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 stdIn =  new Scanner(System.in);
        
        while(true){
            double x = stdIn.nextInt();
            double h = stdIn.nextInt();
            
            if(x == 0 && h == 0){
                break;
            }
            
            System.out.println(x * x + x * Math.sqrt(h * h + x / 2 * x / 2) * 0.5 * 4);
        }
    }
}