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.*;
import java.awt.geom.*;
public class Main {

	private void doit(){
		Scanner sc = new Scanner(System.in);
		while(true){
			int x = sc.nextInt();
			int h = sc.nextInt();
			if((x|h) == 0) break;
			double areaxx = x * x;
			double b = (double)x / 2; 
			double c = Math.sqrt(b * b + h * h);
			double tri = x * c / 2 * 4;
			double res = areaxx + tri;
			System.out.printf("%.6f\n",res);
		}
	}

	public static void main(String[] args) {
		Main obj = new Main();
		obj.doit();
	}
}