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 PYTHON3):

Solution:
import math

while True:
    x = int(input())
    h = int(input())
    if x == 0 and h == 0:
        break


    S = 1/2 * x * 4*(1/4 * x**2 + h**2)**0.5 + x**2
    print(S)