結果
| 問題 | No.3538 Not First Place |
| コンテスト | |
| ユーザー |
👑  hamamu
|
| 提出日時 | 2026-05-08 23:19:45 |
| 言語 | C++23 (gcc 15.2.0 + boost 1.89.0) |
| 結果 |
RE
|
| 実行時間 | - |
| コード長 | 60,348 bytes |
| 記録 | |
| コンパイル時間 | 5,301 ms |
| コンパイル使用メモリ | 380,428 KB |
| 実行使用メモリ | 183,612 KB |
| 最終ジャッジ日時 | 2026-05-08 23:20:41 |
| 合計ジャッジ時間 | 17,900 ms |
|
ジャッジサーバーID （参考情報） |
judge2_0 / judge1_1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 RE * 1 |
| other | AC * 4 TLE * 1 -- * 21 |
ソースコード
#ifndef MYLOCAL
//# pragma GCC target("avx2")//yukiではNG
# pragma GCC optimize("O3")
# pragma GCC optimize("unroll-loops")
#endif
#if defined(NDEBUG)
#undef NDEBUG
#endif
#include "bits/stdc++.h"
using namespace std;
using ll=long long;
using dd=long double;
using pll=pair<ll,ll>;
using tll=tuple<ll,ll,ll>;
using qll=tuple<ll,ll,ll,ll>;
using namespace chrono;
constexpr ll INF = 1201001001001001001;
struct Fast{ Fast(){ cin.tie(0); ios::sync_with_stdio(false); cout<<fixed<<setprecision(numeric_limits<double>::max_digits10); } } fast;
#define EXPAND( x ) x//VS用おまじない
#define overload3(_1,_2,_3,name,...) name
#define overload4(_1,_2,_3,_4,name,...) name
#define overload5(_1,_2,_3,_4,_5,name,...) name
#define rep1(N) for (ll dmyi = 0; dmyi < (N); dmyi++)
#define rep2(i, N) for (ll i = 0; i < (N); i++)
#define rep3(i, S, E) for (ll i = (S); i <= (E); i++)
#define rep4(i, S, E, t) for (ll i = (S); i <= (E); i+=(t))
#define rep(...) EXPAND(overload4(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__))
#define dep3(i, E, S) for (ll i = (E); i >= (S); i--)
#define dep4(i, E, S, t) for (ll i = (E); i >= (S); i-=(t))
#define dep(...) EXPAND(overload4(__VA_ARGS__, dep4, dep3,_,_)(__VA_ARGS__))
#define ALL1(v) (v).begin(), (v).end()
#define ALL2(v,E) (v).begin(), (v).begin()+((E)+1)
#define ALL3(v,S,E) (v).begin()+(S), (v).begin()+((E)+1)
#define all(...) EXPAND(overload3(__VA_ARGS__, ALL3, ALL2, ALL1)(__VA_ARGS__))
template<class T> inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; }return false; }
template<class T> inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; }return false; }
template<class T> [[nodiscard]] inline T limithi(T a,T b){ return min(a,b); }
template<class T> [[nodiscard]] inline T limitlo(T a,T b){ return max(a,b); }
template<class T> inline bool chlimithi(T &a,T b){ return chmin(a,b); }
template<class T> inline bool chlimitlo(T &a,T b){ return chmax(a,b); }
template<class T> inline auto maxe(T &&v,ll S,ll E){ return *max_element(all(v,S,E)); }
template<class T> inline auto maxe(T &&v){ return *max_element(all(v)); }
template<class T> inline auto mine(T &&v,ll S,ll E){ return *min_element(all(v,S,E)); }
template<class T> inline auto mine(T &&v){ return *min_element(all(v)); }
template<class T,class U=typename remove_reference<T>::type::value_type>
inline U sum(T &&v,ll S,ll E) {return accumulate(all(v,S,E),U());}
template<class T> inline auto sum(T &&v) {return sum(v,0,v.end()-v.begin()-1);}
template<class T> inline ll sz(T &&v){ return (ll)v.size(); }
//cin
struct cinutil{
template<class T> static void cin1core(T &a){ cin>>a; }
template<class T,class S> static void cin1core(pair<T,S> &a){
cin1core(a.first),cin1core(a.second);
}
