結果

問題 No.950 行列累乗
ユーザー maroon_kurimaroon_kuri
提出日時 2019-12-14 00:36:07
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 135 ms / 2,000 ms
コード長 16,711 bytes
コンパイル時間 4,209 ms
コンパイル使用メモリ 241,020 KB
実行使用メモリ 31,080 KB
最終ジャッジ日時 2023-09-10 08:08:00
合計ジャッジ時間 8,988 ms
ジャッジサーバーID
（参考情報） 		judge12 / judge11
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 28 ms
30,020 KB
testcase_01 AC 28 ms
30,152 KB
testcase_02 AC 8 ms
28,024 KB
testcase_03 AC 8 ms
28,020 KB
testcase_04 AC 9 ms
28,056 KB
testcase_05 AC 33 ms
30,172 KB
testcase_06 AC 8 ms
27,956 KB
testcase_07 AC 8 ms
28,028 KB
testcase_08 AC 8 ms
28,024 KB
testcase_09 AC 8 ms
27,988 KB
testcase_10 AC 8 ms
27,976 KB
testcase_11 AC 9 ms
28,028 KB
testcase_12 AC 8 ms
28,120 KB
testcase_13 AC 8 ms
28,028 KB
testcase_14 AC 9 ms
27,980 KB
testcase_15 AC 9 ms
27,912 KB
testcase_16 AC 8 ms
28,028 KB
testcase_17 AC 8 ms
28,040 KB
testcase_18 AC 9 ms
28,052 KB
testcase_19 AC 9 ms
28,040 KB
testcase_20 AC 8 ms
28,116 KB
testcase_21 AC 8 ms
27,980 KB
testcase_22 AC 92 ms
30,448 KB
testcase_23 AC 33 ms
30,136 KB
testcase_24 AC 8 ms
27,976 KB
testcase_25 AC 26 ms
29,620 KB
testcase_26 AC 35 ms
30,620 KB
testcase_27 AC 8 ms
28,140 KB
testcase_28 AC 85 ms
30,192 KB
testcase_29 AC 74 ms
30,060 KB
testcase_30 AC 8 ms
27,964 KB
testcase_31 AC 26 ms
29,852 KB
testcase_32 AC 38 ms
30,788 KB
testcase_33 AC 8 ms
27,984 KB
testcase_34 AC 38 ms
30,728 KB
testcase_35 AC 29 ms
30,384 KB
testcase_36 AC 70 ms
29,696 KB
testcase_37 AC 94 ms
30,164 KB
testcase_38 AC 95 ms
30,160 KB
testcase_39 AC 73 ms
29,840 KB
testcase_40 AC 42 ms
30,772 KB
testcase_41 AC 43 ms
30,836 KB
testcase_42 AC 9 ms
28,024 KB
testcase_43 AC 114 ms
30,844 KB
testcase_44 AC 116 ms
30,816 KB
testcase_45 AC 8 ms
27,908 KB
testcase_46 AC 114 ms
30,816 KB
testcase_47 AC 12 ms
28,040 KB
testcase_48 AC 120 ms
30,776 KB
testcase_49 AC 114 ms
31,080 KB
testcase_50 AC 40 ms
30,772 KB
testcase_51 AC 39 ms
30,768 KB
testcase_52 AC 135 ms
30,904 KB
testcase_53 AC 131 ms
30,764 KB
testcase_54 AC 8 ms
28,056 KB
testcase_55 AC 8 ms
28,220 KB
testcase_56 AC 39 ms
31,072 KB
testcase_57 AC 42 ms
30,768 KB
testcase_58 AC 8 ms
28,052 KB
testcase_59 AC 111 ms
30,904 KB
testcase_60 AC 131 ms
30,828 KB
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 # 

