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!

Input

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 $$$s_1, s_2, \ldots, s_{n}$$$ ($$$0 \leq s_1 \lt s_2 \lt \ldots \lt s_{n} \leq c$$$) — the elements of the set $$$s$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$3 \cdot 10^5$$$.

Output

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

Note

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

Exam in MAC

Examples