OJ-Problems-Source/HDOJ/3978_autoAC.cpp

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#include <cstdio>
#include <iostream>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <map>
using namespace std;
#define maxn 10010
typedef long long LL;
int prime[maxn];
map<LL,LL>pika;
void Prime(){
memset(prime,0,sizeof(prime));
for(int i=2;i<maxn;i++){
if(!prime[i]) prime[++prime[0]]=i;
for(int j=1;j<=prime[0]&&prime[j]<maxn/i;j++){
prime[prime[j]*i]=1;
if(i%prime[j]==0){
break;
}
}
}
}
LL factor[100][2];
int fatcnt;
int get_factors(LL n){
fatcnt=0;
LL tmp=n;
for(int i=1;prime[i]<=tmp/prime[i];i++){
factor[fatcnt][1]=0;
if(tmp%prime[i]==0){
factor[fatcnt][0]=prime[i];
while(tmp%prime[i]==0){
tmp/=prime[i];
factor[fatcnt][1]++;
}
fatcnt++;
}
}
if(tmp!=1){
factor[fatcnt][0]=tmp;
factor[fatcnt][1]=1;
fatcnt++;
}
return fatcnt;
}
LL gcd(LL a,LL b){
if(b==0){
return a;
}
else{
return gcd(b,a%b);
}
}
LL lcm(LL a,LL b){
return a/gcd(a,b)*b;
}
struct Matrix{
LL m[2][2];
}E,D;
Matrix Multi(Matrix A,Matrix B,LL mod){
Matrix ans;
for(int i=0;i<2;i++){
for(int j=0;j<2;j++){
ans.m[i][j]=0;
for(int k=0;k<2;k++){
ans.m[i][j]+=(A.m[i][k]*B.m[k][j])%mod;
if(ans.m[i][j]>=mod){
ans.m[i][j]-=mod;
}
}
}
}
return ans;
}
void init(){
memset(E.m,0,sizeof(E.m));
memset(D.m,0,sizeof(D.m));
D.m[0][0]=D.m[0][1]=D.m[1][0]=1;
for(int i=0;i<2;i++){
E.m[i][i]=1;
}
Prime();
}
Matrix Pow(Matrix A,LL e,LL mod){
Matrix ans=E;
while(e){
if(e&1){
ans=Multi(ans,A,mod);
}
A=Multi(A,A,mod);
e>>=1;
}
return ans;
}
LL Pow(LL a,LL b,LL mod){
LL ans=1;
while(b){
if(b&1){
ans=(ans*a)%mod;
}
a=(a*a)%mod;
b>>=1;
}
return ans;
}
int legendre(LL a,LL p){
if(Pow(a,(p-1)>>1,p)==1){
return 1;
}
else{
return -1;
}
}
int f0=1,f1=1;
LL get_fib(LL n,LL mod)
{
if(mod==1) return 0;
return Pow(D,n,mod).m[0][0]%mod;
}
LL fac[maxn],GG[maxn];
LL G(LL p)
{
if(p<maxn && GG[p]!=-1) return GG[p];
LL num;
if(legendre(5,p)==1){
num=p-1;
}
else{
num=2*(p+1);
}
int cnt=0;
for(LL i=1;i*i<=num;i++){
if(num%i==0){
fac[cnt++]=i;
if(i*i!=num){
fac[cnt++]=num/i;
}
}
}
sort(fac,fac+cnt);
LL ans;
for(int i=0;i<cnt;i++){
if(get_fib(fac[i],p)==f0&&get_fib(fac[i]+1,p)==f1){
ans=fac[i];
break;
}
}
if(p<maxn) GG[p]=ans;
return ans;
}
LL find_loop(LL n)
{
if(pika.count(n)){
return pika[n];
}
get_factors(n);
LL ans=1;
for(int i=0;i<fatcnt;i++)
{
LL record=1;
if(factor[i][0]==2) record=3;
else if(factor[i][0]==3) record=8;
else if(factor[i][0]==5) record=20;
else record=G(factor[i][0]);
for(int j=1;j<factor[i][1];j++)
record*=factor[i][0];
ans=lcm(ans,record);
}
return pika[n]=ans;
}
LL loop[10010];
void solve(LL p,LL k){
loop[0]=p;
for(int i=1;i<=k;i++){
loop[i]=find_loop(loop[i-1]);
}
}
int main()
{
pika.clear();
init();
memset(GG,-1,sizeof(GG));
int T,cas=0;
scanf("%d",&T);
LL n,p,k;
while(T--)
{
scanf("%I64d%I64d%I64d",&n,&k,&p);
solve(p,k);
for(int i=k;i>=0;i--){
n=get_fib(n,loop[i]);
}
printf("Case #%d: %I64d\n",++cas,n);
}
return 0;
}