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:
//pakage joney_000[let_me_start]
//
import java.util.*;
import java.lang.*;
import java.io.*;
import java.math.*;
/*
 * Author    : joney_000[let_me_start]
 * Algorithm : N/A
 * Platform  : N/A
 *
 */


/*    The Main Class                */
public class A{
 
  private InputStream inputStream ;
  private OutputStream outputStream ;
  private FastReader in ;
  private PrintWriter out ;
  /*
    Overhead [Additional Temporary Strorage] but provides memory reusibility for multiple test cases.
    Size Limit : 10^5 + 4 
  */
  private final int BUFFER = 50;
  private int    tempints[] = new int[BUFFER];
  private long   templongs[] = new long[BUFFER];
  private double tempdoubles[] = new double[BUFFER];
  private char   tempchars[] = new char[BUFFER];
  //private final long mod = 1000000000+7;
  private final int  INF  = Integer.MAX_VALUE / 10;
  private final long INF_L  = Long.MAX_VALUE / 10;

  public A(){}
  public A(boolean stdIO)throws FileNotFoundException{
    // stdIO = false;
    if(stdIO){
      inputStream = System.in;
      outputStream = System.out;
    }else{
      inputStream = new FileInputStream("output.txt");
      outputStream = new FileOutputStream("output1.txt");
    }
    in = new FastReader(inputStream);
    out = new PrintWriter(outputStream);

  }
  void run()throws Exception{
    int n = i(); int m = i();
    double e[] = new double[n + 2];
    for(int i = 1; i <= n; i++)e[i] = d();
    e[n + 1] = 2e9;
    int u[] = new int[n + 1];
    
    int ptr = 1;
    boolean isValid = false;
    
    for(int i = 1; i <= n - 2; i++){
      if(e[i + 2] - e[i] <= m)isValid = true;
    }

    for(int i = 1; i <= n - 2; i++){
      if(e[i + 2] - e[i] > m)continue;
      ptr = Math.max(ptr, i);
      while(ptr <= n && e[ptr] - e[i] <= m){
        ++ptr;
      }
      u[i] = ptr - 1;
    }

    double ans = -2e9;
    for(int i = 1; i <= n - 2; i++){
      if(e[i + 2] - e[i] > m)continue;
      // out.write(""+ u[i] + " " + ans+"\n");
      ans = Math.max(ans, (e[u[i]] - e[i + 1])/(e[u[i]] - e[i]));
    }

    if(!isValid){
      out.write("-1");
      return;
    }

    out.write(""+ans+"\n");
  }// end run

  void clear(){
    
  }

  //****************************** Gerenal Utilities ***********************//

  void print_r(Object... o){
    out.write("\n"+Arrays.deepToString(o)+"\n");
    out.flush();
  }

  boolean isPrime(long n){
    if(n==1)return false;
    if(n<=3)return true;
    if(n%2==0)return false;
    for(int i=2 ;i <= Math.sqrt(n); i++){
      if(n%i==0)return false;
    }
    return true;
  }
  // sieve
  int[] primes(int n){       // for(int i=1;i<=arr.length-1;i++)out.write(""+arr[i]+" ");
    boolean arr[] = new boolean[n+1];
    Arrays.fill(arr,true);
    arr[1]=false;
    for(int i=2;i<=Math.sqrt(n);i++){
      if(!arr[i])continue;
      for(int j = 2*i ;j<=n;j+=i){
        arr[j]=false;
      }
    }
    LinkedList<Integer> ll = new LinkedList<Integer>();
    for(int i=1;i<=n;i++){  
      if(arr[i])ll.add(i);
    }
    n = ll.size();
    
    int primes[] = new int[n+1];
    for(int i=1;i<=n;i++){
      primes[i]=ll.removeFirst();
    }
    return primes;
  }

  long gcd(long a , long b){
    if(b==0)return a;
    return gcd(b , a%b);
  }

  long lcm(long a , long b){
    if(a==0||b==0)return 0;
    return (a*b)/gcd(a,b);
  }

  long mulmod(long a , long b ,long mod){
    if(a==0||b==0)return 0;
    if(b==1)return a;
    long ans = mulmod(a,b/2,mod);
    ans = (ans*2)% mod;
    if(b%2==1)ans = (a + ans)% mod;
    return ans;
  }
  
  long pow(long a , long b ,long mod){
    if(b==0)return 1;
    if(b==1)return a;
    long ans = pow(a,b/2,mod);
    ans = (ans * ans);
    if(ans >= mod )ans %= mod;

    if(b%2==1)ans = (a * ans);
    if(ans >= mod )ans %= mod;

    return ans;
  }
  // 20*20   nCr Pascal Table
  long[][] ncrTable(){
    long ncr[][] = new long[21][21];
    for(int i=0 ;i<=20 ;i++){ncr[i][0]=1;ncr[i][i]=1;}
      for(int j=0;j<=20 ;j++){
        for(int i=j+1;i<= 20 ;i++){
          ncr[i][j] = ncr[i-1][j]+ncr[i-1][j-1];
        }
      }
    return ncr;
  }
  //*******************************I/O******************************//  
  int i()throws Exception{
    //return Integer.parseInt(br.readLine().trim());
    return in.nextInt();
  }
  int[] is(int n)throws Exception{
  //int arr[] = new int[n+1];
    for(int i=1 ; i <= n ;i++)tempints[i] = in.nextInt();  
      return tempints;
  }
  long l()throws Exception{
    return in.nextLong();
  }
  long[] ls(int n)throws Exception{
    for(int i=1 ; i <= n ;i++)templongs[i] = in.nextLong();  
      return templongs;
  }

