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<iomanip>
#include<cmath>
using namespace std;
int p, q; double s;
int main() {
	while (1) {
		cin >> p >> q; s = 0;
		if (!p) { break; }
		s += p*p;
		s += 2.0 * p * sqrt(q*q + (double)(p*p) / 4);
		cout << fixed << setprecision(15) << s << endl;
	}
}