A positive integer \(p\) is input into a machine. If \(p\) is odd, the machine outputs the integer \(p + 5\). If \(p\) is even, the machine outputs the integer \(p + 11\). This process can be repeated using each successive output as the next input. For example, if the input is \(p = 1\) and the machine is used three times, the final output is \(22\).
If the input is \(p = 2023\) and the machine is used \(101\) times, find the final output.