結果

問題 No.3170 [Cherry 7th Tune KY] Even if you could say "See you ..."
ユーザー noya2
提出日時 2025-05-30 21:54:01
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 4 ms / 4,000 ms
コード長 8,532 bytes
コンパイル時間 3,816 ms
コンパイル使用メモリ 300,988 KB
実行使用メモリ 7,844 KB
最終ジャッジ日時 2025-06-11 23:05:49
合計ジャッジ時間 5,300 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 2
other AC * 40
権限があれば一括ダウンロードができます

ソースコード

diff # 

#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
using namespace std;

#include<bits/stdc++.h>
#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp"
namespace noya2 {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p){
    os << p.first << " " << p.second;
    return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p){
    is >> p.first >> p.second;
    return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v){
    int s = (int)v.size();
    for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
    return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v){
    for (auto &x : v) is >> x;
    return is;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u){
    cin >> t;
    in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u){
    cout << t;
    if (sizeof...(u)) cout << sep;
    out(u...);
}

template<typename T>
void out(const vector<vector<T>> &vv){
    int s = (int)vv.size();
    for (int i = 0; i < s; i++) out(vv[i]);
}

struct IoSetup {
    IoSetup(){
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(7);
    }
} iosetup_noya2;

} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"
namespace noya2{

const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 =  998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";

void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }

} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"

#line 6 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"

namespace noya2{

unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
    if (a == 0 || b == 0) return a + b;
    int n = __builtin_ctzll(a); a >>= n;
    int m = __builtin_ctzll(b); b >>= m;
    while (a != b) {
        int mm = __builtin_ctzll(a - b);
        bool f = a > b;
        unsigned long long c = f ? a : b;
        b = f ? b : a;
        a = (c - b) >> mm;
    }
    return a << std::min(n, m);
}

template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }

long long sqrt_fast(long long n) {
    if (n <= 0) return 0;
    long long x = sqrt(n);
    while ((x + 1) * (x + 1) <= n) x++;
    while (x * x > n) x--;
    return x;
}

template<typename T> T floor_div(const T n, const T d) {
    assert(d != 0);
    return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}

template<typename T> T ceil_div(const T n, const T d) {
    assert(d != 0);
    return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}

template<typename T> void uniq(std::vector<T> &v){
    std::sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}

template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }

template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }

template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }

} // namespace noya2
#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"

#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()

using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;

namespace noya2{

/*　~ (. _________ . /)　*/

}

using namespace noya2;


#line 2 "c.cpp"

