Three-level Laser

1000ms

262144K

Description:

An atom of element X can exist in n distinct states with energies E₁ < E₂ < ... < 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:

initially the atom is in the state i,
we spend E_k - E_i energy to put the atom in the state k,
the atom emits a photon with useful energy E_k - E_j and changes its state to the state j,
the atom spontaneously changes its state to the state i, losing energy E_j - E_i,
the process repeats from step 1.

Let's define the energy conversion efficiency as $\text{[math]}$ , 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.

Input:

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 E₁, E₂, ..., E_n (1 ≤ E₁ < E₂... < E_n ≤ 10⁹). It is guaranteed that all E_i are given in increasing order.

Output:

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 $\text{[math]}$ .