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);
		
			while (true) {
				int x = sc.nextInt();
				int h = sc.nextInt();
				
					if (x == 0 && h == 0) { 
						break;
					}
				double S = surface_area_pyra(x, h);
				System.out.println(S);
			}
		sc.close();

	}

	private static double surface_area_pyra(int x, int h) {
		double x_2 = Math.pow(x, 2);
		double h_2 = Math.pow(h, 2);
		
		double S = x * Math.sqrt(4 * h_2 + x_2) + x_2;
		
		return S;
	}

}