CodeForces - 924B Three-level Laser(贪心)

B. Three-level Laser

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

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

Copy

4 4
1 3 5 7

output

Copy

0.5

input

Copy

10 8
10 13 15 16 17 19 20 22 24 25

output

Copy

0.875

input

Copy

3 1
2 5 10

output

Copy

-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：给你一个递增的序列，求一个最大的n，n=(a[k]-a[j])/(a[k]-a[i]),其中(0=0) (len<=1e5)

思路：首先  n肯定是小于1的。因此我们若要使其最大，就要使k最大，i和j尽可能的最接近且最小。

因此只需要枚举i，j就是i+1，然后每次都求出满足条件的最大的k，取一下最大值即可。

为了保证精度，我用了double，取了14位小数。

代码：

#include
#define ll long long
#define inf 0x3f3f3f3f
using namespace std;
const int maxn=100010;
int n,m,k,f;
double ans,tmp,cnt;
double u,a[maxn],b,c;
char s[maxn];
int main()
{
    int T,cas=1;
    while(cin>>n>>u)
    {
        ans=-1;
        cnt=0;
        for(int i=0;i>a[i];
        int i=0,k=2;
        while(ians) ans=tmp;
            }
            i++;
        }
        if(ans==-1) puts("-1");
        else cout<