_{This problem is a programming version of Problem 182 from projecteuler.net}

The RSA encryption is based on the following procedure:

Generate two distinct primes and .
Compute and .
Find an integer , , such that .

A message in this system is a number in the interval .
A text to be encrypted is then somehow converted to messages (numbers in the interval ).
To encrypt the text, for each message, , is calculated.

To decrypt the text, the following procedure is needed: calculate such that , then for each encrypted message, , calculate .

There exist values of and such that .
We call messages for which unconcealed messages.

An issue when choosing is that there should not be too many unconcealed messages.
For instance, let and .
Then and .
If we choose , then, although it turns out that all possible messages () are unconcealed when calculating .
For any valid choice of there exist some unconcealed messages.
It's important that the number of unconcealed messages is at a minimum.

For given and find the sum of all values of , and , so that the number of unconcealed messages for this value of is at a minimum.