bzoj3122(bsgs)

被取模卡了一天...............

 

#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<algorithm>
#include<cstring>
#include<map>
using namespace std;
typedef long long ll;


void exgcd(ll a,ll b,ll &g,ll &x,ll &y) {if(!b) g=a,x=1,y=0;else exgcd(b,a%b,g,y,x),y-=(a/b)*x;}

ll p,a,b,x1,t;
/////////////////////////
ll pw(ll a, ll b) {
	ll r = 1;
	while(b) {if(b & 1) r = r*a%p; a = a*a%p, b >>= 1;}
	return r;
}
ll bsgs(ll a, ll b,ll p) {
	ll m = sqrt(p)+1, e = 1,g,x,y;
	exgcd(pw(a, m), p, g, x, y);
	ll ni = (x % p + p) % p;
	map<ll, ll> mp;
	mp[1] = 0;
	for(int i = 1; i < m; i++) {
		e = e*a%p;
		if(!mp.count(e)) mp[e] = i;
	}
	for(int i = 0; i < m; i++) {
		if(mp.count(b)) return i*m+mp[b];
		b = b*ni%p;
	}
	return -2;
}  
//////////////////////////
void work()
{
	scanf("%lld%lld%lld%lld%lld",&p,&a,&b,&x1,&t);  
	if (t==x1) {puts("1");return;}
	if (a==0)
	{
		if (t==b) puts("2");
		else puts("-1");
		return ;
	}
	if (a==1)
	{
		if (!b) {puts("-1");return ;}
		ll d,x,y;
		exgcd(b,p,d,x,y);
		x=x*(t-x1);x=(x%p+p)%p;
		printf("%lld\n",x+1);
		return ;
	}
	ll d,x,y;
	exgcd(a-1,p,d,x,y);
	ll c=(x%p+p)%p;
	exgcd((x1+b*c)%p,p,d,x,y);
	if ((b*c+t)%d) {puts("-1");return;}
	x=x*((b*c+t)/d)%(p/d);
	x=(x%(p/d)+(p/d))%(p/d);
	printf("%lld\n",bsgs(a,x,p)+1);
}

int main()
{
	ll T;
	scanf("%lld",&T);
	while (T--) work();	
	return 0;
}