Thrifty Housekeeper
A family has a fondness for homemade round cookies. The lady of the house frequently bakes these cookies, having honed her skills to work swiftly and efficiently. She begins by rolling the dough into a rectangle and marking it with horizontal and vertical lines, spaced apart by the diameter of the cookie. Using a cutter, she then cuts out a circle from each square section of dough, forming the cookies. Any leftover dough is reshaped into another rectangle of the same thickness, and the process is repeated to cut out more cookies. This continues until all the dough is used, or there's a leftover piece too small to cut another cookie, no matter how it's reshaped into a rectangle (maintaining the same thickness).
Given the area of the initial rectangle and the radius of the cookie, determine the maximum number of cookies the lady can produce.
Input
The first line contains two integers separated by a space: S – the area of the initial rectangle of dough (cm²), and R – the radius of the cookie (cm), where 1 ≤ S, R ≤ 2×10⁹.
Output
The first line should contain one integer – the maximum number of cookies of the specified radius that can be made from the available dough.