template<class... Args> static void cin1core(tuple<Args...> &a){
cinTplRec<tuple<Args...>,sizeof...(Args)-1>()(a);
}
template<class T,size_t N>
static void cin1core(array<T,N> &a){ for (int i=0; i<(int)N; ++i) cin>>a[i]; }
private:
template<class Tpl,int i> struct cinTplRec{
void operator()(Tpl &a){ cinTplRec<Tpl,i-1>()(a); cin1core(get<i>(a)); }
};
template<class Tpl> struct cinTplRec<Tpl,0>{
void operator()(Tpl &a){ cin1core(get<0>(a)); }
};
};
template<class T> T cin1(){ T a; cinutil::cin1core(a); return a; }
template<class... Args> tuple<Args...> cins(){ return cin1<tuple<Args...>>(); }
//cout
template<class T,class S> inline ostream &operator<<(ostream &os,const pair<T,S> &a){ return os << a.first << ' ' << a.second; }
template<class T,class S,class R> inline ostream &operator<<(ostream &os,const tuple<T,S,R> &a){ return os << get<0>(a) << ' ' << get<1>(a) << ' ' << get<2>(a); }
template<class T,class S,class R,class Q> inline ostream &operator<<(ostream &os,const tuple<T,S,R,Q> &a){ return os << get<0>(a) << ' ' << get<1>(a) << ' ' << get<2>(a) << ' ' << get<3>(a); }
template<class T> inline ostream &operator<<(ostream &os,const vector<T> &a){ for (ll i=0; i<(ll)a.size(); i++) os<<(i>0?" ":"")<<a[i]; return os; }
inline struct{
system_clock::time_point st = system_clock::now();
ll operator()()const{return duration_cast<microseconds>(system_clock::now()-st).count()/1000;}
} timeget;
template<long long MOD> struct mll_{
using Int = long long;
using ll = long long;
ll val_=0;
/*---- utility ----*/
mll_ &norm(){ return normR().normS(); }//正規化
mll_ &normR(){ val_%=MOD; return *this; }//剰余正規化のみ
mll_ &normS(){ if (val_<0) val_+=MOD; return *this; }//正負正規化のみ
mll_ &normP(){ if (val_>=MOD) val_-=MOD; return *this; }//加算時正規化
mll_ &invsg(){ val_=-val_; return normS(); }//正負反転
ll modinv(int a){//a^-1 mod MOD
int ypre=0,y=1,apre=MOD;
while (a>1){
int t=apre/a;
apre-=a*t,swap(a,apre);
ypre-=y*t,swap(y,ypre);
}
return y<0 ? y+MOD : y;
}
/*---- I/F ----*/
mll_(){}
mll_(ll v): val_(v){ norm(); }
mll_(ll v,bool b): val_(v){} //正規化無のコンストラクタ
Int val()const{ return (Int)val_; }
bool isnone() const { return val_==-1; } //true:値なし
mll_ &none() { val_=-1; return *this; } //値なしにする
mll_ &inv(){ val_=modinv((int)val_); return *this; }
mll_ &operator+=(mll_ b){ val_+=b.val_; return normP(); }
mll_ &operator-=(mll_ b){ val_-=b.val_; return normS(); }
mll_ &operator*=(mll_ b){ val_*=b.val_; return normR(); }
mll_ &operator/=(mll_ b){ return *this*=b.inv(); }
mll_ &operator+=(ll b){ return *this+=mll_(b); }
mll_ &operator-=(ll b){ return *this-=mll_(b); }
mll_ &operator*=(ll b){ return *this*=mll_(b); }
mll_ &operator/=(ll b){ return *this/=mll_(b); }
mll_ operator-()const{ return mll_(*this).invsg(); }
mll_ operator+(mll_ b)const{ return mll_(*this)+=b; }
mll_ operator-(mll_ b)const{ return mll_(*this)-=b; }
mll_ operator*(mll_ b)const{ return mll_(*this)*=b; }
mll_ operator/(mll_ b)const{ return mll_(*this)/=b; }
mll_ operator+(ll b)const{ return mll_(*this)+=b; }
mll_ operator-(ll b)const{ return mll_(*this)-=b; }
mll_ operator*(ll b)const{ return mll_(*this)*=b; }
mll_ operator/(ll b)const{ return mll_(*this)/=b; }
friend mll_ operator+(ll a,mll_ b){ return b+a; }
friend mll_ operator-(ll a,mll_ b){ return -b+a; }
