codeforces 957C -Three-level Laser（二分+数学）

Problem Description

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 , 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 .

 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 .

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

题意：

输入n，u，给你n个数，严格单调递增，数据范围1e9.,然后让你选出三个数，下标分别为i,j,k，(i<j<k),且a[k]-a[i]<=u,求(a[k]-a[j])/(a[k]-a[i])的最大值。

 

思路：

当a[k]为定值时，要求式子最大，则应a[j]较小，a[i]较大。又i<j,所以j=i+1.又题目要求的公式的最大值可化为(a[k]-a[j])/(a[j]-a[i]+a[k]-a[j])，即x/(x+常数）的形式，要使比值最大，则应使x尽可能大，即a[k]-a[j]尽可能大，把i,j看成已知，则需使a[k]尽可能大，由于题目给定a[k]-a[i]<=u，这样我们只需要对于每一个i找到最大的k使得a[k]-a[i]<=u即为起始为i的函数的最大值。

代码：

#include<bits/stdc++.h>
using namespace std;
int n,u;
int a[100005];
int main(){
    while(cin>>n>>u){
        for(int i=1;i<=n;i++){
            cin>>a[i];
        }
        double re=-1;
        for(int i=1;i<=n;i++){
            int low=i+2,high=n;
            int result=-1;
            while(low<=high){
                int mid=(low+high)/2;
                if(a[mid]-a[i]<=u){
                    result=mid;
                    low=mid+1;
                }
                else {
                    high=mid-1;
                }
            }
            if(result!=-1){
                re=max(re,(double)(a[result]-a[i+1])/(double)(a[result]-a[i]));
            }
        }
        if(re==-1){
            cout<<-1<<endl;
        }
        else {
            cout<<re<<endl;
        }
    }
return 0;
}