G. X-mouse in the Campustime limit per test1.5 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThe campus has m rooms numbered from 0 to m - 1. Also the x-mouse lives in the campus. The x-mouse is not just a mouse: each second x-mouse moves from room i to the room i \cdot x \mod{m} (in fact, it teleports from one room to another since it doesn't visit any intermediate room). Starting position of the x-mouse is unknown.You are responsible to catch the x-mouse in the campus, so you are guessing about minimum possible number of traps (one trap in one room) you need to place. You are sure that if the x-mouse enters a trapped room, it immediately gets caught.And the only observation you made is \text{GCD} (x, m) = 1.InputThe only line contains two integers m and x (2 \le m \le 10^{14}, 1 \le x < m, \text{GCD} (x, m) = 1) — the number of rooms and the parameter of x-mouse. OutputPrint the only integer — minimum number of traps you need to install to catch the x-mouse.ExamplesInput4 3Output3Input5 2Output2NoteIn the first example you can, for example, put traps in rooms 0, 2, 3. If the x-mouse starts in one of this rooms it will be caught immediately. If x-mouse starts in the 1-st rooms then it will move to the room 3, where it will be caught.In the second example you can put one trap in room 0 and one trap in any other room since x-mouse will visit all rooms 1..m-1 if it will start in any of these rooms.
Input4 3
Output3
['bitmasks', 'math', 'number theory', '*2600']