#include <bits/stdc++.h>
using namespace std;

using ll=long long;
#define int ll

#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=int(a);i--)
#define per(i,b) gnr(i,0,b)
#define pb push_back
#define eb emplace_back
#define a first
#define b second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif

template<class t,class u> void chmax(t&a,u b){if(a<b)a=b;}
template<class t,class u> void chmin(t&a,u b){if(b<a)a=b;}

template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;

using pi=pair<int,int>;
using vi=vc<int>;

template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
	return os<<"{"<<p.a<<","<<p.b<<"}";
}

template<class t> ostream& operator<<(ostream& os,const vc<t>& v){
	os<<"{";
	for(auto e:v)os<<e<<",";
	return os<<"}";
}

#define mp make_pair
#define mt make_tuple
#define one(x) memset(x,-1,sizeof(x))
#define zero(x) memset(x,0,sizeof(x))
#ifdef LOCAL
void dmpr(ostream&os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
	os<<t<<" ";
	dmpr(os,args...);
}
#define dmp2(...) dmpr(cerr,"Line:",__LINE__,##__VA_ARGS__)
#else
#define dmp2(...) void(0)
#endif

using uint=unsigned;
using ull=unsigned long long;

template<class t,size_t n>
ostream& operator<<(ostream&os,const array<t,n>&a){
	return os<<vc<t>(all(a));
}

template<int i,class T>
void print_tuple(ostream&,const T&){
}

template<int i,class T,class H,class ...Args>
void print_tuple(ostream&os,const T&t){
	if(i)os<<",";
	os<<get<i>(t);
	print_tuple<i+1,T,Args...>(os,t);
}

template<class ...Args>
ostream& operator<<(ostream&os,const tuple<Args...>&t){
	os<<"{";
	print_tuple<0,tuple<Args...>,Args...>(os,t);
	return os<<"}";
}

void print(ll x,int suc=1){
	cout<<x;
	if(suc==1)
		cout<<"\n";
	if(suc==2)
		cout<<" ";
}

ll read(){
	ll i;
	cin>>i;
	return i;
}

vi readvi(int n,int off=0){
	vi v(n);
	rep(i,n)v[i]=read()+off;
	return v;
}

template<class T>
void print(const vector<T>&v,int suc=1){
	rep(i,v.size())
		print(v[i],i==int(v.size())-1?suc:2);
}

string readString(){
	string s;
	cin>>s;
	return s;
}

template<class T>
T sq(const T& t){
	return t*t;
}

//#define CAPITAL
void yes(bool ex=true){
	#ifdef CAPITAL
	cout<<"YES"<<endl;
	#else
	cout<<"Yes"<<endl;
	#endif
	if(ex)exit(0);
}
void no(bool ex=true){
	#ifdef CAPITAL
	cout<<"NO"<<endl;
	#else
	cout<<"No"<<endl;
	#endif
	if(ex)exit(0);
}
void possible(bool ex=true){
	#ifdef CAPITAL
	cout<<"POSSIBLE"<<endl;
	#else
	cout<<"Possible"<<endl;
	#endif
	if(ex)exit(0);
}
void impossible(bool ex=true){
	#ifdef CAPITAL
	cout<<"IMPOSSIBLE"<<endl;
	#else
	cout<<"Impossible"<<endl;
	#endif
	if(ex)exit(0);
}

constexpr ll ten(int n){
	return n==0?1:ten(n-1)*10;
}

const ll infLL=LLONG_MAX/3;

#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif

int topbit(signed t){
	return t==0?-1:31-__builtin_clz(t);
}
int topbit(ll t){
	return t==0?-1:63-__builtin_clzll(t);
}
int botbit(signed a){
	return a==0?32:__builtin_ctz(a);
}
int botbit(ll a){
	return a==0?64:__builtin_ctzll(a);
}
int popcount(signed t){
	return __builtin_popcount(t);
}
int popcount(ll t){
	return __builtin_popcountll(t);
}
bool ispow2(int i){
	return i&&(i&-i)==i;
}
int mask(int i){
	return (int(1)<<i)-1;
}

bool inc(int a,int b,int c){
	return a<=b&&b<=c;
}

template<class t> void mkuni(vc<t>&v){
	sort(all(v));
	v.erase(unique(all(v)),v.ed);
}

ll rand_int(ll l, ll r) { //[l, r]
	#ifdef LOCAL
	static mt19937_64 gen;
	#else
    static random_device rd;
    static mt19937_64 gen(rd());
    #endif
    return uniform_int_distribution<ll>(l, r)(gen);
}

template<class t>
int lwb(const vc<t>&v,const t&a){
	return lower_bound(all(v),a)-v.bg;
}

using uint=unsigned;
using ull=unsigned long long;

