結果

問題 No.2362 Inversion Number of Mod of Linear
コンテスト
ユーザー maroon_kuri
提出日時 2023-06-24 17:12:27
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,551 ms / 2,000 ms
コード長 13,540 bytes
コンパイル時間 3,568 ms
コンパイル使用メモリ 252,128 KB
最終ジャッジ日時 2025-02-15 02:05:56
ジャッジサーバーID
（参考情報） 		judge1 / judge1
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ファイルパターン 結果
sample AC * 2
other AC * 8
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ソースコード

diff # 

#ifndef LOCAL
#pragma GCC optimize ("Ofast")
#pragma GCC optimize ("unroll-loops")
#endif

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

using ll=long long;
#define int ll


//デバッグ実行でオーバーフローするとコアダンプしがち

using int128=__int128_t;
using uint128=unsigned __int128_t;

istream& operator>>(istream&is,int128&res){
	res=0;
	string s;is>>s;
	int head=0;
	int128 w=1;
	if(s[0]=='-'){
		w=-1;
		head++;
	}
	while(head<int(s.size())){
		res=res*10+s[head++]-'0';
	}
	res*=w;
	return is;
}
ostream& operator<<(ostream&os,int128 i){
	if(i==0)
		return os<<0;
	static char buf[100];
	if(i<0){
		os<<"-";
		i=-i;
	}
	int p=0;
	while(i){
		buf[p++]='0'+i%10;
		i/=10;
	}
	reverse(buf,buf+p);
	buf[p]=0;
	return os<<buf;
}
ostream& operator<<(ostream&os,uint128 i){
	if(i==0)
		return os<<0;
	static char buf[100];
	int p=0;
	while(i){
		buf[p++]='0'+i%10;
		i/=10;
	}
	reverse(buf,buf+p);
	buf[p]=0;
	return os<<buf;
}
int128 abs128(int128 a){
	return a<0?-a:a;
}
int botbit(int128 a){
	const int128 m=(int128(1)<<64)-1;
	if(a&m)return __builtin_ctzll(ll(a));
	else return __builtin_ctzll(ll(a>>64))+64;
}
int128 gcd(int128 a,int128 b){
	if(a<0)a=-a;
	if(b<0)b=-b;
	if(a==0)return b;
	if(b==0)return a;
	int128 s=botbit(a|b);
	a>>=botbit(a);
	do{
		b>>=botbit(b);
		if(a>b)swap(a,b);
		b-=a;
	}while(b);
	return a<<s;
}
const int128 inf128=int128(1)<<122;


#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
#define si(x) int(x.size())
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif

template<class t,class u> bool chmax(t&a,u b){if(a<b){a=b;return true;}else return false;}
template<class t,class u> bool chmin(t&a,u b){if(b<a){a=b;return true;}else return false;}

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__,##__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<<"}";
}

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;
}

pi readpi(int off=0){
	int a,b;cin>>a>>b;
	return pi(a+off,b+off);
}

template<class t>
void print_single(t x,int suc=1){
	cout<<x;
	if(suc==1)
		cout<<"\n";
	if(suc==2)
		cout<<" ";
}

template<class t,class u>
void print_single(const pair<t,u>&p,int suc=1){
	print_single(p.a,2);
	print_single(p.b,suc);
}

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

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

template<class T,size_t N>
void print_single(const array<T,N>&v,int suc=1){
	rep(i,N)
		print_single(v[i],i==int(N)-1?suc:2);
}

template<class T>
void print(const T&t){
	print_single(t);
}

template<class T,class ...Args>
void print(const T&t,const Args&...args){
	print_single(t,2);
	print(args...);
}

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

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

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

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 topbit(ull 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 botbit(ull a){
	return a==0?64:__builtin_ctzll(a);
}
int popcount(signed t){
	return __builtin_popcount(t);
}
int popcount(ll t){
	return __builtin_popcountll(t);
}
int popcount(ull t){
	return __builtin_popcountll(t);
}
int bitparity(ll t){
	return __builtin_parityll(t);
}
bool ispow2(int i){
	return i&&(i&-i)==i;
}
ll mask(int i){
	return (ll(1)<<i)-1;
}
ull umask(int i){
	return (ull(1)<<i)-1;
}
ll minp2(ll n){
	if(n<=1)return 1;
	else return ll(1)<<(topbit(n-1)+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 mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
	#endif*/
	return uniform_int_distribution<ll>(l, r)(gen);
}

ll rand_int(ll k){ //[0,k)
	return rand_int(0,k-1);
}

template<class t>
void myshuffle(vc<t>&a){
	rep(i,si(a))swap(a[i],a[rand_int(0,i)]);
}

