Problem: 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 <image>, 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 <image>.

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 <image>.

In the second example choose states 4, 5 and 9, so that the energy conversion efficiency becomes equal to <image>.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.StringTokenizer;
/*
 * 
 * daiict
 *
 * 
 * 
 */

public class pprac
{
	FastScanner in;
	PrintWriter out;

	static int countc = 0;
	static int minm = countc;

	static ArrayList[] adj;
	static ArrayList[] aadj;
	static int last;
	static int n;
	static int m;

	static int[] dp1;
	static int[] dp2;
	static int color[];
	static int visited[];
	static int[] arr;
	static long[] brr;
	static double ans;
	static int array[];
	static int start[];
	static int finish[];
	static int pref[];
	static int tree[];
	static int maxval = 32;

	static int ttt[];
	static int sum = 0;
	static String s;

	static int cc = 0;
	static long min = Long.MAX_VALUE;

	static ArrayList<Integer> segt[];

	// for dfs do not delete
	static int dir[][] =
	{
			{ 1, 0 },
			{ 0, 1 },
			{ 0, -1 },
			{ -1, 0 } };

	static int[] seg;
	static long count = 1;
	static long mod = (long) 1e9 + 7;

	static int parent[];
	static int size[];

	static int[] l;
	static int[] r;
	static int[] next;
	static int[] cnt;
	static int[] block;

	static int bblock = 1001;

	static HashSet<String> set;
	static HashSet<String> set2;

	static int low[];
	static int disc[];
	static int time;
	static int acn[];

	static HashMap<Long, Integer> map;

	static class Pair implements Comparable<Pair>
	{
		int x;
		int y;
		int i;

		Pair(int l, int m, int i)
		{

			this.x = l;
			this.y = m;
			this.i = i;

		}

		public int compareTo(Pair p)
		{

			if (this.x / bblock == p.x / bblock)
			{
				return (int) (this.y - p.y);
			}
			return (int) (this.x / bblock - p.x / bblock);
		}

		public String toString()
		{
			return x + " " + y;
		}

		public boolean equals(Object o)
		{
			if (o instanceof Pair)
			{
				Pair a = (Pair) o;

				return this.x == a.x;
			}

			return false;
		}

		public int hashCode()
		{
			return new Long(x).hashCode() * 31 + new Long(y).hashCode();
		}

	}

	public static int gcd(int a, int b)
	{
		if (b == 0)
			return a;
		return gcd(b, a % b);
	}

	void build(int n)
	{ // build the tree
		for (int i = n - 1; i > 0; --i)
			seg[i] = Math.min(seg[i << 1], seg[i << 1 | 1]);
	}

	public static void modify(int p, int val, int n)
	{ // set value at position
		// p
		for (seg[p += n] = val; p > 1; p >>= 1)
			seg[p >> 1] = Math.min(seg[p], seg[p ^ 1]);
	}

	int query(int l, int r, int n)
	{ // sum on interval [l, r)
		int res = Integer.MAX_VALUE;

		if (l > r)
		{
			return res;
		}

		for (l += n, r += n; l < r; l >>= 1, r >>= 1)
		{
			if ((l & 1) == 1)
				res = Math.min(res, seg[l++]);
			if ((r & 1) == 1)
				res = Math.min(res, seg[--r]);
		}
		return res;
	}

	// public static void update(int x,int val){
	// while(x<=maxval){
	// tree[x] += val;
	// x = (x&-x);
	// }
	// }

	public static int read(int idx)
	{
		int sum = 0;

		while (idx >= 0)
		{
			sum += tree[idx];
			idx -= (idx & (-idx));
		}

		return sum;
	}

	public static int find(int i)
	{
		if (parent[i] != i)
		{
			return find(parent[i]);
		}

		return i;
	}

	public static void union(int a, int b)
	{
		int x = find(a);
		int y = find(b);

		if (x != y)
		{
			if (size[x] > size[y])
			{
				size[x] += size[y];
				parent[y] = x;
			} else
			{
				size[y] += size[x];
				parent[x] = y;
			}
		}
	}

			/* static */ void solve() throws NumberFormatException, InputMismatchException, IOException
	{

		// Scanner in = new Scanner(System.in);

		int n = in.nextInt();
		long m = in.nextLong();

		long arr[] = new long[n];

		for (int i = 0; i < n; i++)
		{
			arr[i] = in.nextLong();
		}

		long range = arr[n - 1];

		double ans = 0;

		for (int i = 0; i < n; i++)
		{
			long u = m;

			long dest = u + arr[i];

			if (dest > range)
			{
				dest = range;
				if (i < n - 2)
				{
					ans = Math.max(ans, (range - arr[i + 1]) / (double) (range - arr[i]));
					continue;
				} else
				{
					continue;
				}
			}

			int ll = i;
			int rr = n - 1;
			int mm = i;

			while (ll < rr)
			{
				mm = (ll + rr) / 2;
				if (ll == rr - 1)
				{
					if (arr[rr] <= dest)
					{
						ll = rr;
					}
					break;
				}

				if (arr[mm] > dest)
				{
					rr = mm - 1;
				} else if (arr[mm] <= dest)
				{
					ll = mm;
				}
			}
			// out.println(i + " " + ll + " " + dest + " " + arr[ll]);
			if (ll > i + 1)
			{
				ans = Math.max(ans, (arr[ll] - arr[i + 1]) / (double) (arr[ll] - arr[i]));
			}
		}

		if (ans != 0)
			out.println(ans);
		else
			out.println(-1);

