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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.FileNotFoundException;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Asgar Javadov
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        MathUtils.Rational minus = new MathUtils.Rational(-1, 1);
        MathUtils.Rational temp = new MathUtils.Rational(0, 1);

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt();
            int u = in.nextInt();

            int[] e = in.readIntArray(n);

            MathUtils.Rational mx = new MathUtils.Rational(-1, 1);

            for (int i = 0; i + 2 < n; ++i) {
                temp = compute(i, u, e);
                if (mx.compareTo(temp) < 0) {
                    mx.setUp(temp.up);
                    mx.setDown(temp.down);
                }
            }

            out.println(mx.getValue());
        }

        private MathUtils.Rational compute(int i, int u, int[] e) {
            int pos = ArrayUtils.upperBound(e, e[i] + u);
            if (pos < i + 2)
                return minus;

            temp.setUp(e[pos] - e[i + 1]);
            temp.setDown(e[pos] - e[i]);
            return temp;
        }

    }

    static class ArrayUtils {
        public static int upperBound(int[] array, int val) {
            int low = 0, high = array.length - 1;
            while (low <= high) {
                int mid = (low + high) >> 1;
                if (val < array[mid]) high = mid - 1;
                else low = mid + 1;
            }
            return high;
        }

    }

    static class OutputWriter extends PrintWriter {
        public OutputWriter(OutputStream outputStream) {
            super(outputStream);
        }

        public OutputWriter(Writer writer) {
            super(writer);
        }

        public OutputWriter(String filename) throws FileNotFoundException {
            super(filename);
        }

        public void close() {
            super.close();
        }

    }

    static class InputReader extends BufferedReader {
        StringTokenizer tokenizer;

        public InputReader(InputStream inputStream) {
            super(new InputStreamReader(inputStream), 32768);
        }

        public InputReader(String filename) {
            super(new InputStreamReader(Thread.currentThread().getContextClassLoader().getResourceAsStream(filename)));
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(readLine());
                } catch (IOException e) {
                    throw new RuntimeException();
                }
            }
            return tokenizer.nextToken();
        }

        public Integer nextInt() {
            return Integer.valueOf(next());
        }

        public int[] readIntArray(int size) {
            int[] array = new int[size];
            for (int i = 0; i < size; i++)
                array[i] = nextInt();
            return array;
        }

    }

    static class MathUtils {
        public static class Rational implements Comparable<MathUtils.Rational> {
            public int up;
            public int down;

            public Rational(int up, int down) {
                if (down == 0)
                    throw new IllegalArgumentException("denominator can't be zero.");
                this.up = up;
                this.down = down;
                if (down < 0) {
                    this.up = -up;
                    this.down = -down;
                }
            }


            public int compareTo(MathUtils.Rational o) {
                return Long.compare(this.up * (long) o.down, this.down * (long) o.up);
            }

            public void setUp(int up) {
                this.up = up;
            }

            public void setDown(int down) {
                if (down == 0)
                    throw new IllegalArgumentException("denominator can't be zero.");
                this.down = down;
                if (down < 0) {
                    this.down = -down;
                    this.up = -up;
                }
            }

            public double getValue() {
                return this.up / (double) this.down;
            }


            public boolean equals(Object o) {
                if (this == o) return true;
                if (!(o instanceof MathUtils.Rational)) return false;

                MathUtils.Rational rational = (MathUtils.Rational) o;
                return this.compareTo(rational) == 0;
            }


            public int hashCode() {
                int result = up;
                result = 31 * result + down;
                return result;
            }

        }

    }
}