// https://yukicoder.me/submissions/408117

namespace chocorusk {

typedef pair<ll, int> P;
ll p;
using arr=array<ll, 2>;
using Mat=array<arr, 2>;
Mat matmul(Mat a, Mat b){
	Mat c={};
	for(int i=0; i<2; i++){
		for(int j=0; j<2; j++){
			for(int k=0; k<2; k++){
				(c[i][j]+=a[i][k]*b[k][j])%=p;
			}
		}
	}
	return c;
}
Mat matpow(Mat a, ll k){
	Mat ap=a, ans={};
	ans[0][0]=ans[1][1]=1;
	while(k){
		if(k&1) ans=matmul(ap, ans);
		ap=matmul(ap, ap);
		k>>=1;
	}
	return ans;
}
Mat e, ainv;
bool nuee;
ll matlog(Mat a, Mat b, ll d){
	ll sq=1;
	while(sq*sq<d) sq++;
	vector<pair<Mat, int>> vp(sq);
	vp[0]=make_pair(e, 0);
	for(int i=1; i<sq; i++){
		vp[i]=make_pair(matmul(vp[i-1].first, a), i);
	}
	auto cp=[](pair<Mat, int> x, pair<Mat, int> y){
		for(int i=0; i<2; i++){
			for(int j=0; j<2; j++){
				if(x.first[i][j]!=y.first[i][j]) return x.first[i][j]<y.first[i][j];
			}
		}
		return x.second<y.second;
	};
	sort(vp.begin(), vp.end(), cp);
	Mat ap=matpow(ainv, sq);
	for(int i=0; i<sq; i++){
		int t=lower_bound(vp.begin(), vp.end(), make_pair(b, 0), cp)-vp.begin();
		if(t<sq && vp[t].first==b){
			if(i*sq+vp[t].second<d){
                if(i==0 && vp[t].second==0){
                    nuee=1;
                    if(t+1<sq && vp[t].first==vp[t+1].first) return vp[t+1].second;
                }else{
                    return i*sq+vp[t].second;
                }
            }
		}
		b=matmul(b, ap);
	}
	return -1;
}
ll gcd(ll a, ll b){
    if(b==0) return a;
    return gcd(b, a%b);
}
ll powmod(ll a, ll k, ll mod){
    ll ap=a, ans=1;
    while(k){
        if(k&1){
            ans*=ap;
            ans%=mod;
        }
        ap=ap*ap;
        ap%=mod;
        k>>=1;
    }
    return ans;
}
ll inv(ll a, ll m){
    ll b=m, x=1, y=0;
    while(b>0){
        ll t=a/b;
        swap(a-=t*b, b);
        swap(x-=t*y, y);
    }
    return (x%m+m)%m;
}
ll discretelog(ll x, ll y, ll m){
    ll p=1%m;
    for(int i=0; i<=30; i++){
        if(p==y) return i;
        (p*=x)%=m;
    }
    ll g=gcd(x, m);
    ll m1=m;
    for(ll i=2; i*i<=g; i++){
        if(g%i==0){
            while(g%i==0) g/=i;
            while(m1%i==0) m1/=i;
        }
    }
    if(g>1){
        while(m1%g==0) m1/=g;
    }
    if(y%(m/m1)!=0) return -1;
    x%=m1, y%=m1;
    ll d=1;
    while(d*d<m1) d++;
    ll invx=inv(x, m1);
    unordered_map<ll, ll> mp; //yx^(-b)
    ll y1=y;
    for(ll i=0; i<d; i++){
        mp[y1]=i;
        (y1*=invx)%=m1;
        if(y1==y) break;
    }
    ll xd=powmod(x, d, m1);
    ll q=1%m1;
    for(ll i=0; i<d; i++){
        auto itr=mp.find(q);
        if(itr!=mp.end()){
            return i*d+itr->second;
        }
        (q*=xd)%=m1;
    }
    return -1;
}
ll order(ll a){
    if(a==1) return 1;
    return discretelog(a, inv(a, p), p)+1;
}
int main_()
{
	cin>>p;
	Mat a, b;
	cin>>a[0][0]>>a[0][1]>>a[1][0]>>a[1][1]>>b[0][0]>>b[0][1]>>b[1][0]>>b[1][1];
    if (b[0][0] == 1 && b[0][1] == 0 && b[1][0] == 0 && b[1][1] == 1){
        cout << 0 << endl;
        return 0;
    }
	if(a==b){
		cout<<1<<endl;
		return 0;
	}
	Mat a2=matmul(a, a);
	if(a2==b){
		cout<<2<<endl;
		return 0;
	}
	if(a2[0][0]==0 && a2[0][1]==0 && a2[1][0]==0 && a2[1][1]==0){
		cout<<-1<<endl;
		return 0;
	}
    ll ad=(a[0][0]*a[1][1]-a[0][1]*a[1][0]%p+p)%p, bd=(b[0][0]*b[1][1]-b[0][1]*b[1][0]%p+p)%p;
	if(ad==0){
		e=matpow(a, p-1), ainv=matpow(a, p-2);
        ll n=matlog(a, b, p);
        if(n==-1){
            cout<<-1<<endl;
            return 0;
        }
        if(matpow(a, n)==b) cout<<n<<endl;
        else cout<<-1<<endl;
        return 0;
	}else{
		e[0][0]=e[1][1]=1;
        if(matpow(a, p*p-1)==e) ainv=matpow(a, p*p-2);
        else ainv=matpow(a, p*(p-1)-1);
	}
	ll r=discretelog(ad, bd, p), m=order(ad);
    if(r==-1){
        cout<<-1<<endl;
        return 0;
    }
    Mat ap=matpow(a, m), c=matmul(b, matpow(ainv, r));
    ainv=matpow(ainv, m);
    nuee=0;
    ll q=matlog(ap, c, 2*p+1);
    if(q==-1){
        cout<<-1<<endl;
        return 0;
    }
    if(nuee && r>0) q=0;
    if(matpow(a, q*m+r)==b) cout<<q*m+r<<endl;
    else cout<<-1<<endl;
	return 0;
}

} // namespace chocorusk

void solve(){
    chocorusk::main_();
}

int main(){
    int t = 1; in(t);
    while (t--) { solve(); }
}
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