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.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.util.*;
import java.util.Map.Entry;

public class Main
{
	private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;
	private SpaceCharFilter filter;
	private PrintWriter pw;
	private long mod = 1000000000
			+ 7;

	private StringBuilder ans_sb;
	private long sum = 0;
	private int[] cnt;

	private void soln()
	{
		int n = nextInt();
		int u = nextInt();
		int[] es = new int[n];
		for (int i = 0; i < n; i++)
		{
			es[i] = nextInt();
		}
		double ans1 = 0;
		long a1 = 0;
		long a2 = 0;
		for (int i = 0; i < n
				- 2; i++)
		{
			if (es[i + 2]
					- es[i] > u)
				continue;
			int l = i
					+ 2;
			int r = n
					- 1;
			int ans = 0;
			while (l <= r)
			{
				int mid = ((l
						+ r) >> 1);
				if (es[mid]
						- es[i] <= u)
				{
					l = mid + 1;
					ans = mid;
				} else
				{
					r = mid - 1;
				}
			}
			long ek = es[ans];
			long ei = es[i];
			long ej = es[i
					+ 1];
			if (ans1 == 0)
			{
				a1 = ek - ej;
				a2 = ek - ei;
				ans1 = 1;
			} else
			{
				long d1 = ek
						- ej;
				long d2 = ek
						- ei;
				if (d1 * a2 > a1
						* d2)
				{
					a1 = d1;
					a2 = d2;
				}
			}
			// double tmp1 = (ek-ej)/(ek-ei);
			// debug(tmp1);
			// ans1 = Math.max(ans1, tmp1);
		}
		if (ans1 == 0)
			pw.println(
					-1);
		else
			pw.println(
					((double) a1)
							/ ((double) a2));
		/*
		 * int[] ms = nextIntArray(n); int max = 0; int[] ans = new int[n]; int[] pref =
		 * new int[n]; for(int i=0;i<n;i++) { if(max<ms[i]) { int diff = ms[i] - max;
		 * pref[i-diff+1]++; pref[i]--; max = ms[i]; }else { ans[i] = max - ms[i]; } }
		 * //debug(ans); int add = 0; long aa = 0; for(int i=0;i<n;i++) { add +=
		 * pref[i]; ans[i] += add; aa += (long)ans[i]; } // debug(ans); pw.println(aa);
		 */
	}

	class BitsetLong
	{

		static final int LOG = 6;
		static final int SIZE = 1 << LOG;
		static final int MASK = SIZE
				- 1;

		private long[] data;

		public BitsetLong(
				int n)
		{
			data = new long[(n >> LOG)
					+ 2];
		}

		void set(
				int i)
		{
			data[i >> LOG] |= 1L << (i
					& MASK);
		}

		void unset(
				int i)
		{
			data[i >> LOG] &= ~(1L << (i
					& MASK));
		}

		void flip(
				int i)
		{
			data[i >> LOG] ^= 1L << (i
					& MASK);
		}

		int get(int i)
		{
			return (int) ((data[i >> LOG] >>> (i
					& MASK))
					& 1);
		}

		void print()
		{
			for (int i = 0; i < data.length; i++)
			{
				System.out
						.print(Long
								.toString(
										data[i],
										2));
			}
			System.out
					.println();
		}

		long getWord(
				int i)
		{
			if (i <= -SIZE
					|| (i >> LOG)
							+ 1 >= data.length)
			{
				return 0;
			}
			int rem = i
					& MASK;
			int idx = i >> LOG;

			if (rem == 0)
			{
				return data[idx];
			}

			long head = idx < 0
					? 0
					: (data[idx] >>> rem);
			long tail = data[idx
					+ 1] << (SIZE
							- rem);

			return head
					| tail;
		}
	}

	int count(
			long[] bs,
			int len)
	{
		int ret = 0;
		for (int i = 0; i << 6 < len; i++)
		{
			if (((i + 1) << 6) <= len)
			{
				ret += Long
						.bitCount(
								bs[i]);
			} else
			{
				int rem = len
						& 63;
				ret += Long
						.bitCount(
								bs[i] << (64
										- rem));
			}
		}
		return ret;
	}

	private class Pair
			implements
			Comparable<Pair>
	{
		int v, i,
				j;

		public Pair(
				int a,
				int b,
				int c)
		{
			v = a;
			i = b;
			j = c;
		}