//initfact();
//const uint mod=998244353;
//const uint mod=1000000007;
uint mod=1;
struct mint{
	uint v;
	mint(ll vv=0){s(vv%mod+mod);}
	mint& s(uint vv){
		v=vv<mod?vv:vv-mod;
		return *this;
	}
	mint operator-()const{return mint()-*this;}
	mint& operator+=(const mint&rhs){return s(v+rhs.v);}
	mint&operator-=(const mint&rhs){return s(v+mod-rhs.v);}
	mint&operator*=(const mint&rhs){
		v=ull(v)*rhs.v%mod;
		return *this;
	}
	mint&operator/=(const mint&rhs){return *this*=rhs.inv();}
	mint operator+(const mint&rhs)const{return mint(*this)+=rhs;}
	mint operator-(const mint&rhs)const{return mint(*this)-=rhs;}
	mint operator*(const mint&rhs)const{return mint(*this)*=rhs;}
	mint operator/(const mint&rhs)const{return mint(*this)/=rhs;}
	mint pow(int n)const{
		mint res(1),x(*this);
		while(n){
			if(n&1)res*=x;
			x*=x;
			n>>=1;
		}
		return res;
	}
	mint inv()const{return pow(mod-2);}
	/*mint inv()const{
		int x,y;
		int g=extgcd(v,mod,x,y);
		assert(g==1);
		if(x<0)x+=mod;
		return mint(x);
	}*/
	friend mint operator+(int x,const mint&y){
		return mint(x)+y;
	}
	friend mint operator-(int x,const mint&y){
		return mint(x)-y;
	}
	friend mint operator*(int x,const mint&y){
		return mint(x)*y;
	}
	friend mint operator/(int x,const mint&y){
		return mint(x)/y;
	}
	friend ostream& operator<<(ostream&os,const mint&m){
		return os<<m.v;
	}
	bool operator<(const mint&r)const{return v<r.v;}
	bool operator==(const mint&r)const{return v==r.v;}
	bool operator!=(const mint&r)const{return v!=r.v;}
	explicit operator bool()const{
		return v;
	}
};

const int vmax=(1<<21)+10;
mint fact[vmax],finv[vmax],invs[vmax];
void initfact(){
	fact[0]=1;
	rng(i,1,vmax){
		fact[i]=fact[i-1]*i;
	}
	finv[vmax-1]=fact[vmax-1].inv();
	for(int i=vmax-2;i>=0;i--){
		finv[i]=finv[i+1]*(i+1);
	}
	for(int i=vmax-1;i>=1;i--){
		invs[i]=finv[i]*fact[i-1];
	}
}
mint choose(int n,int k){
	return fact[n]*finv[n-k]*finv[k];
}
mint binom(int a,int b){
	return fact[a+b]*finv[a]*finv[b];
}
mint catalan(int n){
	return binom(n,n)-(n-1>=0?binom(n-1,n+1):0);
}

