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  1. Practice
  2. Mathematics
  3. Fundamentals
  4. Cutting Paper Squares

Cutting Paper Squares

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:
    example-cutting-squares.png

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:

cutting-paper-squares.png

Because it took her two cuts to get pieces of size , we print as our answer.