	}

	public static void dfs(int i, int l)
	{
		if (visited[i] == 1)
		{
			return;
		}

		visited[i] = 1;

		if (adj[i].size() > l)
		{
			countc++;
		}

		for (int j = 0; j < adj[i].size(); j++)
		{
			dfs((int) adj[i].get(j), adj[i].size());
		}

	}

	public static void add(int i)
	{
		low[disc[i]]++;
		disc[i]++;
	}

	public static void uu(int arr[], int i, int f)
	{
		if (i == 1)
		{
			return;
		}
		int next = i / 2;
		int x = 0;
		if (i % 2 == 0)
		{
			x = i + 1;
		} else
		{
			x = i - 1;
		}

		if (f == 1)
		{
			arr[next] = arr[i] ^ arr[x];
		} else
		{
			arr[next] = arr[i] | arr[x];
		}

		uu(arr, next, 1 - f);
	}

	public static String reverse(String s)
	{

		String ans = "";

		for (int i = s.length() - 1; i >= 0; i--)
		{
			ans += s.charAt(i);
		}

		return ans;

	}

	public static long sum(long x)
	{
		return x < 10 ? x : x % 10 + sum(x / 10);
	}

	public static long gcd(long x, long y)
	{
		if (x == 0)
			return y;
		else
			return gcd(y % x, x);
	}

	static long inv(long x, long mod)
	{
		long r, y;
		for (r = 1, y = mod - 2; y != 0; x = x * x % mod, y >>= 1)
		{
			if ((y & 1) == 1)
				r = r * x % mod;

		}
		return r;
	}

	public static long pow(long x, long y, long n)
	{
		if (y == 0)
			return 1 % n;
		if (y % 2 == 0)
		{
			long z = pow(x, y / 2, n);
			return (z * z) % n;
		}
		return ((x % n) * pow(x, y - 1, n)) % n;
	}

	public static boolean isPrime(long a)
	{
		// Corner cases
		if (a <= 1)
			return false;
		if (a <= 3)
			return true;

		// This is checked so that we can skip
		// middle five numbers in below loop
		if (a % 2 == 0 || a % 3 == 0)
			return false;

		for (long i = 5; i * i <= a; i = i + 6)
			if (a % i == 0 || a % (i + 2) == 0)
				return false;

		return true;
	}

	void run() throws NumberFormatException, InputMismatchException, IOException
	{
		in = new FastScanner();
		out = new PrintWriter(System.out);

		solve();

		out.close();
	}

	class FastScanner
	{
		BufferedReader br;
		StringTokenizer st;

		public FastScanner()
		{
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next()
		{
			while (st == null || !st.hasMoreTokens())
			{
				try
				{
					st = new StringTokenizer(in.br.readLine());
				} catch (IOException e)
				{
					// TODO Auto-generated catch block
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt()
		{
			return Integer.parseInt(next());
		}

		long nextLong()
		{
			return Long.parseLong(next());
		}

		double nextDouble()
		{
			return Double.parseDouble(next());
		}
	}

	public static void main(String[] args) throws NumberFormatException, InputMismatchException, IOException
	{
		// new Thread(null ,new Runnable(){
		// public void run(){
		// try{
		//
		// test();
		//
		// } catch(Exception e){
		// e.printStackTrace();
		// }
		// }
		// },"1",1<<26).start();
		// }
		// static StringBuilder sb;
		// public static void test() throws IOException{
		// sb=new StringBuilder();
		// int t=1;
		// while(t-->0){
		//
		// solve();
		//
		// }
		//

		new pprac().run();
	}

}

class Node
{
	int a;
	int b;

	public Node(int i, int j)
	{
		this.a = i;
		this.b = j;

	}

}

class MyComp implements Comparator<String>
{

	int c = 0;

	MyComp(int d)
	{
		c = d;
	}

	@Override
	public int compare(String a, String b)
	{

		// < == -1

		String arr[] = a.split(" ");
		String brr[] = b.split(" ");

		return arr[c].compareTo(brr[c]);

	}

}

class MyComp2 implements Comparator<Node>
{

	@Override
	public int compare(Node a, Node b)
	{

		// < == -1

		if (a.b > b.b)
		{
			return -1;
		} else
		{
			return 1;
		}

	}

}