template<class num>
struct Vector{
	vector<num> v;
	Vector(int s=0){
		v.resize(s,num(0));
	}
	int size()const{
		return v.size();
	}
	num& operator[](int i){
		return v[i];
	}
	num const& operator[](int i)const{
		return v[i];
	}
	Vector& operator+=(const Vector&rhs){
		assert(size()==rhs.size());
		rep(i,size())
			v[i]+=rhs[i];
		return *this;
	}
	Vector& operator-=(const Vector&rhs){
		assert(size()==rhs.size());
		rep(i,size())
			v[i]-=rhs[i];
		return *this;
	}
	Vector& operator*=(const num&x){
		rep(i,size())
			v[i]*=x;
		return *this;
	}
	Vector& operator/=(const num&x){
		num y=num(1)/x;
		rep(i,size())
			v[i]*=y;
		return *this;
	}
	Vector operator+(const Vector&rhs)const{
		return Vector(*this)+=rhs;
	}
	Vector operator-(const Vector&rhs)const{
		return Vector(*this)-=rhs;
	}
	Vector operator*(const num&x)const{
		return Vector(*this)*=x;
	}
	Vector operator/(const num&x)const{
		return Vector(*this)/=x;
	}
	bool operator==(const Vector&rhs)const{
		return v==rhs.v;
	}
};

template<class num>
num dot(const Vector<num>&a,const Vector<num>&b){
	assert(a.size()==b.size());
	const int s=a.size();
	num ans(0);
	rep(i,s)
		ans+=a[i]*b[i];
	return ans;
}

template<class num>
ostream&operator<<(ostream&os,const Vector<num>&v){
	return os<<v.v;
}

template<class num>
struct Matrix{
	using V=Vector<num>;
	vector<V> m;
	Matrix(int s=0,num z=num(0)){
		m.resize(s,V(s));
		rep(i,size())
			m[i][i]=z;
	}
	int size()const{
		return m.size();
	}
	Matrix operator*(const Matrix&rhs)const{
		assert(size()==rhs.size());
		Matrix res(size());
		rep(i,size())rep(j,size())rep(k,size())
			res[i][j]+=m[i][k]*rhs[k][j];
		return res;
	}
	Matrix& operator*=(const Matrix&rhs){
		return *this=(*this)*rhs;
	}
	V operator*(const V&rhs)const{
		assert(size()==rhs.size());
		V res(size());
		rep(i,size())
			res[i]=dot(m[i],rhs);
		return res;
	}
	V& operator[](int i){
		return m[i];
	}
	V const& operator[](int i) const{
		return m[i];
	}
	Matrix& operator/=(const num&r){
		rep(i,m.size())m[i]/=r;
		return *this;
	}
	Matrix operator/(const num&r)const{
		return Matrix(*this)/=r;
	}
	bool operator==(const Matrix&rhs)const{
		return m==rhs.m;
	}
};

template<class num>
ostream&operator<<(ostream&os,const Matrix<num>&x){
	const int s=x.size();
	os<<"----------"<<endl;
	rep(i,s){
		rep(j,s){
			os<<x[i][j];
			if(j==s-1){
				os<<endl;
			}else{
				os<<" ";
			}
		}
	}
	return os<<"----------";
}

mint phi;

struct F{
	mint a,b;
	F(mint aa=0,mint bb=0):a(aa),b(bb){}
	F operator-()const{
		return F(-a,-b);
	}
	F& operator+=(const F&r){
		a+=r.a;
		b+=r.b;
		return *this;
	}
	F operator+(const F&r)const{
		return F(*this)+=r;
	}
	F& operator-=(const F&r){
		a-=r.a;
		b-=r.b;
		return *this;
	}
	F operator-(const F&r)const{
		return F(*this)-=r;
	}
	F operator*(const F&r)const{
		return F(a*r.a+b*r.b*phi,a*r.b+b*r.a);
	}
	F& operator*=(const F&r){
		return *this=*this*r;
	}
	F& operator/=(const F&r){
		return *this*=r.inv();
	}
	F operator/(const F&r)const{
		return F(*this)/=r;
	}
	F pow(int n)const{
		F res{1,0},x=*this;
		while(n){
			if(n&1)res=res*x;
			x=x*x;
			n>>=1;
		}
		return res;
	}
	F inv()const{
		return pow(ll(mod)*mod-2);
	}
	bool operator<(const F&r)const{
		if(a!=r.a)return a<r.a;
		else return b<r.b;
	}
	bool operator==(const F&r)const{
		return a==r.a&&b==r.b;
	}
	bool operator!=(const F&r)const{
		return a!=r.a||b!=r.b;
	}
	bool is_zero()const{
		return a.v==0&&b.v==0;
	}
	explicit operator bool()const{
		return a||b;
	}
};

ostream&operator<<(ostream&os,const F&f){
	return os<<"{"<<f.a<<","<<f.b<<"}";
}

vi factors(int x){
	vi res;
	for(int i=2;i*i<=x;i+=(i==2?1:2)){
		if(x%i==0){
			res.pb(i);
			while(x%i==0)
				x/=i;
		}
	}
	if(x>1)res.pb(x);
	sort(all(res));
	return res;
}

