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Rectangle cutting - MarisaOJ: Marisa Online Judge

Rectangle cutting

Time limit: 1000 ms
Memory limit: 256 MB

Given an a×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 first line contains 2 integers a,b.

Output

  • Print one integer, the minimum number of moves.

Constraints

  • 1≤a,b≤500.

Example

Input:

3 5

Output:

3