friend mll_ operator*(ll a,mll_ b){ return b*a; }
friend mll_ operator/(ll a,mll_ b){ return mll_(a)/b; }
bool operator==(mll_ b)const{ return val_==b.val_; }
bool operator!=(mll_ b)const{ return val_!=b.val_; }
bool operator==(ll b)const{ return *this==mll_(b); }
bool operator!=(ll b)const{ return *this!=mll_(b); }
friend bool operator==(ll a,mll_ b){ return mll_(a)==b; }
friend bool operator!=(ll a,mll_ b){ return mll_(a)!=b; }
friend ostream &operator<<(ostream &os,mll_ a){ return os << a.val_; }
friend istream &operator>>(istream &is,mll_ &a){ return is >> a.val_; }
mll_ pow(ll k)const{
mll_ ret(1,false),a(*this);
for (; k>0; k>>=1,a*=a) if (k&1)ret*=a;
return ret;
}
static constexpr int mod() { return MOD; }
//enum{ modll=MOD };
};
template<class T> struct Vector: vector<T>{
using Int = long long;
using vT=vector<T>;
using cvT=const vector<T>;
using cT=const T;
using vT::vT; //親クラスのコンストラクタの隠蔽を回避
using vT::begin,vT::end,vT::insert,vT::erase;
auto it(Int i){ return begin()+i; }
auto it(Int i)const{ return begin()+i; }
Vector(cvT& b):vT(b){}
Vector(vT&& b):vT(move(b)){}
Vector(int n,cT& x):vT(n,x){}// ┬ 型推論のためラッパー
Vector(long long n,cT& x):vT(n,x){}
template<class S> Vector(const Vector<S>& b):vT(b.begin(),b.end()){}
template<class S> Vector(const vector<S>& b):vT(b.begin(),b.end()){}
Vector(Int n,T s,T d){ iota(n,s,d); }
Vector(Int n,function<T(Int)> g):vT(n){ for(Int i=0;i<n;++i) (*this)[i]=g(i); }
Vector &operator+=(cvT &b){ assert(size()==b.size()); for(Int i=0;i<size();++i) (*this)[i]+=b[i]; return *this; }
Vector &operator-=(cvT &b){ assert(size()==b.size()); for(Int i=0;i<size();++i) (*this)[i]-=b[i]; return *this; }
Vector &operator*=(cvT &b){ assert(size()==b.size()); for(Int i=0;i<size();++i) (*this)[i]*=b[i]; return *this; }
Vector &operator/=(cvT &b){ assert(size()==b.size()); for(Int i=0;i<size();++i) (*this)[i]/=b[i]; return *this; }
Vector &operator%=(cvT &b){ assert(size()==b.size()); for(Int i=0;i<size();++i) (*this)[i]%=b[i]; return *this; }
Vector &operator+=(const Vector<T> &b){ return *this+=(cvT&)b; }
Vector &operator-=(const Vector<T> &b){ return *this-=(cvT&)b; }
Vector &operator*=(const Vector<T> &b){ return *this*=(cvT&)b; }
Vector &operator/=(const Vector<T> &b){ return *this/=(cvT&)b; }
Vector &operator%=(const Vector<T> &b){ return *this%=(cvT&)b; }
Vector operator+(cvT &b){ return Vector(*this)+=b; }
Vector operator-(cvT &b){ return Vector(*this)-=b; }
Vector operator*(cvT &b){ return Vector(*this)*=b; }
Vector operator/(cvT &b){ return Vector(*this)/=b; }
Vector operator%(cvT &b){ return Vector(*this)%=b; }
Vector operator+(const Vector<T> &b){ return Vector(*this)+=b; }
Vector operator-(const Vector<T> &b){ return Vector(*this)-=b; }
Vector operator*(const Vector<T> &b){ return Vector(*this)*=b; }
Vector operator/(const Vector<T> &b){ return Vector(*this)/=b; }
Vector operator%(const Vector<T> &b){ return Vector(*this)%=b; }
template<class S> Vector &operator+=(S x){ for(T &e: *this) e+=x; return *this; }
template<class S> Vector &operator-=(S x){ for(T &e: *this) e-=x; return *this; }
template<class S> Vector &operator*=(S x){ for(T &e: *this) e*=x; return *this; }
template<class S> Vector &operator/=(S x){ for(T &e: *this) e/=x; return *this; }
