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
import math
def main():
    for line in sys.stdin:
        x = int(line)
        h = int(input())

        if x != 0 and h != 0:
            s1 = x * math.sqrt(4 * (h ** 2) + x ** 2)
            s2 = s1 + x ** 2
            print("{:.6f}".format(s2))
        else:
            break

if __name__ == "__main__":
    main()