		@Override
		public int compareTo(
				Pair arg0)
		{
			return this.v
					- arg0.v;
		}
	}

	private class Bridge
	{
		private LinkedList<Edge>[] graph;
		private LinkedList<Integer>[] tree;
		private int t;
		private boolean[] isBridge;
		private int[] cno;

		public Bridge(
				int n,
				int m)
		{
			pre(n, m);
		}

		private class Edge
		{
			int u, v,
					i;

			public Edge(
					int a,
					int b,
					int c)
			{
				u = a;
				v = b;
				i = c;
			}
		}

		private void pre(
				int n,
				int m)
		{
			graph = new LinkedList[n];
			tree = new LinkedList[n];
			for (int i = 0; i < m; i++)
			{
				int u = nextInt()
						- 1;
				int v = nextInt()
						- 1;
				Edge e = new Edge(
						u,
						v,
						i);
				graph[u].add(
						e);
				graph[v].add(
						e);
			}
			isBridge = new boolean[m];
			cno = new int[n];
			boolean[] v = new boolean[n];
			int[] arr = new int[n];
			for (int i = 0; i < n; i++)
				if (!v[i])
					dfs(i, null,
							v,
							arr);
		}

		private int dfs(
				int u,
				Edge e,
				boolean[] v,
				int[] arr)
		{
			v[u] = true;
			arr[u] = t++;
			int min = arr[u];
			Iterator<Edge> it = graph[u]
					.listIterator();
			while (it
					.hasNext())
			{
				Edge x = it
						.next();
				int w = x.u;
				if (x.u == u)
					w = x.v;
				if (!v[w])
					min = Math
							.min(min,
									dfs(w, x,
											v,
											arr));
				else if (x != e)
					min = Math
							.min(min,
									arr[w]);
			}
			if (min == arr[u]
					&& e != null)
				isBridge[e.i] = true;
			return min;
		}

		private void bfs(
				int u,
				int cmpNo,
				Queue<Integer>[] q,
				boolean[] v)
		{
			int cur = cmpNo;
			cno[cur] = cmpNo;
			q[cur].add(
					u);
			v[u] = true;
			while (!q[cur]
					.isEmpty())
			{
				int x = q[cur]
						.poll();
				Iterator<Edge> it = graph[x]
						.listIterator();
				while (it
						.hasNext())
				{
					Edge x1 = it
							.next();
					int w = x1.u;
					if (w == x)
						w = x1.v;
					if (!v[w])
					{
						if (isBridge[x1.i])
						{
							tree[cur]
									.add(0, cmpNo
											+ 1);
							tree[cmpNo
									+ 1].add(
											0,
											cur);
							bfs(w, cmpNo
									+ 1,
									q,
									v);
						} else
						{
							bfs(w, cmpNo,
									q,
									v);
						}
					}
				}
			}
		}
	}

	private String solveEqn(
			long a,
			long b)
	{
		long x = 0,
				y = 1,
				lastx = 1,
				lasty = 0,
				temp;
		while (b != 0)
		{
			long q = a
					/ b;
			long r = a
					% b;
			a = b;
			b = r;
			temp = x;
			x = lastx
					- q * x;
			lastx = temp;
			temp = y;
			y = lasty
					- q * y;
			lasty = temp;
		}
		return lastx
				+ " "
				+ lasty;
	}

	private void debug(
			Object... o)
	{
		System.out
				.println(
						Arrays.deepToString(
								o));
	}

	private long pow(
			long a,
			long b,
			long c)
	{
		if (b == 0)
			return 1;
		long p = pow(
				a,
				b / 2,
				c);
		p = (p * p)
				% c;
		return (b
				% 2 == 0)
						? p
						: (a * p)
								% c;
	}

