Surface Area of Quadrangular Pyramid

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

inputFormat

outputFormat

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

样例

6
4
7
9
0
0

96.000000
184.192455

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