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 static java.lang.Math.*;
import static java.util.Arrays.*;

public class Main {

	int INF = 1 << 28;

	void run() {
		Scanner sc = new Scanner(System.in);
		for(;;) {
			int x = sc.nextInt();
			int y = sc.nextInt();
			if( (x|y) == 0 ) break;
			
			System.out.println( (1.0*x*x + 2.0*x*sqrt(1.0*y*y+1.0*x*x/4) ) );
		}
	}

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

	void debug(Object... os) {
		System.err.println(Arrays.deepToString(os));
	}
}