template<class S> Vector &operator%=(S x){ for(T &e: *this) e%=x; return *this; }
template<class S> Vector operator+(S x)const{ return Vector(*this)+=x; }
template<class S> Vector operator-(S x)const{ return Vector(*this)-=x; }
template<class S> Vector operator*(S x)const{ return Vector(*this)*=x; }
template<class S> Vector operator/(S x)const{ return Vector(*this)/=x; }
template<class S> Vector operator%(S x)const{ return Vector(*this)%=x; }
Vector &operator--(int){ return *this-=1; }
Vector &operator++(int){ return *this+=1; }
Vector operator-()const{ return Vector(*this)*=-1; }
template<class S> friend Vector operator-(S x,const Vector &a){ return -a+=x; }
T& at(Int i){ assert(i>=0); if(n()<=i)vT::resize(i+1); return vT::operator[](i); }
Vector slice(Int l,Int r,Int d=1)const{
Vector ret;
for(Int i=l;(d>0&&i<=r)||(d<0&&r<=i);i+=d) ret.push_back((*this)[i]);
return ret;
}
Int size()const{ return (Int)vT::size(); }
Int n()const{ return size(); }
Vector &push_back(cT& x,Int n=1){ for(Int i=0;i<n;++i){ vT::push_back(x); } return *this; }
Vector &pop_back(Int n=1){ for(Int i=0;i<n;++i){ vT::pop_back(); } return *this; }
Vector &push_front(cT& x,Int n=1){ this->insert(0,x,n); return *this; }
Vector &pop_front(Int n=1){ erase(0,n-1); return *this; }
T pull_back(){ T x=move(vT::back()); vT::pop_back(); return x; }
T pull_front(){ T x=move(vT::front()); erase(0); return x; }
Vector &insert(Int i,cT& x,Int n=1){ insert(it(i),n,x); return *this; }
Vector &insert(Int i,cvT& b){ insert(it(i),b.begin(),b.end()); return *this; }
Vector &erase(Int i){ erase(it(i)); return *this; }
Vector &erase(Int l,Int r){ erase(it(l),it(r+1)); return *this; }
Vector &erase(const Vector<Int> &idxs){
for (Int I=0; I<idxs.n(); ++I){
Int l=idxs[I]+1, r = (I<idxs.n()-1) ? idxs[I+1] : this->n();
copy(it(l),it(r),it(l-I-1));//[l,r)を前にI+1個ずらす
}
vT::resize(this->n()-idxs.n());
return *this;
}
Vector &eraseall(cT& x){ return eraseall(0,size()-1,x); }
Vector &eraseall(Int l,Int r,cT& x){ erase(remove(it(l),it(r+1),x),it(r+1)); return *this; }
template<class Pr> Vector &eraseif(Pr pr){ return eraseif(0,size()-1,pr); }
template<class Pr> Vector &eraseif(Int l,Int r,Pr pr){ erase(remove_if(it(l),it(r+1),pr),it(r+1)); return *this; }
Vector &concat(cvT &b,Int n=1){
cvT B = (&b==this) ? *this : vT{};
for(int i=0;i<n;++i) this->insert(size(),(&b==this)?B:b);
return *this;
}
Vector repeat(Int n){ return Vector{}.concat(*this,n); }
Vector &reverse(Int l=0,Int r=-1){ r+=r<0?size():0; std::reverse(it(l),it(r+1)); return *this; }
Vector &rotate(Int m){ return rotate(0,size()-1,m); }
Vector &rotate(Int l,Int r,Int m){ std::rotate(it(l),it(m),it(r+1)); return *this; }
Vector &sort(Int l=0,Int r=-1){ r+=r<0?size():0; std::sort(it(l),it(r+1)); return *this; }
Vector &rsort(Int l=0,Int r=-1){ return sort(l,r).reverse(l,r); }
template<class Pr> Vector &sort(Pr pr){ return sort(0,size()-1,pr); }
template<class Pr> Vector &sort(Int l,Int r,Pr pr){ std::sort(it(l),it(r+1),pr); return *this; }
template<int key> Vector &sortbykey(Int l=0,Int r=-1){
r+=r<0?size():0;
sort(l,r,[](cT &x,cT &y){return get<key>(x)<get<key>(y);});
return *this;
}
Vector &uniq(){ erase(unique(begin(),end()),end()); return *this; }
