Problem: Create a program that outputs the surface area S of a square cone with a height of h, with a square with one side x as the base. However, assume that the line segment connecting the apex and the center of the base is orthogonal to the base. Also, x and h are positive integers less than or equal to 100.

Input

Given multiple datasets. Each dataset is given in the following format:


x
h


When both x and h are 0, it indicates the end of input.



Output

Output S (real number) on one line for each data set. The output may contain an error of 0.00001 or less.

Example

Input

6
4
7
9
0
0


Output

96.000000
184.192455

Solution (in CPP):

Solution:
#include <iostream>
#include <cstdio>
#include <cmath>
using namespace std;

int main(void)
{
  while (true)
  {
    double x, h;
    cin >> x >> h;
    if (x == 0 and h == 0) break;
    double t_h = hypot(x/2, h);
    double result = x * t_h * 2 + pow(x, 2);
    printf("%.6lf\n", result);
  }
  return 0;
}