[Sdoi2013]随机数生成器（BSGS）

#include<cstdio>
#include<cstring>
#include<cmath>
#include<iostream>
#include<map>
using namespace std;
typedef long long ll;
struct Thash{
    static const int MOD=233333;
    static const int MAXN=1e6+5;
    int tot,head[MOD+100],next[MAXN],h[MAXN],val[MAXN];
    inline void clear(){tot=0;memset(head,0,sizeof head);}
    inline void insert(int H,int VAL){
        for(int i=head[H%MOD];i;i=next[i]) if(h[i]==H){val[i]=VAL;return ;}
        next[++tot]=head[H%MOD];head[H%MOD]=tot;h[tot]=H;val[tot]=VAL;
    }
    inline int get(int H){
        for(int i=head[H%MOD];i;i=next[i]) if(h[i]==H) return val[i];
        return 0;
    }
}M;
int T;
ll p,a,b,x1,t;
inline int read(){
    int x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
ll fpow(ll a,ll p,ll mod){
    ll res=1;
    for(;p;p>>=1,a=a*a%mod) if(p&1) res=res*a%mod;
    return res;
}
void exgcd(ll a,ll b,ll &d,ll &x,ll &y){
    if(!b){d=a;x=1;y=0;return ;}
    exgcd(b,a%b,d,y,x);
    y-=x*(a/b);
}
ll BSGS(ll A,ll B,ll mod){
    A%=mod;
    if(!A){
        if(!B) return 1;
        return -1;
    }
    ll m=sqrt(mod)+1,ni=fpow(A,mod-m-1,mod);
    ll t=1,y=1;
    M.clear();
    M.insert(1,m+1); 
    for(int i=1;i<m;i++){
        t=t*A%mod;
        if(!M.get(t)) M.insert(t,i);
    }
    for(int i=0;i<m;i++){
        int u=M.get(B*y%mod); 
        if(u){
            if(u==m+1) u=0;
            return i*m+u;
        }
        y=y*ni%mod;
    }
    return -1;
}
ll calc1(){
    ll z=(t-x1+p)%p,d,x,y;
    exgcd(b,p,d,x,y);
    if(z%d) return -1;z/=d;
    x=x*z%p;
    if(x<0) x+=p;
    return x+1;
}
ll calc2(){
    ll c=fpow(a-1,p-2,p),A=(x1+b*c)%p,z=(b*c+t)%p,d,x,y;
    exgcd(A,p,d,x,y);
    if(z%d) return -1;z/=d;
    if(x<p) x=x%p+p;
    d=BSGS(a,x*z%p,p);
    if(~d) return d+1;
    return -1;
}
ll solve(){
    if(x1==t) return 1;
    if(!a){
        if(b==t) return 2;
        else return -1;
    }
    if(a==1) return calc1();
    return calc2();
}
int main(){
    freopen("random.in","r",stdin);
    freopen("random.out","w",stdout);
    for(T=read();T--;){
        p=read();a=read();b=read();x1=read();t=read();
        printf("%lld
",solve());
    }
    return 0;
}