#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
#include <cstring>
using namespace std;
typedef long long LL;
bool w[500][500];
bool v[500][500];
class DoNotTurn {
public:
int minimumTurns(int N, int X0, int A, int B, int Y0, int C, int D, int P, int M)
{
// input
memset(w, 0, sizeof w);
memset(v, 0, sizeof v);
LL X=X0%P, Y=Y0%P;
for(int i=1; i<=M; ++i)
{
if( !((X%N)==0 && (Y%N)==0 || (X%N)==N-1 && (Y%N)==N-1) )
w[X%N][Y%N] = 1;
X = (X*A+B) % P;
Y = (Y*C+D) % P;
}
// solve
vector< pair<int,int> > Q(1, make_pair(0,0)); v[0][0]=1;
for(int step=-1; !Q.empty(); ++step)
{
vector< pair<int,int> > Q2;
for(int i=0; i<Q.size(); ++i)
{
int x = Q[i].first;
int y = Q[i].second;
if( x==N-1 && y==N-1 )
return step;
int dx[] = {-1, +1, 0, 0};
int dy[] = {0, 0, -1, +1};
for(int d=0; d<4; ++d)
{
for(int k=1 ;; ++k) {
int xx = x + dx[d]*k;
int yy = y + dy[d]*k;
if( xx<0 || N<=xx || yy<0 || N<=yy || w[xx][yy] )
break;
if( !v[xx][yy] ) {
v[xx][yy] = true;
Q2.push_back( make_pair(xx,yy) );
}
}
}
}
Q.swap(Q2);
}
return -1;
}
};
// BEGIN CUT HERE
#include <ctime>
double start_time;string timer() { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
template <typename T> string print_array(const vector<T> &V) { ostringstream os; os << "{ "; for (typename vector<T>::const_iterator iter = V.begin(); iter != V.end(); ++iter) os << '\"' << *iter << "\","; os << " }"; return os.str(); }
int verify_case(const int &Expected, const int &Received) { if (Expected == Received) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl; cerr << "\tExpected: \"" << Expected << '\"' << endl; cerr << "\tReceived: \"" << Received << '\"' << endl; } return 0;}
template<int N> struct Case_ { Case_(){start_time=clock();} };
char Test_(...);
int Test_(Case_<0>) {
int N = 2;
int X0 = 0;
int A = 0;
int B = 1;
int Y0 = 0;
int C = 0;
int D = 1;
int P = 10;
int M = 2;
int RetVal = 1;
return verify_case(RetVal, DoNotTurn().minimumTurns(N, X0, A, B, Y0, C, D, P, M)); }
int Test_(Case_<1>) {
int N = 3;
int X0 = 0;
int A = 1;
int B = 1;
int Y0 = 1;
int C = 1;
int D = 0;
int P = 3;
int M = 3;
int RetVal = -1;
return verify_case(RetVal, DoNotTurn().minimumTurns(N, X0, A, B, Y0, C, D, P, M)); }
int Test_(Case_<2>) {
int N = 3;
int X0 = 0;
int A = 1;
int B = 1;
int Y0 = 1;
int C = 1;
int D = 1;
int P = 3;
int M = 3;
int RetVal = 3;
return verify_case(RetVal, DoNotTurn().minimumTurns(N, X0, A, B, Y0, C, D, P, M)); }
int Test_(Case_<3>) {
int N = 10;
int X0 = 911111;
int A = 845499;
int B = 866249;
int Y0 = 688029;
int C = 742197;
int D = 312197;
int P = 384409;
int M = 40;
int RetVal = 12;
return verify_case(RetVal, DoNotTurn().minimumTurns(N, X0, A, B, Y0, C, D, P, M)); }
int Test_(Case_<4>) {
int N = 5;
int X0 = 23;
int A = 2;
int B = 3;
int Y0 = 35;
int C = 5;
int D = 7;
int P = 9;
int M = 3;
int RetVal = 2;
return verify_case(RetVal, DoNotTurn().minimumTurns(N, X0, A, B, Y0, C, D, P, M)); }
int Test_(Case_<5>) {
int N = 2;
int X0 = 0;
int A = 0;
int B = 0;
int Y0 = 0;
int C = 0;
int D = 0;
int P = 1;
int M = 0;
int RetVal = 1;
return verify_case(RetVal, DoNotTurn().minimumTurns(N, X0, A, B, Y0, C, D, P, M)); }
int Test_(Case_<6>) {
int N = 500;
int X0 = 0;
int A = 0;
int B = 0;
int Y0 = 0;
int C = 0;
int D = 0;
int P = 1;
int M = 0;
int RetVal = 1;
return verify_case(RetVal, DoNotTurn().minimumTurns(N, X0, A, B, Y0, C, D, P, M)); }
template<int N> void Run_() { cerr << "Test Case #" << N << "..." << flush; Test_(Case_<N>()); Run_<sizeof(Test_(Case_<N+1>()))==1 ? -1 : N+1>(); }
template<> void Run_<-1>() {}
int main() { Run_<0>(); }
// END CUT HERE