CF924B.Three-level Laser

An atom of element X can exist in n distinct states with energies _E_1 < _E_2 < ... < E__n. Arkady wants to build a laser on this element, using a three-level scheme. Here is a simplified description of the scheme.

Three distinct states i, j and k are selected, where i < j < k. After that the following process happens:

1. initially the atom is in the state i,
2. we spend E__k - E__i energy to put the atom in the state k,
3. the atom emits a photon with useful energy E__k - E__j and changes its state to the state j,
4. the atom spontaneously changes its state to the state i, losing energy E__j - E__i,
5. the process repeats from step 1.

Let's define the energy conversion efficiency as , i. e. the ration between the useful energy of the photon and spent energy.

Due to some limitations, Arkady can only choose such three states that E__k - E__i ≤ U.

Help Arkady to find such the maximum possible energy conversion efficiency within the above constraints.

元素 X 的一个原子可以处于 $n$ 个不同的能态，其能量分别为 $E_1 < E_2 < \dots < E_n$。Arkady 希望利用该元素构建一台激光器，采用三能级方案。该方案的简化描述如下：

选取三个互异的能态 $i$、$j$ 和 $k$，满足 $i < j < k$。随后发生如下过程：

1. 原子初始处于能态 $i$；
2. 我们消耗 $E_k - E_i$ 的能量，将原子激发至能态 $k$；
3. 原子发射一个具有有用能量 $E_k - E_j$ 的光子，并跃迁至能态 $j$；
4. 原子通过自发辐射跃迁回能态 $i$，释放能量 $E_j - E_i$；
5. 过程从第 1 步起重复进行。

我们定义能量转换效率为
，
即：光子的有用能量与所消耗能量之比。

由于某些限制，Arkady 只能选择满足 $E_k - E_i \leq U$ 的三能态组合。

请帮助 Arkady 在上述约束条件下，找出可能达到的最大能量转换效率。

The first line contains two integers n and U (3 ≤ n ≤ 105, 1 ≤ U ≤ 109) — the number of states and the maximum possible difference between E__k and E__i.

The second line contains a sequence of integers _E_1, _E_2, ..., E__n (1 ≤ _E_1 < _E_2... < E__n ≤ 109). It is guaranteed that all E__i are given in increasing order.

第一行包含两个整数 $n$ 和 $U$（$3 \leq n \leq 10^5$，$1 \leq U \leq 10^9$）—— 分别表示状态的数量以及 $E_k$ 与 $E_i$ 之间可能的最大差值。

第二行包含一个整数序列 $E_1,\ E_2,\ \dots,\ E_n$（$1 \leq E_1 < E_2 < \dots < E_n \leq 10^9$）。保证所有 $E_i$ 均以递增顺序给出。

If it is not possible to choose three states that satisfy all constraints, print -1.

Otherwise, print one real number η — the maximum possible energy conversion efficiency. Your answer is considered correct its absolute or relative error does not exceed 10 - 9.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if .

如果无法选择三个满足所有约束条件的状态，则输出 -1。

否则，输出一个实数 η —— 最大可能的能量转换效率。当你的答案的绝对误差或相对误差不超过 $10^{-9}$ 时，即视为正确。

形式化地，设你的答案为 $a$，评测组的答案为 $b$。若满足

则你的答案视为正确。

In the first example choose states 1, 2 and 3, so that the energy conversion efficiency becomes equal to .

In the second example choose states 4, 5 and 9, so that the energy conversion efficiency becomes equal to .

在第一个例子中，选择状态 1、2 和 3，使得能量转换效率等于 。

在第二个例子中，选择状态 4、5 和 9，使得能量转换效率等于 。