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 first line contains 2 integers $a, b$.
### Output
- Print one integer, the minimum number of moves.
### Constraints
- $1 \le a, b \le 500$.
### Example
Input:
```
3 5
```
Output:
```
3
```
