D. Exam in MACtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThe Master's Assistance Center has announced an entrance exam, which consists of the following.The candidate is given a set s of size n and some strange integer c. For this set, it is needed to calculate the number of pairs of integers (x, y) such that 0 \leq x \leq y \leq c, x + y is not contained in the set s, and also y - x is not contained in the set s.Your friend wants to enter the Center. Help him pass the exam!InputEach test consists of multiple test cases. The first line contains a single integer t (1 \leq t \leq 2 \cdot 10^4) — the number of test cases. The description of the test cases follows.The first line of each test case contains two integers n and c (1 \leq n \leq 3 \cdot 10^5, 1 \leq c \leq 10^9) — the size of the set and the strange integer.The second line of each test case contains n integers s_1, s_2, \ldots, s_{n} (0 \leq s_1 < s_2 < \ldots < s_{n} \leq c) — the elements of the set s.It is guaranteed that the sum of n over all test cases does not exceed 3 \cdot 10^5.OutputFor each test case, output a single integer — the number of suitable pairs of integers.ExampleInput
83 31 2 31 179574 60 3 5 61 115 100 2 4 8 105 101 3 5 7 94 102 4 6 73 1000000000228 1337 998244353Output
3
16139
10
2
33
36
35
499999998999122959
NoteIn the first test case, the following pairs are suitable: (0, 0), (2, 2), (3, 3).In the third test case, the following pairs are suitable: (0, 1), (0, 2), (0, 4), (1, 3), (2, 6), (3, 4), (3, 5), (4, 5), (4, 6), (5, 6).
83 31 2 31 179574 60 3 5 61 115 100 2 4 8 105 101 3 5 7 94 102 4 6 73 1000000000228 1337 998244353
3 16139 10 2 33 36 35 499999998999122959 
['binary search', 'combinatorics', 'implementation', 'math', '*1800']