E. Congruence Equationtime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputGiven an integer x. Your task is to find out how many positive integers n (1 \leq n \leq x) satisfy n \cdot a^n \equiv b \quad (\textrm{mod}\;p), where a, b, p are all known constants.InputThe only line contains four integers a,b,p,x (2 \leq p \leq 10^6+3, 1 \leq a,b < p, 1 \leq x \leq 10^{12}). It is guaranteed that p is a prime.OutputPrint a single integer: the number of possible answers n.ExamplesInput2 3 5 8Output2Input4 6 7 13Output1Input233 233 10007 1Output1NoteIn the first sample, we can see that n=2 and n=8 are possible answers.
Input2 3 5 8
Output2
['chinese remainder theorem', 'math', 'number theory', '*2100']