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Statement

 Goal

Starting at coordinates (0,0) with D[0]=0, a random direction generator D[n+1] = (a*D[n]+b) mod m tells you which direction to go next (where D mod 4=0,1,2,3 indicates Up, Down, Left, Right). How many steps does it take to get back to (0,0)?
Input
Line 1: a
Line 2: b
Line 3: m
Output
The number of steps.
Constraints
1≤ a,b,m ≤ 100,000
steps ≤ 500,000
Example
Input
8
3
7
Output
2

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