Online JudgeProblem SetAuthorsOnline ContestsUser
Web Board
Home Page
Statistical Charts
Submit Problem
Online Status
Update your info
Authors ranklist
Current Contest
Past Contests
Scheduled Contests
Award Contest
User ID:
Random Gap
Time Limit: 3000MSMemory Limit: 65536K
Total Submissions: 5700Accepted: 1534


The pseudo-random number genegators (or RNGs for short) are widely used in statistical calculations. One of the simplest and ubiquitious is the linear congruence RNG, that calculates the n-th random number Rn as Rn = (aRn - 1 + c) mod m, where a, c and m are constants. For example, the sequence for a = 15, c = 7, m = 100 and starting value R0 = 1 is 1, 22, 37, 62, 37, 62, ...

Linear RNG is very fast, and can yield surprisinly good sequence of random numbers, given the right choice of constants. There are various measures of RNG quality, and your task is to calculate one of them, namely the longest gap between members of the sequence. More precisely, given the values of a, c, m, and R0, find such two elements Ri < Rj that:
  1. there are no other Rk that Ri ≤ Rk ≤ Rj,
  2. the difference Rj − Ri is maximal.


Input contains integer numbers a c m R0.
0 ≤ a, c, R0 ≤ 107, 1 ≤ m ≤ 16000000, am + c < 232.


Output should contain the single number -- the maximal difference found.

Sample Input

15 7 100 1

Sample Output



Northeastern Europe 2004, Far-Eastern Subregion

[Submit]   [Go Back]   [Status]   [Discuss]

Home Page   Go Back  To top

All Rights Reserved 2003-2013 Ying Fuchen,Xu Pengcheng,Xie Di
Any problem, Please Contact Administrator