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 sys
f = sys.stdin


while True:
    x, h = (int(f.readline()) for i in range(2))
    if x == h == 0:
        break
    triangle_height = (h ** 2 + (x / 2) ** 2) ** 0.5
    s = x ** 2 + 4 * x * triangle_height / 2
    print('{:.6f}'.format(s))