Three-level Laser

题意翻译

有一个长度为$n(n\le 10^5)$的严格单调递增整数序列$\{E\}(E_i\le 10^9)$，求$i,j,k(i<j<k)$使得$\eta=\frac{E_k-E_j}{E_k-E_i}$最大且$E_k-E_i\le U(U\le 10^9)$，输出这个$\eta$。

题目描述

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.

输入输出格式

输入格式

The first line contains two integers $ n $ and $ U $ ( $ 3<=n<=10^{5} $ , $ 1<=U<=10^{9} $ ) — 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}<=10^{9} $ ). It is guaranteed that all $ E_{i} $ are given in increasing order.

输出格式

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 .

输入输出样例

输入样例 #1

4 4
1 3 5 7

输出样例 #1

0.5

输入样例 #2

10 8
10 13 15 16 17 19 20 22 24 25

输出样例 #2

0.875

输入样例 #3

3 1
2 5 10

输出样例 #3

-1

说明

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 .

题意翻译

有一个长度为$n(n\le 10^5)$的严格单调递增整数序列$\{E\}(E_i\le 10^9)$，求$i,j,k(i<j<k)$使得$\eta=\frac{E_k-E_j}{E_k-E_i}$最大且$E_k-E_i\le U(U\le 10^9)$，输出这个$\eta$。