//require a^s=1
//minimum n s.t. a^n=b, 0<=n<=s-1
//or -1 if infeasible
template<class t>
int discrete_log(t a,t b,int s){
	dmp2(a,b,s);
	
	assert(a.pow(s)==t(1));
	
	const int L=ceil(sqrt(s));
	int ans=inf;
	
	map<t,int> v;
	{
		t x=a.pow(L);
		t cur(1);
		for(int i=0;i<s;i+=L){
			if(!v.count(cur))v[cur]=i;
			cur*=x;
		}
	}
	t x=a.inv();
	dmp(x);
	t cur(1);
	rep(i,L){
		t y=b*cur;
		if(v.count(y))
			chmin(ans,v[y]+i);
		cur*=x;
	}
	
	if(ans>=s)
		ans=-1;
	else{
		dmp(L);
		dmp(ans);
		assert(inc(0,ans,s-1));
		assert(a.pow(ans)==b);
	}
	
	return ans;
}

//require a^s=1
//returns minimum p s.t. a^p=1
template<class t>
int mult_period(t a,int s){
	vi f=factors(s);
	int p=s;
	for(auto v:f){
		while(p%v==0){
			if(a.pow(p/v)==t(1))
				p/=v;
			else
				break;
		}
	}
	return p;
}

//require b^s=1
//pair of
//minimum n s.t. a*b^n=c,0<=n<=s-1
//and period
//or (-1,-1) if infeasible
template<class t>
pi discrete_log_helper(t a,t b,t c,int s){
	dmp2(a,b,c,s);
	if(!a||!b){
		if(!c)return pi(0,1);
		else return pi(-1,-1);
	}
	assert(b.pow(s)==t(1));
	int w=discrete_log(b,c*a.inv(),s);
	if(w==-1)return pi(-1,-1);
	return pi(w,mult_period(b,s));
}

int norm_mod(int a,int p){
	a%=p;
	if(a<0)a+=p;
	return a;
}

//p: odd (not necessarily prime)
//10^18 サイズの入力で動くはず（未検証）
int jacobi(int a,int p){
	a=norm_mod(a,p);
	auto neg=[](int x){return x%2?-1:1;};
	if(a==0) return p==1;
	else if(a%2) return neg(((p-1)&(a-1))>>1)*jacobi(p%a,a);
	else return neg(((p&15)*(p&15)-1)/8)*jacobi(a/2,p);
}

//yosupo sqrt mod
//LOJ 150
//p: prime
//0<=a<p
//returns minimum solution
int sqrt_mod(int a,int p){
	if(p==2)return a%2;
	if(a==0)return 0;
	if(jacobi(a,p)==-1)return -1;
	int b,c;
	do{
		b=rand_int(0,p-1);
		c=norm_mod(b*b-a,p);
	}while(jacobi(c,p)!=-1);
	auto mul=[&](pi x,pi y){
		return pi(norm_mod(x.a*y.a+x.b*y.b%p*c,p),norm_mod(x.a*y.b+x.b*y.a,p));
	};
	pi x(b,1),cur(1,0);
	int n=(p+1)/2;
	while(n){
		if(n&1)cur=mul(cur,x);
		x=mul(x,x);
		n>>=1;
	}
	assert(cur.b==0);
	return min(cur.a,p-cur.a);
}

int extgcd(int a,int b,int&x,int&y){
	if(b==0){
		x=1;
		y=0;
		return a;
	}else{
		int g=extgcd(b,a%b,y,x);
		y-=a/b*x;
		return g;
	}
}

