Min Cost Permutation (Easy Version)

3000ms

262144K

Description:

The 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 $$$y$$$.

Input:

Each 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 $$$5 \cdot 10^3$$$.

Output:

For each test case, output $$$n$$$ integers $$$b_1,\dots,b_n$$$, the lexicographically smallest permutation of $$$a$$$ that achieves the minimum $$$\sum\limits_{i=1}^{n-1} |b_{i+1}-b_i-c|$$$.

Sample Input:

3
6 -7
3 1 4 1 5 9
3 2
1 3 5
1 2718
2818

Sample Output:

9 3 1 4 5 1
1 3 5
2818

Note:

In 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 $$$b$$$.

Informação

Provedor Codeforces

Código CF1844F1