-b_i-c| is 0, and b = [1,3,5] is the lexicographically smallest permutation of a that achieves this.In the third test case, there is only one permutation b.
36 -73 1 4 1 5 93 21 3 51 27182818
9 3 1 4 5 1 1 3 5 2818 
['brute force', 'constructive algorithms', 'greedy', 'math', '*2600']