Happy Bottle
As we all remember, Balbes survived a sword strike to the heart during a duel with Shurik, thanks to a bottle of wine hidden under his coat. This bottle was stolen from the warehouse where the duel took place.
After this incident, Balbes believes that stealing a bottle of wine from the warehouses he and his "friends" plan to rob after getting out of prison will bring him luck.
He noticed that bottles in warehouses are stored on shelves in a pyramid shape. Each bottle rests on two bottles from the row below. The bottles in the bottom row are fixed on the shelves, and each subsequent row has one less bottle than the row below. The base of each bottle is a circle with a radius of 1. The minimum distance between the centers of adjacent bottles is 2, and the maximum is 3.
Balbes has an intuition for which bottle in the warehouse will be lucky. He knows the row number where it is located and its position in that row. Balbes wants to know the coordinates of the center of the bottom of this bottle to easily find it in the dark.
Input
The first line contains the number N - the number of bottles in the bottom row. The next N lines provide the X-coordinates of the centers of the bottles in the bottom row (all Y-coordinates for these bottles are 1). Each coordinate is a real number with exactly 2 decimal places. The coordinates are listed from left to right.
Following this, there are two lines specifying: an integer row - the row number where the lucky bottle is located. Rows are numbered from bottom to top, starting at one. An integer index - the position of the lucky bottle in its row. Bottles in each row are numbered from left to right, starting at one.
Output
Two numbers on two lines - the first line contains the decimal representation of the X-coordinate of the center of the lucky bottle with exactly 3 decimal places, and the second line contains the decimal representation of the Y-coordinate of the center of the lucky bottle with exactly 3 decimal places.
To ensure the coordinates x and y are not incorrectly rounded due to calculation errors, all tests will satisfy the condition that the numbers 1000*x and 1000*y are at least 0.001 away from the nearest half-integers (i.e., numbers of the form x+0.5 for an integer x).
Constraints
The number of elements N in the lowbottle array is between 1 and 5 inclusive.
Elements of the lowbottle array are real numbers from 0 to 20 inclusive with exactly 2 decimal places. If A and B are two numbers in neighboring elements of the array, then B is between A + 2 and A + 3 inclusive.
The number row is between 1 and N inclusive.
The number index is between 1 and N - row + 1 inclusive.