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

vvc<int> readGraph(int n,int m){
	vvc<int> g(n);
	rep(i,m){
		int a,b;
		cin>>a>>b;
		//sc.read(a,b);
		a--;b--;
		g[a].pb(b);
		g[b].pb(a);
	}
	return g;
}

vvc<int> readTree(int n){
	return readGraph(n,n-1);
}

vc<ll> presum(const vi&a){
	vc<ll> s(si(a)+1);
	rep(i,si(a))s[i+1]=s[i]+a[i];
	return s;
}
//BIT で数列を管理するときに使う (CF850C)
template<class t>
vc<t> predif(vc<t> a){
	gnr(i,1,si(a))a[i]-=a[i-1];
	return a;
}
template<class t>
vvc<ll> imos(const vvc<t>&a){
	int n=si(a),m=si(a[0]);
	vvc<ll> b(n+1,vc<ll>(m+1));
	rep(i,n)rep(j,m)
		b[i+1][j+1]=b[i+1][j]+b[i][j+1]-b[i][j]+a[i][j];
	return b;
}

//verify してないや
void transvvc(int&n,int&m){
	swap(n,m);
}
template<class t,class... Args>
void transvvc(int&n,int&m,vvc<t>&a,Args&...args){
	assert(si(a)==n);
	vvc<t> b(m,vi(n));
	rep(i,n){
		assert(si(a[i])==m);
		rep(j,m)b[j][i]=a[i][j];
	}
	a.swap(b);
	transvvc(n,m,args...);
}
//CF854E
void rotvvc(int&n,int&m){
	swap(n,m);
}
template<class t,class... Args>
void rotvvc(int&n,int&m,vvc<t>&a,Args&...args){
	assert(si(a)==n);
	vvc<t> b(m,vi(n));
	rep(i,n){
		assert(si(a[i])==m);
		rep(j,m)b[m-1-j][i]=a[i][j];
	}
	a.swap(b);
	rotvvc(n,m,args...);
}

//ソートして i 番目が idx[i]
//CF850C
template<class t>
vi sortidx(const vc<t>&a){
	int n=si(a);
	vi idx(n);iota(all(idx),0);
	sort(all(idx),[&](int i,int j){return a[i]<a[j];});
	return idx;
}
//vs[i]=a[idx[i]]
//例えば sortidx で得た idx を使えば単にソート列になって返ってくる
//CF850C
template<class t>
vc<t> a_idx(const vc<t>&a,const vi&idx){
	int n=si(a);
	assert(si(idx)==n);
	vc<t> vs(n);
	rep(i,n)vs[i]=a[idx[i]];
	return vs;
}
//CF850C
vi invperm(const vi&p){
	int n=si(p);
	vi q(n);
	rep(i,n)q[p[i]]=i;
	return q;
}

template<class t,class s=t>
s SUM(const vc<t>&a){
	return accumulate(all(a),s(0));
}

template<class t>
t MAX(const vc<t>&a){
	return *max_element(all(a));
}

template<class t>
t MIN(const vc<t>&a){
	return *min_element(all(a));
}

template<class t>
pair<t,int> MINi(const vc<t>&a){
	auto itr=min_element(all(a));
	return mp(*itr,itr-a.bg);
}

template<class t,class u>
pair<t,u> operator+(const pair<t,u>&a,const pair<t,u>&b){
	return mp(a.a+b.a,a.b+b.b);
}

vi vid(int n){
	vi res(n);iota(all(res),0);
	return res;
}

template<class S>
S getrev(S s){
	reverse(all(s));
	return s;
}

pi operator+(pi a,pi b){return pi(a.a+b.a,a.b+b.b);}

template<class t>
t gpp(vc<t>&vs){
	assert(si(vs));
	t res=move(vs.back());
	vs.pop_back();
	return res;
}

//Bytecamp 2022 Day2 L
template<class num,int S>
struct Vector:array<num,S>{
	Vector operator-()const{
		Vector v;
		rep(i,S)v[i]=-(*this)[i];
		return v;
	}
	Vector& operator+=(const Vector&rhs){
		rep(i,S)(*this)[i]+=rhs[i];
		return *this;
	}
	Vector& operator-=(const Vector&rhs){
		rep(i,S)(*this)[i]-=rhs[i];
		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){
		rep(i,S)(*this)[i]*=x;
		return *this;
	}
	Vector& operator/=(const num&x){
		num y=num(1)/x;
		rep(i,S)(*this)[i]*=y;
		return *this;
	}
	/*Vector& operator*=(const Vector&rhs){
		rep(i,S)(*this)[i]*=rhs[i];
		return *this;
	}
	Vector& operator/=(const Vector&rhs){
		rep(i,S)(*this)[i]/=rhs[i];
		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;
	}
};

