Disclamer: a bit upset with the problem statement this pseudocode tells us that the sequence is actually linear(arithmetical) and (mathematecaly) unbounded from the top. so there is no use of Q%(2<<30) except once so the sequence is a = p*a+q there is no chance to repeate the value except overflow but we do not know what data type we should use for the sequence and it is machine specific. as the result: the solution

int main() {
    /* Enter your code here. Read input from STDIN. Print output to STDOUT */   
    unsigned int N,S,P,Q;
    cin>>N>>S>>P>>Q;
    Q %=(2<<30);
    
    unsigned int a0,a;
    a0 = S%(2<<30);
    
    for(unsigned int i=0; i<N-1;i++){
        a = a0*P+Q;
        if (a0==a){
            N= i;
            break;}
        a0=a;
    }

cout<<N;

} debuged on test case 8 worked for my local PC for unsigned long but for HackerRank envirement only for unsigned int