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 PYTHON):

Solution:
import math

def suicide(x, h):
    r2 = (math.sqrt(2)*x*0.5)**2 + h**2
    t2 = r2 - (0.5*x)**2
    t = math.sqrt(t2)
    S = x*x + 4*(x*t*0.5)
    print S

import sys

x = 0
h = 0
for line in sys.stdin:
    if x == 0:
        x = int(line.rstrip())
    elif x:
        h = int(line.rstrip())
    if x  and h :
        suicide(x, h)
        x = 0
        h = 0