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 <algorithm>
#include <cstdio>
#include <cmath>
using namespace std;

int main() {
  int x, h;
  while(scanf("%d%d", &x, &h) && (x | h)) {
    double m = sqrt(h*h + x*x/2.0);
    double s = (m*2+x)/2.0;
    double S = sqrt(s*(s-m)*(s-m)*(s-x));
    printf("%.10f\n", 4*S + x*x);
  }
}