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:
while(1):
    x,h = [int(input()) for i in range(2)]
    if x == 0 and h == 0:
        break
    x,h = [float(i) for i in [x,h]]
    tot = x**2 + 4*0.5*x*(h**2 + (x/2)**2)**(0.5)
    print("{:.6f}".format(tot))