timus1084

A goat in a kitchen garden

http://acm.timus.ru/problem.aspx?space=1&num=1084

Time Limit: 2.0 second

Memory Limit: 1 000 K

Someone has let a goat in a square kitchen-garden and had bound it to a stake. The stake is driven into the ground in the very midst of the square. The goat is hungry as a hunter and very voracious, and eats everything that can be reached without leaving the square and tearing the roap. What area of the kitchen-garden will be ate round?

Input

contains lengths of the garden sides and a cord length in meters (natural numbers not exceeding 100, located in one line and separated with a space).

Output

should contain an area of the kitchen-garden (in square meters to within 3 symbols after a decimal point), ate round by the goat.

Sample Input

10 6

Sample Output

95.091

/*Written by czk*/
#include <iostream>
#include <iomanip>
#include <cmath>
using namespace std;

int main()
{
  int n, r;
  cin >> n >> r;
  if(n >= 2*r) {
    cout << fixed <<showpoint << setprecision(3) << 3.14159266*r*r << endl;
  } else if(n < r *1.41421356237){
    cout << fixed <<showpoint << setprecision(3) << 1.0*n*n << endl;
  } else {
    double theta = acos(n/2.0/r);
    cout << fixed << showpoint <<setprecision(3) << sin(theta)*r*n*2+r*r*(3.14159266-theta*4) << endl;
  }
}