CF1408C.Discrete Acceleration

There is a road with length $l$ meters. The start of the road has coordinate $0$, the end of the road has coordinate $l$.

There are two cars, the first standing at the start of the road and the second standing at the end of the road. They will start driving simultaneously. The first car will drive from the start to the end and the second car will drive from the end to the start.

Initially, they will drive with a speed of $1$ meter per second. There are $n$ flags at different coordinates $a_1, a_2, \ldots, a_n$. Each time when any of two cars drives through a flag, the speed of that car increases by $1$ meter per second.

Find how long will it take for cars to meet (to reach the same coordinate).

有一条长度为 $l$ 米的道路。道路起点坐标为 $0$，终点坐标为 $l$。

道路上有两辆汽车：第一辆车停在道路起点，第二辆车停在道路终点。它们将同时出发：第一辆车从起点驶向终点，第二辆车从终点驶向起点。

初始时，两辆车的速度均为 $1$ 米/秒。道路上共有 $n$ 面旗帜，分别位于不同坐标 $a_1, a_2, \ldots, a_n$ 处。每当任意一辆车经过一面旗帜时，该车的速度增加 $1$ 米/秒。

求两辆车相遇（即到达同一坐标）所需的时间。

The first line contains one integer $t$ ($1 \leq t \leq 10^4$): the number of test cases.

The first line of each test case contains two integers $n$, $l$ ($1 \leq n \leq 10^5$, $1 \leq l \leq 10^9$): the number of flags and the length of the road.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ in the increasing order ($1 \leq a_1 \lt a_2 \lt \ldots \lt a_n \lt l$).

It is guaranteed that the sum of $n$ among all test cases does not exceed $10^5$.

第一行包含一个整数 $t$（$1 \leq t \leq 10^4$）：测试用例的数量。

每个测试用例的第一行包含两个整数 $n$、$l$（$1 \leq n \leq 10^5$，$1 \leq l \leq 10^9$）：旗帜的数量和道路的长度。

第二行包含 $n$ 个严格递增的整数 $a_1, a_2, \ldots, a_n$（$1 \leq a_1 \lt a_2 \lt \ldots \lt a_n \lt l$）。

保证所有测试用例中 $n$ 的总和不超过 $10^5$。

For each test case print a single real number: the time required for cars to meet.

Your answer will be considered correct, if its absolute or relative error does not exceed $10^{-6}$. More formally, if your answer is $a$ and jury's answer is $b$, your answer will be considered correct if $\frac{|a-b|}{\max{(1, b)}} \leq 10^{-6}$.

对于每个测试用例，输出一个实数：汽车相遇所需的时间。

若你的答案的绝对误差或相对误差不超过 $10^{-6}$，则视为正确。更准确地说，若你的答案为 $a$，而评测机的答案为 $b$，当且仅当 $\frac{|a-b|}{\max{(1, b)}} \leq 10^{-6}$ 时，你的答案被视为正确。

In the first test case cars will meet in the coordinate $5$.

The first car will be in the coordinate $1$ in $1$ second and after that its speed will increase by $1$ and will be equal to $2$ meters per second. After $2$ more seconds it will be in the coordinate $5$. So, it will be in the coordinate $5$ in $3$ seconds.

The second car will be in the coordinate $9$ in $1$ second and after that its speed will increase by $1$ and will be equal to $2$ meters per second. After $2$ more seconds it will be in the coordinate $5$. So, it will be in the coordinate $5$ in $3$ seconds.

In the second test case after $1$ second the first car will be in the coordinate $1$ and will have the speed equal to $2$ meters per second, the second car will be in the coordinate $9$ and will have the speed equal to $1$ meter per second. So, they will meet after $\frac{9-1}{2+1} = \frac{8}{3}$ seconds. So, the answer is equal to $1 + \frac{8}{3} = \frac{11}{3}$.

在第一个测试用例中，两辆车将在坐标 $5$ 处相遇。

第一辆车在 $1$ 秒后将到达坐标 $1$，此后其速度增加 $1$，变为 $2$ 米/秒。再经过 $2$ 秒，它将到达坐标 $5$。因此，它将在 $3$ 秒时到达坐标 $5$。

第二辆车在 $1$ 秒后将到达坐标 $9$，此后其速度增加 $1$，变为 $2$ 米/秒。再经过 $2$ 秒，它将到达坐标 $5$。因此，它也将在 $3$ 秒时到达坐标 $5$。

在第二个测试用例中，$1$ 秒后，第一辆车将位于坐标 $1$，速度为 $2$ 米/秒；第二辆车将位于坐标 $9$，速度为 $1$ 米/秒。因此，它们将在 $\frac{9-1}{2+1} = \frac{8}{3}$ 秒后相遇。故答案为 $1 + \frac{8}{3} = \frac{11}{3}$。