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