Amy bought a unique aquarium at a flea market, and she asked you to help her pour water into it.

The aquarium consists of n hollow columns with heights h_1, h_2, \dots, h_n that are glued together. For example, an aquarium consisting of 10 columns with heights (9, 5, 4, 7, 3, 6, 5, 2, 4, 8) looks like this:

Now she asks you to start pouring V liters of water into column q (1-based indexing), but you are afraid of overfilling, so you agreed to write a program to help both of you. The program should tell you how high the water level will be, measured from the bottom of column q, after you are done pouring V liters of water into it.

Note that water may overflow from one column to adjacent columns (at the same rate to the left and right), and it might also spill out of the aquarium.

Input:

The first line contains an integer n, which is the number of columns in the aquarium.

The second line contains h_1, h_2, \dots, h_n, which are the column heights (floating-point numbers).

The third line contains two integers q and V, where q is the index of the column into which to pour the water, and V is the number of liters to pour.

Output:

Output the water level W, measured from the bottom of column q, after pouring V liters of water into column q.

Your solution will be accepted if the absolute difference |your answer − the correct answer| is less than 0.01.

Constraints

• 0 < n < 10^4
• 1.0 < h_i < 10^6
• 1 \leq q \leq n
• 1.0 < V < 10^{12}

Example 1

Input:

10
9 5 4 7 3 6 5 2 4 8
6 72

Output:

8

Example 2

Input:

10
9 7 5 3 1 2 4 6 8 10 
5 11

Output:

3.66667

For a better understanding of Example 1, look at the following pictures: After pouring 10 liters of water into column 6, we will have the following state:

And after pouring two more liters:

In the end, after pouring all 72 liters of water, we will reach the following state, and column 6 will have a height of 8: