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 {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		Scanner cin = new Scanner(System.in);
		while(true){
			int x=cin.nextInt();
			int h=cin.nextInt();
			if(x+h==0){
				break;
			}
			double hen = Math.sqrt(Math.pow((double)x*Math.sqrt(2)/2.0, 2) + Math.pow(h, 2));
			double a =  Math.sqrt(Math.pow(hen, 2) - Math.pow((double)x/2.0, 2));
			double tri = (double)x*a/2.0;
			System.out.printf("%.6f\n", tri*4+x*x);
		}
	}

}