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Statement

 Goal

A linear congruential generator (LCG) is a pseudorandom number generator algorithm defined by the recurrence relation:
lcg(seed) = (a * seed + c) % m

LCGs are notably used by Java's Math.random(). It is sometimes useful to be able to check the value given by the random number generator a number of steps in the future or in the past, given the current internal seed of the LCG.

You are given the seed, the parameters a, c and m of an LCG and the number of steps.

If steps is positive you must return the result of the composition of the lcg function steps times.
lcg(lcg(...lcg(seed)))

If steps is negative you must return the result of the composition of the reverse of the lcg function.
lcg^-1(lcg^-1(...lcg^-1(seed)))


Hint: The reverse of an LCG is also an LCG. The composition of two LCGs is also an LCG.
Input
Line 1: Three space separated integers a, c and m for the LCG parameters.
Line 2: An integer seed
Line 3: An integer steps
Output
Line 1 : The output of the LCG, starting at seed and repeating steps times.
Constraints
0 ≤ a < 2^64
0 ≤ c < 2^64
1 ≤ m < 2^64, m is a power of 2
0 ≤ seed < 2^64
-2^63 <= steps < 2^63
Example
Input
5 3 8
0
1
Output
3

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