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Time Limit: 1.0 Seconds Memory Limit: 65536K

Total Runs: 1910 Accepted Runs: 931

Computers normally cannot generate really random numbers, but
frequently are used to generate sequences of pseudo-random
numbers. These are generated by some algorithm, but appear for all
practical purposes to be really random. Random numbers are used in
many applications, including simulation. *M*. ### Input

Each input line will contain four integer values, in order, for
*Z*, *I*, *M*, and *L*. The last line will contain
four zeroes, and marks the end of the input data. *L* will be
less than *M*. ### Output

For each input line, display the case number (they are sequentially
numbered, starting with 1) and the length of the sequence of
pseudo-random numbers before the sequence is repeated. ### Sample Input

### Sample Output

A common pseudo-random number generation technique is called the
linear congruential method. If the last pseudo-random number generated
was *L*, then the next number is generated by evaluating
(*Z* × *L* + *I*) mod *M*, where
*Z* is a constant multiplier, *I* is a constant
increment, and *M* is a constant modulus. For example, suppose
*Z* is 7, *I* is 5, and *M* is 12. If the first
random number (usually called the *seed*) is 4, then we can
determine the next few pseudo-random numbers are follows:

As you can see, the sequence of pseudo-random numbers generated by this technique repeats after six numbers. It should be clear that the longest sequence that can be generated using this technique is limited by the modulus,Last Random Number,L| (Z×L+I)| Next Random Number, (Z×L+I) modM----------------------|---------|---------------------------------- 4 | 33 | 9 9 | 68 | 8 8 | 61 | 1 1 | 12 | 0 0 | 5 | 5 5 | 40 | 4

In this problem you will be given sets of values for *Z*,
*I*, *M*, and the seed, *L*. Each of these will have no
more than four digits. For each such set of values you are to
determine the length of the cycle of pseudo-random numbers that will
be generated. But be careful -- the cycle might not begin with the
seed!

7 5 12 4 5173 3849 3279 1511 9111 5309 6000 1234 1079 2136 9999 1237 0 0 0 0

Case 1: 6 Case 2: 546 Case 3: 500 Case 4: 220

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