Code Submission Evaluation System Login

CSES Problem Set

Rectangle Cutting


Task | Statistics


CSES - Rectangle CuttingCSES - Rectangle Cutting

Time limit:1.00 s Memory limit:512 MB

Given an $a \times b$ rectangle, your task is to cut it into squares. On each move you can select a rectangle and cut it into two rectangles in such a way that all side lengths remain integers. What is the minimum possible number of moves?

Input

The only input line has two integers $a$ and $b$.

Output

Print one integer: the minimum number of moves.

Constraints
Example

Input:
3 5

Output:
3