Vector &sortq(){ return sort().uniq(); }
Vector &fill(cT& x){ return fill(0,size()-1,x); }
Vector &fill(Int l,Int r,cT& x){ std::fill(it(l),it(r+1),x); return *this; }
Vector ©(Int i,cvT &b,Int n=1){//A[i]スタートでbをn回分コピー
for (int t=0; t<n; ++t) for (int j=0; j<(int)b.size(); ++j){
if (i>=size()) return *this;
if (i>=0) (*this)[i]=b[j];
i++;
}
return *this;
}
template<class S=Int> Vector &iota(Int n,T s=0,S d=1){
vT::resize(n);
if(n==0) return *this;
(*this)[0]=s;
for(int i=1;i<n;++i) (*this)[i]=(*this)[i-1]+d;
return *this;
}
Int count(cT& x)const{ return count(0,size()-1,x); }
Int count(Int l,Int r,cT& x)const{ return Int(std::count(it(l),it(r+1),x)); }
template<class Pr> Int countif(Pr pr)const{ return countif(0,size()-1,pr); }
template<class Pr> Int countif(Int l,Int r,Pr pr)const{ return Int(count_if(it(l),it(r+1),pr)); }
Int find(cT& x)const{ return find(0,size()-1,x); }
Int find(Int l,Int r,cT& x)const{ return Int(std::find(it(l),it(r+1),x)-begin()); }
Int rfind(cT& x)const{ return rfind(0,size()-1,x); }
Int rfind(Int l,Int r,cT& x)const{
for (int i=r;i>=l;--i) if ((*this)[i]==x) return i;
return l-1;
}
template<class Pr> Int findif(Pr pr)const{ return findif(0,size()-1,pr); }
template<class Pr> Int findif(Int l,Int r,Pr pr)const{ return Int(find_if(it(l),it(r+1),pr)-begin()); }
Vector<Int> findall(cT& x)const{ return findall(0,size()-1,x); }
Vector<Int> findall(Int l,Int r,cT& x)const{ return findallif(l,r,[&](cT& y){return y==x;}); }
template<class Pr> Vector<Int> findallif(Pr pr)const{ return findallif(0,size()-1,pr); }
template<class Pr> Vector<Int> findallif(Int l,Int r,Pr pr)const{
Vector<Int> ret;
for(Int i=l;i<=r;++i) if(pr((*this)[i])) ret.push_back(i);
return ret;
}
Int flooridx(cT& x)const{ return Int(upper_bound(begin(),end(),x)-begin()-1); }
Int ceilidx(cT& x)const{ return Int(lower_bound(begin(),end(),x)-begin()); }
Int leftnmof(cT& x)const{ return flooridx(x)+1; }
Int rightnmof(cT& x)const{ return size()-ceilidx(x); }
bool contains(cT& x)const{ Int i=flooridx(x); return i>=0 && (*this)[i]==x; }
template<class Pr> Int flooridx(cT& x,Pr pr)const{ return Int(upper_bound(begin(),end(),x,pr)-begin()-1); }
template<class Pr> Int ceilidx(cT& x,Pr pr)const{ return Int(lower_bound(begin(),end(),x,pr)-begin()); }
template<class Pr> Int leftnmof(cT& x,Pr pr)const{ return flooridx(x,pr)+1; }
template<class Pr> Int rightnmof(cT& x,Pr pr)const{ return size()-ceilidx(x,pr); }
template<class Pr> bool contains(cT& x,Pr pr)const{ Int i=flooridx(x,pr); return i>=0 && (*this)[i]==x; }
template<class S> using VV = Vector<Vector<S>>; template<class S> using sVV = vector<vector<S>>;
template<class S> using VVV = Vector<VV<S>>; template<class S> using sVVV = vector<sVV<S>>;
template<class S> using VVVV = Vector<VVV<S>>; template<class S> using sVVVV = vector<sVVV<S>>;
template<class S> using VVVVV = Vector<VVVV<S>>; template<class S> using sVVVVV = vector<sVVVV<S>>;
auto tostd()const{ return tov(*this); }
template <class S> static vector<S> tov(const Vector<S>&v){ return v; }
template <class S> static sVV<S> tov(const VV<S> &v){ sVV<S> ret; for(auto&& e:v) ret.push_back(e); return ret; }