	private long gcd(
			long n,
			long l)
	{
		if (l == 0)
			return n;
		return gcd(
				l,
				n % l);
	}

	public static void main(
			String[] args)
			throws Exception
	{
		new Thread(
				null,
				new Runnable()
				{
					@Override
					public void run()
					{
						new Main()
								.solve();
					}
				},
				"1",
				1 << 26).start();
		// new Main().solve();
	}

	public StringBuilder solve()
	{
		InputReader(
				System.in);
		/*
		 * try { InputReader(new FileInputStream("C:\\Users\\hardik\\Desktop\\in.txt"));
		 * } catch(FileNotFoundException e) {}
		 */
		pw = new PrintWriter(
				System.out);
		// ans_sb = new StringBuilder();
		soln();

		pw.close();
		// System.out.println(ans_sb);
		return ans_sb;
	}

	public void InputReader(
			InputStream stream1)
	{
		stream = stream1;
	}

	private boolean isWhitespace(
			int c)
	{
		return c == ' '
				|| c == '\n'
				|| c == '\r'
				|| c == '\t'
				|| c == -1;
	}

	private boolean isEndOfLine(
			int c)
	{
		return c == '\n'
				|| c == '\r'
				|| c == -1;
	}

	private int read()
	{
		if (numChars == -1)
			throw new InputMismatchException();
		if (curChar >= numChars)
		{
			curChar = 0;
			try
			{
				numChars = stream
						.read(buf);
			} catch (IOException e)
			{
				throw new InputMismatchException();
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}

	private int nextInt()
	{
		int c = read();
		while (isSpaceChar(
				c))
			c = read();
		int sgn = 1;
		if (c == '-')
		{
			sgn = -1;
			c = read();
		}
		int res = 0;
		do
		{
			if (c < '0'
					|| c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(
				c));
		return res
				* sgn;
	}

	private long nextLong()
	{
		int c = read();
		while (isSpaceChar(
				c))
			c = read();
		int sgn = 1;
		if (c == '-')
		{
			sgn = -1;
			c = read();
		}
		long res = 0;
		do
		{
			if (c < '0'
					|| c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(
				c));
		return res
				* sgn;
	}

	private String nextToken()
	{
		int c = read();
		while (isSpaceChar(
				c))
			c = read();
		StringBuilder res = new StringBuilder();
		do
		{
			res.appendCodePoint(
					c);
			c = read();
		} while (!isSpaceChar(
				c));
		return res
				.toString();
	}

	private String nextLine()
	{
		int c = read();
		while (isSpaceChar(
				c))
			c = read();
		StringBuilder res = new StringBuilder();
		do
		{
			res.appendCodePoint(
					c);
			c = read();
		} while (!isEndOfLine(
				c));
		return res
				.toString();
	}

	private int[] nextIntArray(
			int n)
	{
		int[] arr = new int[n];
		for (int i = 0; i < n; i++)
		{
			arr[i] = nextInt();
		}
		return arr;
	}

	private long[] nextLongArray(
			int n)
	{
		long[] arr = new long[n];
		for (int i = 0; i < n; i++)
		{
			arr[i] = nextLong();
		}
		return arr;
	}

	private void pArray(
			int[] arr)
	{
		for (int i = 0; i < arr.length; i++)
		{
			System.out
					.print(arr[i]
							+ " ");
		}
		System.out
				.println();
		return;
	}

	private void pArray(
			long[] arr)
	{
		for (int i = 0; i < arr.length; i++)
		{
			System.out
					.print(arr[i]
							+ " ");
		}
		System.out
				.println();
		return;
	}

	private boolean isSpaceChar(
			int c)
	{
		if (filter != null)
			return filter
					.isSpaceChar(
							c);
		return isWhitespace(
				c);
	}

	private char nextChar()
	{
		int c = read();
		while (isSpaceChar(
				c))
			c = read();
		char c1 = (char) c;
		while (!isSpaceChar(
				c))
			c = read();
		return c1;
	}

	private interface SpaceCharFilter
	{
		public boolean isSpaceChar(
				int ch);
	}
}