3652: Pseudorandom Sequence Period
Time Limit: 2 Sec Memory Limit: 256 MBSubmit: 0 Solved: 0
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Description
Polycarpus has recently got interested in sequences of pseudorandom numbers. He learned that many programming languages generate such sequences in a similar way: 
(for i≥1). Here a, b, m are constants, fixed for the given realization of the pseudorandom numbers generator, r0 is the so-called randseed (this value can be set from the program using functions like RandSeed(r) or srand(n)), and 
denotes the operation of taking the remainder of division.
For example, if a=2,b=6,m=12,r0=11, the generated sequence will be: 4,2,10,2,10,2,10,2,10,2,10,....
Polycarpus realized that any such sequence will sooner or later form a cycle, but the cycle may occur not in the beginning, so there exist a preperiod and a period. The example above shows a preperiod equal to 1 and a period equal to 2.
Your task is to find the period of a sequence defined by the given values of a,b,m and r0. Formally, you have to find such minimum positive integer t, for which exists such positive integer k, that for any i≥k: ri=ri+t.
The single line of the input contains four integers a, b, m and r0 (1≤m≤105,0≤a,b≤1000,0≤r0<m), separated by single spaces.
Print a single integer − the period of the sequence.
2 6 12 11
2
2 3 5 1
4
3 6 81 9
1
The first sample is described above.
In the second sample the sequence is (starting from the first element): 0,3,4,1,0,3,4,1,0,...
In the third sample the sequence is (starting from the first element): 33,24,78,78,78,78,...