template <class S> static sVVV<S> tov(const VVV<S> &v){ sVVV<S> ret; for(auto&& e:v) ret.push_back(e.tostd()); return ret; }
template <class S> static sVVVV<S> tov(const VVVV<S> &v){ sVVVV<S> ret; for(auto&& e:v) ret.push_back(e.tostd()); return ret; }
template <class S> static sVVVVV<S> tov(const VVVVV<S> &v){ sVVVVV<S> ret; for(auto&& e:v) ret.push_back(e.tostd()); return ret; }
};
#if 0
#define MODLL (1000000007LL)
#else
#define MODLL (998244353LL)
#endif
using mll = mll_<MODLL>;
//using mll = fraction;
namespace atcoder {
//======== from internal_type_traits.hpp
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T,__int128_t>::value ||
std::is_same<T,__int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T,__uint128_t>::value ||
std::is_same<T,unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
} // namespace internal
//======== from internal_bit.hpp
namespace internal {
using std::bit_ceil;
inline int countr_zero(unsigned int n) {
#ifdef _MSC_VER
unsigned long index;
_BitScanForward(&index,n);
return index;
#else
return __builtin_ctz(n);
#endif
}
constexpr int countr_zero_constexpr(unsigned int n) {
int x = 0;
while (!(n & (1 << x))) x++;
return x;
}
} // namespace internal
//======== from internal_math.hpp
namespace internal {
constexpr long long safe_mod(long long x,long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
constexpr long long pow_mod_constexpr(long long x,long long n,int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x,m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
long long t = d;
long long y = pow_mod_constexpr(a,t,n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
constexpr std::pair<long long,long long> inv_gcd(long long a,long long b) {
a = safe_mod(a,b);
if (a == 0) return {b, 0};
long long s = b,t = a;
long long m0 = 0,m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u;
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
if (m0 < 0) m0 += b / s;
return {s, m0};
}
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g,(m - 1) / divs[i],m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
} // namespace internal
//======== from modint.hpp
namespace internal {
struct modint_base {};
struct static_modint_base: modint_base {};
} // namespace internal
template <int m,std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint: internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint(): _v(0) {}
template <class T,internal::is_signed_int_t<T>* = nullptr>
static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T,internal::is_unsigned_int_t<T>* = nullptr>
static_modint(T v) {
_v = (unsigned int)(v % umod());
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this,r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
}
else {
auto eg = internal::inv_gcd(_v,m);
assert(eg.first == 1);
return eg.second;
}
}
friend mint operator+(const mint& lhs,const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs,const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs,const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs,const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs,const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs,const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base,T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
