CF1935D.Exam in MAC

普及/提高-

通过率：0%

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题目描述

The 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!

输入格式

Each 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 $3 \cdot 10^5$ .

输出格式

For each test case, output a single integer — the number of suitable pairs of integers.

输入输出样例

输入#1

8
3 3
1 2 3
1 179
57
4 6
0 3 5 6
1 1
1
5 10
0 2 4 8 10
5 10
1 3 5 7 9
4 10
2 4 6 7
3 1000000000
228 1337 998244353

输出#1

3
16139
10
2
33
36
35
499999998999122959

说明/提示

In 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: $(0, 1)$ , $(0, 2)$ , $(0, 4)$ , $(1, 3)$ , $(2, 6)$ , $(3, 4)$ , $(3, 5)$ , $(4, 5)$ , $(4, 6)$ , $(5, 6)$ .

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