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 static java.lang.Math.*;
import java.text.DecimalFormat;
import java.util.Scanner;
public class Main{
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		DecimalFormat df1 = new DecimalFormat("########.000000");
		while(sc.hasNext()){
			int x = sc.nextInt();
			int h = sc.nextInt();
			if((x == 0 && h == 0) || (x > 100 || h > 100)) break;
			double sh = sqrt(pow(0.5*x,2) + pow(h,2));
			double S = pow(x,2) + 4*(0.5*x*sh);
			System.out.println(df1.format(S));
		}
	}
}