  double d()throws Exception{
    return in.nextDouble();
  }
  double[] ds(int n)throws Exception{
    for(int i=1 ; i <= n ;i++)tempdoubles[i] = in.nextDouble();  
      return tempdoubles;
  }
  char c()throws Exception{
    return in.nextCharacter();
  }
  char[] cs(int n)throws Exception{
    for(int i=1 ; i <= n ;i++)tempchars[i] = in.nextCharacter();  
      return tempchars;
  }
  String s()throws Exception{
    return in.nextLine();
  }
  BigInteger bi()throws Exception{
    return in.nextBigInteger();
  }
//***********************I/O ENDS ***********************//
//*********************** 0.3%f [precision]***********************//
/* roundoff upto 2 digits 
   double roundOff = Math.round(a * 100.0) / 100.0;
                    or
   System.out.printf("%.2f", val);
          
*/
/*
  print upto 2 digits after decimal
  val = ((long)(val * 100.0))/100.0;
  
*/    

    private void closeResources(){
     out.flush();
     out.close();
     return;
    }
    public static void main(String[] args) throws java.lang.Exception{
    //let_me_start Shinch Returns 


    /*  
        // Old Reader Writer
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter out=new BufferedWriter(new OutputStreamWriter(System.out));
    BufferedReader br=new BufferedReader(new FileReader("input.txt"));
        BufferedWriter out=new BufferedWriter(new FileWriter("output.txt"));
    */   
        A driver = new A(true);
        
        driver.run();

        driver.closeResources();
        return ;

      }  

    }

    class FastReader{

      private boolean finished = false;

      private InputStream stream;
      private byte[] buf = new byte[4 * 1024];
      private int curChar;
      private int numChars;
      private SpaceCharFilter filter;

      public FastReader(InputStream stream){
        this.stream = stream;
      }

      public 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++];
      }

      public int peek(){
        if (numChars == -1){
          return -1;
        }
        if (curChar >= numChars){
          curChar = 0;
          try{
            numChars = stream.read (buf);
          } catch (IOException e){
            return -1;
          }
          if (numChars <= 0){
            return -1;
          }
        }
        return buf[curChar];
      }

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

      public 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;
      }

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

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

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

      private String readLine0(){
        StringBuilder buf = new StringBuilder ();
        int c = read ();
        while (c != '\n' && c != -1){
          if (c != '\r'){
            buf.appendCodePoint (c);
          }
          c = read ();
        }
        return buf.toString ();
      }

      public String nextLine(){
        String s = readLine0 ();
        while (s.trim ().length () == 0)
          s = readLine0 ();
        return s;
      }

      public String nextLine(boolean ignoreEmptyLines){
        if (ignoreEmptyLines){
          return nextLine ();
        }else{
          return readLine0 ();
        }
      }

      public BigInteger nextBigInteger(){
        try{
          return new BigInteger (nextString ());
        } catch (NumberFormatException e){
          throw new InputMismatchException ();
        }
      }

      public char nextCharacter(){
        int c = read ();
        while (isSpaceChar (c))
          c = read ();
        return (char) c;
      }

      public double nextDouble(){
        int c = read ();
        while (isSpaceChar (c))
          c = read ();
        int sgn = 1;
        if (c == '-'){
          sgn = -1;
          c = read ();
        }
        double res = 0;
        while (!isSpaceChar (c) && c != '.'){
          if (c == 'e' || c == 'E'){
            return res * Math.pow (10, nextInt ());
          }
          if (c < '0' || c > '9'){
            throw new InputMismatchException ();
          }
          res *= 10;
          res += c - '0';
          c = read ();
        }
        if (c == '.'){
          c = read ();
          double m = 1;
          while (!isSpaceChar (c)){
            if (c == 'e' || c == 'E'){
              return res * Math.pow (10, nextInt ());
            }
            if (c < '0' || c > '9'){
              throw new InputMismatchException ();
            }
            m /= 10;
            res += (c - '0') * m;
            c = read ();
          }
        }
        return res * sgn;
      }

      public boolean isExhausted(){
        int value;
        while (isSpaceChar (value = peek ()) && value != -1)
          read ();
        return value == -1;
      }

      public String next(){
        return nextString ();
      }

      public SpaceCharFilter getFilter(){
        return filter;
      }

      public void setFilter(SpaceCharFilter filter){
        this.filter = filter;
      }

      public interface SpaceCharFilter{
        public boolean isSpaceChar(int ch);
      }
    }
    /******************** Pair class ***********************/

  class Pair implements Comparable<Pair>{
     public int a;
     public int b;
          public int c;
     public Pair(){
      this.a = 0;
      this.b = 0;
    }
    public Pair(int a,int b, int c){
      this.a = a;
      this.b = b;
      this.c = c;
    }
    public int compareTo(Pair p){
      if(this.a==p.a){
       return this.b-p.b;  
     }
     return p.a-this.a; 
   }
   public String toString(){
    return "a="+this.a+" b="+this.b;
  }

}