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| #include<bits/stdc++.h>
using namespace std;
typedef long long s64;
const int ONE = 10000005;
map <int,int> f;
int T;
int type,y,z,MOD;
int Jc[ONE];
int C[1005][1005];
int get()
{
int res=1,Q=1; char c;
while( (c=getchar())<48 || c>57)
if(c=='-')Q=-1;
if(Q) res=c-48;
while((c=getchar())>=48 && c<=57)
res=res*10+c-48;
return res*Q;
}
int Quickpow(int a,int b,int MOD)
{
int res=1;
while(b)
{
if(b&1) res=(s64)res*a%MOD;
a=(s64)a*a%MOD;
b>>=1;
}
return res;
}
namespace PC
{
int Make_C(int a,int b,int MOD)
{
C[0][0]=1;
for(int i=1;i<=a;i++)
{
C[i][0]=1;
for(int j=1;j<=b;j++)
C[i][j] = (C[i-1][j]+C[i-1][j-1]) % MOD;
}
return C[a][b];
}
int C(int n,int m,int MOD)
{
int up = Jc[n];
int down = (s64)Jc[m] * Jc[n-m] % MOD;
return (s64)up * Quickpow(down,MOD-2,MOD) % MOD;
}
int Lucas(int n,int m,int MOD)
{
Jc[0]=1;
for(int i=1;i<=MOD;i++) Jc[i] = (s64)Jc[i-1] * i % MOD;
int res = 1;
while(n && m)
{
res = (s64)res * C(n%MOD,m%MOD,MOD) % MOD;
n/=MOD; m/=MOD;
}
return res;
}
}
namespace PB
{
int Make_min(int a,int b,int MOD)
{
int res=1;
if(res==b) return 0;
f.clear();
for(int i=1;i<=100000;i++)
{
res = (s64)res * a % MOD;
if(f[res]) return -1;
f[res] = 1;
if(res==b) return i;
}
return -1;
}
int BSGS(int A,int B,int MOD)
{
if(A % MOD == 0) return -1;
int m = sqrt(MOD) + 1;
f.clear();
int record = B % MOD;
for(int i=1;i<=m;i++)
{
record = (s64) record * A % MOD;
f[record] = i;
}
int A_m = Quickpow(A,m,MOD);
record = 1;
for(int i=1;i<=m;i++)
{
record = (s64)record * A_m % MOD;
if(f[record])
{
int x = (i * m %MOD- f[record]+MOD) %MOD;
return x;
}
}
return -1;
}
}
int main()
{
T=get();
while(T--)
{
type=get();
y=get(); z=get(); MOD=get();
if(type==1) printf("%d\n",Quickpow(y,z,MOD));
if(type==3)
{
if(z<=1000 && y<=1000)
printf("%d\n",PC::Make_C(z,y,MOD));
else
printf("%d\n",PC::Lucas(z,y,MOD));
}
if(type==2)
{
if(z<=1000 && y<=1000)
{
int res=PB::Make_min(y,z,MOD);
if(res==-1) printf("Math Error\n");
else printf("%d\n",res);
}
else
{
int res=PB::BSGS(y,z,MOD);
if(res==-1) printf("Math Error\n");
else printf("%d\n",res);
}
}
}
}
|
