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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
long long a[1000000], i, j, k, n, u, samax, PreL, PreR;
double smax = -10e9;
long long bs(long long x, long long L, long long R) {
  long long mid = (L + R) / 2;
  if (a[mid] == x || a[R] == x || a[L] == x) return (x);
  if (x <= a[L]) return (a[L]);
  if (x >= a[R]) return (a[R]);
  if (x > a[mid]) {
    L = mid;
    samax = max(samax, a[mid]);
  }
  if (x < a[mid]) R = mid;
  if (PreL == L && PreR == R) return (-1);
  PreL = L;
  PreR = R;
  return (max(samax, bs(x, L, R)));
}
int main() {
  std::cout.precision(9);
  cin >> n >> u;
  for (i = 1; i <= n; ++i) cin >> a[i];
  sort(a + 1, a + 1 + n);
  for (i = 1; i <= n; ++i) {
    j = i + 1;
    samax = 0;
    PreR = n;
    PreL = 1;
    k = bs(a[i] + u, 1, n);
    if (k == -1) continue;
    if (k - a[i] <= u && k - a[i] != 0)
      smax = max(smax, (double)(k - a[j]) / (k - a[i]));
  }
  if (smax <= 0)
    cout << "-1";
  else
    cout << smax << endl;
  return 0;
}