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

//CF CodeTon4 H
template<class num,int S>
struct Matrix:Vector<Vector<num,S>,S>{
	using V=Vector<num,S>;
	Matrix operator*(const Matrix&rhs)const{
		Matrix res{};
		rep(i,S)rep(j,S)rep(k,S)
			res[i][j]+=(*this)[i][k]*rhs[k][j];
		return res;
	}
	Matrix& operator*=(const Matrix&rhs){
		return *this=(*this)*rhs;
	}
	V operator*(const V&rhs)const{
		V res{};
		rep(i,S)
			res[i]=dot((*this)[i],rhs);
		return res;
	}
	static Matrix getid(){
		Matrix res{};
		rep(i,S)res[i][i]=1;
		return res;
	}
};

const int S=5;
using V=Vector<int128,S>;
using M=Matrix<int128,S>;

M matpow(M a,int n){
	M res=M::getid();
	while(n){
		if(n&1)res*=a;
		a*=a;
		n>>=1;
	}
	return res;
}

V matpow_V(M a,int n,V res){
	while(n){
		if(n&1)res=a*res;
		a*=a;
		n>>=1;
	}
	return res;
}

//f(x)=(hx+start)/w という直線を考える
//(0,0) からスタートする．
//まず (0,floor(f(0))) まで移動し，移動するたびに B をかける
//その後以下の操作を N 回繰り返す
//(x,y) から (x+1,y) へ移動．A をかける
//(x,y) から (x,floor(f(x))) まで移動．移動するたびに B をかける
//A|B をかけるというのは m->(A|B)m という遷移
//最終的な行列を返す
//多分 O(log(w+h)) 回くらいの行列乗算だと思う
//stress-tested
M gauss_sum_matrix(int w,int h,int start,int n,M A,M B){
	assert(0<w);
	assert(0<=h);
	assert(0<=start);
	assert(0<=n);
	
	M L=M::getid(),R=M::getid();
	bool rev=false;
	while(1){
		if(w<=start){
			int k=start/w;
			if(!rev){
				R=matpow(B,k)*R;
			}else{
				L=L*matpow(A,k);
			}
			start%=w;
		}
		if(n==0)break;
		if(w<=h){
			int k=h/w;
			if(!rev){
				A=matpow(B,k)*A;
			}else{
				B=B*matpow(A,k);
			}
			h%=w;
		}else{
			int need=h?(w-start+h-1)/h:inf;
			if(n<need){
				if(!rev){
					R=matpow(A,n)*R;
				}else{
					L=L*matpow(B,n);
				}
				n=0;
			}else{
				if(!rev){
					R=B*matpow(A,need)*R;
				}else{
					L=L*matpow(B,need)*A;
				}
				start=(h*need+start)%w;
				n-=need;
				
				int p=(h*n+start)/w,q=(h*n+start)%w;
				swap(w,h);
				start=q;
				n=p;
				rev=!rev;
			}
		}
	}
	
	return L*R;
}

int128 sub(int n,int m,int x,int y,int w,int d){
	M A{
		  1,0,0,0,0,
		  x,1,0,0,0,
		  d,0,1,0,0,
		x*d,d,x,1,0,
		  0,0,0,1,1
	};
	M B{
		1 ,0,0 ,0,0,
		-m,1,0 ,0,0,
		0 ,0,1 ,0,0,
		0 ,0,-m,1,0,
		0 ,0,0 ,0,1
	};
	V v{1,y,w,y*w,0};
	M z=gauss_sum_matrix(m,x,y,n,A,B);
	return (z*v)[4];
}

void slv(){
	int n,m,x,y;cin>>n>>m>>x>>y;
	
	int128 ans=0;
	
	ans+=sub(n,m,x,0,n,-1);
	ans+=sub(n,m,x,y,(n-1),-2);
	
	assert(ans%m==0);
	print(ans/m);
}

signed main(){
	cin.tie(0);
	ios::sync_with_stdio(0);
	cout<<fixed<<setprecision(20);
	
	int t;cin>>t;rep(_,t)
	slv();
}
0