A Math Contest P4 - Circle Cutting

View as PDF

Submit solution

Points: 7
Time limit: 2.0s
Memory limit: 256M

Problem type

Consider the unit circle, the circle with radius 1 centred at (0, 0). You will place N-1 horizontal lines such that the circle is cut into N regions with equal areas.

Find the equations of all of the lines.


2 \le N \le 2 \times 10^5

Input Specification

The only line contains an integer, N.

Output Specification

Output N-1 lines. The ith line should contain a floating-point number c_i such that the ith horizontal line has the equation y = c_i. These numbers should be output in increasing order.

Your answer will be accepted if each value is within an absolute error of 10^{-9}.

Sample Input


Sample Output



There are no comments at the moment.