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.

Input

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.

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 .

Note

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 .