//x*y=g mod m
//returns (g,y)
pi modinv(int x,int m){
	int a,b;
	int g=extgcd(x,m,a,b);
	if(a<0)a+=m/g;
	return pi(g,a);
}

//x = a mod b
//x = c mod d
// => x = p mod q
//returns (p,q) or (-1,-1) if infeasible
pi crt(int a,int b,int c,int d){
	if(b<d){
		swap(a,c);
		swap(b,d);
	}
	c%=d;
	int g,e;
	tie(g,e)=modinv(b,d);
	int k=(c-a);
	if(k%g)return pi(-1,-1);
	k/=g;
	int m=b/g*d;
	int x=(a+k*e%(d/g)*b)%m;
	if(x<0)x+=m;
	return pi(x,m);
}

/*
void imp(){
	cout<<-1<<endl;
	exit(0);
}

void answer(int a){
	cout<<a<<endl;
	exit(0);
}
*/

template<class t>
t det22(const Matrix<t>&a){
	return a[0][0]*a[1][1]-a[0][1]*a[1][0];
}

template<class t>
Matrix<t> inv22(const Matrix<t>&a){
	Matrix<t> res(2);
	res[0][0]=a[1][1];
	res[1][0]=-a[1][0];
	res[0][1]=-a[0][1];
	res[1][1]=a[0][0];
	dmp(res*a);
	t d=det22(a);
	assert(d);
	return res/d;
}

pi mergeans(pi a,pi b){
	if(a==pi(-1,-1)||b==pi(-1,-1))return pi(-1,-1);
	return crt(a.a,a.b,b.a,b.b);
}
int normans(pi a){
	if(a==pi(-1,-1))return -1;
	int w=a.a;
	if(w==0)w+=a.b;
	return w;
}

template<class t>
t general_pow(t a,int n){
	if(n>=0)return a.pow(n);
	else return a.pow(-n).inv();
}

//solve the problem given two distinct eigenvalues
template<class t>
int solve_sub(Matrix<mint> aa,Matrix<mint> bb,t p,t q,int relka){
	Matrix<t> a(2);
	rep(i,2)rep(j,2)
		a[i][j]=aa[i][j];
	Matrix<t> b(2);
	rep(i,2)rep(j,2)
		b[i][j]=bb[i][j];
	auto getvec=[&](t w){
		Vector<t> res(2);
		if(a[0][0]!=w){
			res[0]=-a[0][1];
			res[1]=a[0][0]-w;
		}else{
			res[0]=a[1][1]-w;
			res[1]=-a[1][0];
		}
		return res;
	};
	Vector<t> v[2];
	v[0]=getvec(p);
	v[1]=getvec(q);
	rep(i,2){
		dmp(v[i]);
		assert(a*v[i]==v[i]*(i==0?p:q));
	}
	Matrix<t> w(2);
	rep(i,2)rep(j,2)
		w[i][j]=v[j][i];
	
	dmp(w);
	Matrix<t> winv=inv22(w);
	dmp(winv);
	
	dmp(w*winv);
	
	t ad=det22(a);
	assert(ad==p*q);
	
	Matrix<t> tar=winv*b*w;
	dmp(tar);
	
	if(tar[1][0]||tar[0][1])return -1;
	t bd=tar[0][0]*tar[1][1];
	
	int off,z;
	tie(off,z)=discrete_log_helper(t(1),ad,bd,mod-1);
	if(off==-1)return -1;
	
	auto waf=[&](t g,t h){
		h/=g.pow(off);
		g=g.pow(z);
		int x,per;
		tie(x,per)=discrete_log_helper(t(1),g,h,relka);
		if(x==-1)return pi(-1,-1);
		return pi(off+z*x,z*per);
	};
	
