Turn Counting on a Grid

You are given a grid where the starting point is at \((1,1)\) (top-left corner) and the destination is at \((M,N)\). You can only move to the right or down (i.e. only along integer grid intersections).

A turn is defined as a change in your moving direction (from right to down or from down to right). Note that if you move continuously in one direction, it does not count as a turn.

Your task is to calculate the minimum and maximum number of turns among all valid paths from the start to the destination.

Clarifications:

• If either \(M=1\) or \(N=1\), you are moving in a straight line, and both the minimum and maximum number of turns will be \(0\).
• For a grid where both \(M>1\) and \(N>1\):
• The minimum number of turns is \(1\) (e.g. moving all the way in one direction and then turning and continuing in the other).
• The maximum number of turns is achieved by alternating directions as often as possible. Let the number of right moves be \(R = N-1\) and down moves be \(D = M-1\). Then the maximum number of turns is computed as follows:
  • If \(R = D\), then maximum turns = \(2R - 1\).
  • If \(R \neq D\), then maximum turns = \(2\min(R,D)\).

Input Format: Two space-separated integers \(M\) and \(N\) representing the dimensions of the grid.

Output Format: Two integers separated by a space: the minimum number of turns and the maximum number of turns.

inputFormat

The input consists of one line containing two integers \(M\) and \(N\) (separated by a space), where \(M,N \ge 1\).

outputFormat

Output a single line with two integers separated by a space: the minimum and maximum number of turns required to reach from \((1,1)\) to \((M,N)\).

sample

2 2

1 1