Mary has an piece of paper that she wants to cut into pieces according to the following rules:
- She can only cut one piece of paper at a time, meaning she cannot fold the paper or layer already-cut pieces on top of one another.
- Each cut is a straight line from one side of the paper to the other side of the paper. For example, the diagram below depicts the three possible ways to cut a piece of paper:
Given and , find and print the minimum number of cuts Mary must make to cut the paper into squares that are unit in size.
Input Format
A single line of two space-separated integers denoting the respective values of and .
Constraints
Output Format
Print a long integer denoting the minimum number of cuts needed to cut the entire paper into squares.
Sample Input
3 1
Sample Output
2
Explanation
Mary first cuts the piece of paper into a piece and a piece. She then cuts the piece into two pieces:
Because it took her two cuts to get pieces of size , we print as our answer.