	return normans(mergeans(
		waf(p,tar[0][0]),
		waf(q,tar[1][1])
	));
}

int solve_simple(Matrix<mint> a,Matrix<mint> b){
	assert(a[0][1]==0);
	assert(a[1][0]==0);
	if(b[0][1]||b[1][0])return -1;
	return normans(mergeans(
		discrete_log_helper(mint(1),a[0][0],b[0][0],mod-1),
		discrete_log_helper(mint(1),a[1][1],b[1][1],mod-1)
	));
}

int solve(Matrix<mint> a,Matrix<mint> b,int brutethreshold=2){
	phi=0;
	if(mod<=brutethreshold){
		Matrix<mint> cur(2,1);
		rep(i,mod*mod){
			if(i){
				if(cur==b){
					return i;
				}
			}
			cur*=a;
		}
		return -1;
	}
	
	mint c=-a[0][0]-a[1][1];
	mint d=a[0][0]*a[1][1]-a[0][1]*a[1][0];
	
	dmp2(c,d);
	if(d==0){
		if(a==b)return 1;
		pi ans(0,1);
		rep(i,2)rep(j,2){
			pi x=discrete_log_helper(a[i][j],-c,b[i][j],mod-1);
			ans=mergeans(x,ans);
		}
		int ret=normans(ans);
		if(ret>=0)ret++;
		return ret;
	}else{
		mint dis=c*c/4-d;
		dmp(dis);
		if(dis==0){
			mint alpha=-c/2;
			Matrix<mint> apri=a;
			apri[0][0]-=alpha;
			apri[1][1]-=alpha;
			
			dmp(alpha);
			
			Vector<mint> v(2);
			if(apri[0][0]||apri[1][0])
				v[0]=1;
			else if(apri[0][1]||apri[1][1])
				v[1]=1;
			else
				return solve_simple(a,b);
			
			Vector<mint> u=apri*v;
			
			Matrix<mint> w(2);
			w[0][0]=u[0];
			w[1][0]=u[1];
			w[0][1]=v[0];
			w[1][1]=v[1];
			auto winv=inv22(w);
			
			auto tar=winv*b*w;
			
			if(tar[1][0])return -1;
			if(tar[0][0]!=tar[1][1])return -1;
			
			pi k=discrete_log_helper(mint(1),alpha,tar[0][0],mod-1);
			if(k==pi(-1,-1))return -1;
			
			mint z=tar[0][1]/general_pow(alpha,k.a-1);
			mint x=(z-k.a)/k.b;
			
			int res=k.a+x.v*k.b;
			if(res==0)res=k.b*mod;
			return res;
		}else{
			int s=sqrt_mod(dis.v,mod);
			dmp(s);
			if(s!=-1){
				return solve_sub(a,b,-c/2+s,-c/2-s,mod-1);
			}else{
				phi=dis;
				return solve_sub(a,b,F(-c/2,1),F(-c/2,-1),mod+1);
			}
		}
	}
}

bool isprime(int p){
	for(int i=2;i*i<=p;i+=(i==2?1:2))
		if(p%i==0)return false;
	return true;
}

signed main(){
	cin.tie(0);
	ios::sync_with_stdio(0);
	cout<<fixed<<setprecision(20);
	
	int n;cin>>n;
	if(n>0){
		mod=n;
		
		Matrix<mint> a(2),b(2);
		rep(i,2)rep(j,2)cin>>a[i][j].v;
		rep(i,2)rep(j,2)cin>>b[i][j].v;
		
		cout<<solve(a,b)<<endl;
	}else{
		rep(_,100000){
			do{
				mod=rand_int(100,200);
			}while(!isprime(mod));
			
			Matrix<mint> a(2),b(2);
			rep(i,2)rep(j,2)
				a[i][j]=rand_int(0,mod-1);
			rep(i,2)rep(j,2)
				b[i][j]=rand_int(0,mod-1);
			{
				cout<<mod<<endl;
				cout<<a<<endl;
				cout<<b<<endl;
			}	
			int x=solve(a,b);
			int y=solve(a,b,inf);
			
			if(x!=y){
				cout<<mod<<endl;
				cout<<a<<endl;
				cout<<b<<endl;
				exit(1);
			}
		}
	}
}
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