Ellipse

Description

There is an beautiful ellipse whose curve equation is:

.

There is a parallelogram named P inscribed in this ellipse. At the same time, the parallelogram P is externally tangent to some circle center at the origin (0,0).

Now your task is to output the maximum and minimum area of P among all possible conditions.

Input

The input consists of multiple test cases.

For each test case, there is exactly one line consists of two integers a and b. 0 < b <= a <= 10⁹

Output

For each test case, output one line of two one-space splited numbers: the maximum area and the minimum area. The absolute or relative error of the coordinates should be no more than 10^-6.

Sample Input

1 1

Sample Output

2 2

题意：一个椭圆内切一个平行四边形，平行四边形里内切一个以原点为圆心的圆

解题思路：（这撒比的题意，和刘哲贤学姐愣是猜了两个多小时）最后能出的题都出了，他俩在搞下雨的那个数学题，我在看题，画来画去最后还是觉得里面内切一个圆才合适，好好高中几何学的够硬，比划着找出来两个临界状态，但是最后一句话，说了保留精度，但是案例没有输出小数点，唉~弄得最后这个题没出，还是比完赛才试着改了改提交了。

感悟：灵光一闪太**的重要了；

代码：

#include

#include

using namespace std;

int main()

{

    double a,b;

    while(scanf("%lf%lf",&a,&b)!=EOF)

        printf("%f %f\n",2*a*b,(4*a*a*b*b)/(a*a+b*b));

    return 0;

}