1 #include<cstdio> 2 #include<iostream> 3 #include<map> 4 #include<cmath> 5 #define ll long long 6 using namespace std; 7 ll T,p,a,b,c,x1,t; 8 map<ll,ll> mp; 9 ll exgcd(ll b,ll p,ll &x,ll &y) 10 { 11 if(!p) 12 { 13 x=1; 14 y=0; 15 return b; 16 } 17 ll t1=exgcd(p,b%p,x,y); 18 ll t=x; 19 x=y; 20 y=t-b/p*y; 21 return t1; 22 } 23 ll kuai(ll a,ll k,ll p) 24 { 25 ll ans=1; 26 for(;k;) 27 { 28 if(k%2) 29 ans=(ans*a)%p; 30 k/=2; 31 a=(a*a)%p; 32 } 33 return ans; 34 } 35 ll pan(ll y,ll z,ll p) 36 { 37 mp.clear(); 38 ll m=ceil(sqrt(p)),t=1; 39 mp[1]=m+1; 40 for(ll i=1;i<m;i++) 41 { 42 t=t*y%p; 43 mp[t]=i; 44 } 45 ll T=kuai(y,p-m-1,p),ine=1; 46 for(ll k=0;k<=m;k++) 47 { 48 ll i=mp[z*ine%p]; 49 if(i) 50 { 51 if(i==m+1) 52 i=0; 53 return k*m+i+1; 54 } 55 ine=ine*T%p; 56 } 57 return -1; 58 } 59 ll solve() 60 { 61 if(x1==t) 62 return 1; 63 if(a==0) 64 { 65 if(b==t) 66 return 2; 67 return -1; 68 } 69 if(a==1) 70 { 71 c=(t-x1+p)%p; 72 ll x,y; 73 ll t1=exgcd(b,p,x,y); 74 if(c%t1) 75 return -1; 76 c/=t1; 77 x=x*c%p; 78 for(;x<0;x+=p); 79 return x+1; 80 } 81 if(a>1) 82 { 83 c=kuai(a-1,p-2,p); 84 ll x,y,d=(b*c+t)%p; 85 ll t1=exgcd((x1+b*c)%p,p,x,y); 86 if(d%t1) 87 return -1; 88 d/=t1; 89 x=x*d%p; 90 for(;x<0;x+=p); 91 a%=p; 92 x%=p; 93 if(!a&&!x) 94 return 2; 95 if(!a) 96 return -1; 97 return pan(a,x,p); 98 } 99 } 100 int main() 101 { 102 scanf("%lld",&T); 103 for(int i=1;i<=T;i++) 104 { 105 scanf("%lld%lld%lld%lld%lld",&p,&a,&b,&x1,&t); 106 printf("%lld ",solve()); 107 } 108 return 0; 109 }
当 a==0时，判断b，当a==1时，exgcd否则BSGS