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:
# Aizu Problem 0073: Surface Area of Quadrangular Pyramid
#
import sys, math, os

# read input:
PYDEV = os.environ.get('PYDEV')
if PYDEV=="True":
    sys.stdin = open("sample-input.txt", "rt")


while True:
    x = int(input())
    h = int(input())
    if x == h == 0:
        break
    h_x = math.sqrt(h**2 + x**2 / 4)
    A = x**2 + 2 * x * h_x
    print("%.6f" % A)