Preparing NOJ

Three-level Laser

1000ms 262144K

Description:

An atom of element X can exist in n distinct states with energies E1 < E2 < ... < En. 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 Ek - Ei energy to put the atom in the state k,
  3. the atom emits a photon with useful energy Ek - Ej and changes its state to the state j,
  4. the atom spontaneously changes its state to the state i, losing energy Ej - Ei,
  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 Ek - Ei ≤ 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 Ek and Ei.

The second line contains a sequence of integers E1, E2, ..., En (1 ≤ E1 < E2... < En ≤ 109). It is guaranteed that all Ei 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 .

Sample Input:

4 4
1 3 5 7

Sample Output:

0.5

Sample Input:

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

Sample Output:

0.875

Sample Input:

3 1
2 5 10

Sample Output:

-1

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 .

Info

CodeForces

Provider CodeForces

Origin VK Cup 2018 - Round 2

Code CF924B

Tags

binary searchgreedytwo pointers

Submitted 14

Passed 4

AC Rate 28.57%

Date 03/04/2019 16:17:01

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