A11661. 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.

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.

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 .

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 .