The only difference between this problem and the easy 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$$$ if and only if one of the following holds:
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.
The first line of each test case contains two integers $$$n$$$ and $$$c$$$ ($$$1 \le n \le 2 \cdot 10^5$$$, $$$-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$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.
For each test case, output $$$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|$$$.
36 -73 1 4 1 5 93 21 3 51 27182818
9 3 1 4 5 1 1 3 5 2818
In the first test case, it can be proven that the minimum possible value of $$$\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$$$.
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