#63 정사각형 타일링

Statement

Statement language

There is a rectangle of size $A \times B$ .

This rectangle will be filled with with square tiles without any remaining spaces. You can purchase square tiles as follows:

By paying a cost of $c$ , you receive $1$ square tile of size $c\times c$ .

Find the minimum cost required to fill the entire rectangle with square tiles without any remaining spaces.

Input

The input is given in the following format.

$A\ B$

Output

Print the minimum cost required.

Constraints

$1 \le A \le 10^{18}$ .
$1 \le B \le 10^{18}$ .

Subtasks

#	Score	Constraints
1	9	$A=B$ .
2	21	Either $A$ is a multiple of $B$ , or $B$ is a multiple of .

Samples

Input

6 4

Output

If you use $6$ square tiles with a side length of $2$ , the cost is $12$ . However, this is not optimal.

Instead, if you fill it with one square tile with a side length of $4$ and two square tiles with a side length of $2$ , the cost is $4 + 2 +$ . It can be shown that is the minimum cost.