Discrete Acceleration

题意翻译

### 题目描述 数轴的原点和位置为 $l$ 的点上各有一个初始速度为 $1m/s$ 的小车,在原点的小车向右开,在 $l$ 位置的小车向左开.在位置 $0$ 到 $l$ 间有 $n$ 个旗子,第 $i$ 个的位置为 $a_{i}$ ,当两辆小车中任意一辆经过一个旗子,它的速度就增加 $1m/s$ ,求两车相遇时间. ### 输入输出格式 第一行输入一个整数 $T(1 \leq T \leq 10^4)$ 表示测试数据个数. 接下来对于每个测试数据,第一行包含两个整数 $n,l$ 表示旗子数量和第二辆小车的位置.第二行包含 $n$ 个整数 $a_{1},a_{2},a_{3},...,a_{n}$ ,其中$a_{i}$ 个表示第 $i$ 个旗子的位置. 对于每个测试数据输出一个实数表示两车相遇时间.当你的答案与实际答案差的绝对值小于等于 $10^{-6}$ 时便认为答案正确.

题目描述

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).

输入输出格式

输入格式

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 < a_2 < \ldots < a_n < l $ ). It is guaranteed that the sum of $ n $ among all test cases does not exceed $ 10^5 $ .

输出格式

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} $ .

输入输出样例

输入样例 #1

5
2 10
1 9
1 10
1
5 7
1 2 3 4 6
2 1000000000
413470354 982876160
9 478
1 10 25 33 239 445 453 468 477

输出样例 #1

3.000000000000000
3.666666666666667
2.047619047619048
329737645.750000000000000
53.700000000000000

说明

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} $ .