human
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 .

Examples

Input

4 4
1 3 5 7

Output

0.5

Input

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

Output

0.875

Input

3 1
2 5 10

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 .
Solve the task in PYTHON.

Write me a Python program to find such the maximum possible energy conversion efficiency within the above constraints?
assistant
#Here is Python program to find such the maximum possible energy conversion efficiency within the above constraints.

"""
________        _____________              ______
___  __ \____  ____  __ \__(_)__   _______ ___  /
__  /_/ /_  / / /_  /_/ /_  /__ | / /  __ `/_  /
_  ____/_  /_/ /_  _, _/_  / __ |/ // /_/ /_  /
/_/     _\__, / /_/ |_| /_/  _____/ \__,_/ /_/
        /____/

https://github.com/Cheran-Senthil/PyRival
Copyright (c) 2018 Cheran Senthilkumar
"""
from __future__ import division, print_function

import cmath
import itertools
import math
import operator as op
import sys
from atexit import register
from bisect import bisect_left, bisect_right

# import random
# from collections import Counter, MutableSequence, defaultdict, deque
# from copy import deepcopy
# from decimal import Decimal
# from difflib import SequenceMatcher
# from heapq import heappop, heappush

if sys.version_info[0] < 3:
    from io import BytesIO as stream
    # from fractions import Fraction
    # from fractions import gcd
    # from cPickle import dumps
    # from Queue import PriorityQueue, Queue
else:
    from io import StringIO as stream
    # from functools import reduce
    # from fractions import Fraction
    # from math import gcd
    # from pickle import dumps
    # from queue import PriorityQueue, Queue

if sys.version_info[0] < 3:
    class dict(dict):
        def items(self):
            return dict.iteritems(self)

        def keys(self):
            return dict.iterkeys(self)

        def values(self):
            return dict.itervalues(self)

    input = raw_input
    range = xrange

    filter = itertools.ifilter
    map = itertools.imap
    zip = itertools.izip

def sync_with_stdio(sync=True):
    """
    Sets whether the standard Python streams are allowed to buffer their I/O.

    Parameters
    ----------
    sync : bool, optional
        The new synchronization setting. Default is True.
    """
    global input, flush

    if sync:
        flush = sys.stdout.flush
    else:
        sys.stdin = stream(sys.stdin.read())
        input = lambda: sys.stdin.readline().rstrip('\r\n')

        sys.stdout = stream()
       ...