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 JAVA):

Solution:
import java.util.Scanner;

public class Main {
	public static void main(String args[]) {
		Scanner sc = new Scanner(System.in);
		int x, h;
		
		x = sc.nextInt();
		h = sc.nextInt();
		while (x + h != 0) {
			double s = 0.0;
			double bottom = x * x * 1.0;
			double height = Math.sqrt(h * h * 1.0 + x * x * 1.0 / 4);
			double triangle = x * 1.0 * height / 2;
			
			s = bottom + 4 * triangle;
			System.out.println(s);
			
			x = sc.nextInt();
			h = sc.nextInt();
		}
	}
}