} // namespace internal
//======== from convoution.hpp
namespace internal {
template <class mint,
int g = internal::primitive_root<mint::mod()>,
internal::is_static_modint_t<mint>* = nullptr>
struct fft_info {
static constexpr int rank2 = countr_zero_constexpr(mint::mod() - 1);
std::array<mint,rank2 + 1> root; // root[i]^(2^i) == 1
std::array<mint,rank2 + 1> iroot; // root[i] * iroot[i] == 1
std::array<mint,std::max(0,rank2 - 2 + 1)> rate2;
std::array<mint,std::max(0,rank2 - 2 + 1)> irate2;
std::array<mint,std::max(0,rank2 - 3 + 1)> rate3;
std::array<mint,std::max(0,rank2 - 3 + 1)> irate3;
fft_info() {
root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
iroot[rank2] = root[rank2].inv();
for (int i = rank2 - 1; i >= 0; i--) {
root[i] = root[i + 1] * root[i + 1];
iroot[i] = iroot[i + 1] * iroot[i + 1];
}
{
mint prod = 1,iprod = 1;
for (int i = 0; i <= rank2 - 2; i++) {
rate2[i] = root[i + 2] * prod;
irate2[i] = iroot[i + 2] * iprod;
prod *= iroot[i + 2];
iprod *= root[i + 2];
}
}
{
mint prod = 1,iprod = 1;
for (int i = 0; i <= rank2 - 3; i++) {
rate3[i] = root[i + 3] * prod;
irate3[i] = iroot[i + 3] * iprod;
prod *= iroot[i + 3];
iprod *= root[i + 3];
}
}
}
};
template <class mint,internal::is_static_modint_t<mint>* = nullptr>
void butterfly(std::vector<mint>& a) {
int n = int(a.size());
int h = internal::countr_zero((unsigned int)n);
static const fft_info<mint> info;
int len = 0; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
while (len < h) {
if (h - len == 1) {
int p = 1 << (h - len - 1);
mint rot = 1;
for (int s = 0; s < (1 << len); s++) {
int offset = s << (h - len);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p] * rot;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
if (s + 1 != (1 << len))
rot *= info.rate2[countr_zero(~(unsigned int)(s))];
}
len++;
}
else {
// 4-base
int p = 1 << (h - len - 2);
mint rot = 1,imag = info.root[2];
for (int s = 0; s < (1 << len); s++) {
mint rot2 = rot * rot;
mint rot3 = rot2 * rot;
int offset = s << (h - len);
for (int i = 0; i < p; i++) {
auto mod2 = 1ULL * mint::mod() * mint::mod();
auto a0 = 1ULL * a[i + offset].val();
auto a1 = 1ULL * a[i + offset + p].val() * rot.val();
auto a2 = 1ULL * a[i + offset + 2 * p].val() * rot2.val();
auto a3 = 1ULL * a[i + offset + 3 * p].val() * rot3.val();
auto a1na3imag =
1ULL * mint(a1 + mod2 - a3).val() * imag.val();
auto na2 = mod2 - a2;
a[i + offset] = a0 + a2 + a1 + a3;
a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
a[i + offset + 2 * p] = a0 + na2 + a1na3imag;
a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
}
if (s + 1 != (1 << len))
rot *= info.rate3[countr_zero(~(unsigned int)(s))];
}
len += 2;
}
}
}
template <class mint,internal::is_static_modint_t<mint>* = nullptr>
void butterfly_inv(std::vector<mint>& a) {
int n = int(a.size());
int h = internal::countr_zero((unsigned int)n);
static const fft_info<mint> info;
int len = h; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
while (len) {
if (len == 1) {
int p = 1 << (h - len);
mint irot = 1;
for (int s = 0; s < (1 << (len - 1)); s++) {
int offset = s << (h - len + 1);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p];
a[i + offset] = l + r;
a[i + offset + p] =
(unsigned long long)(mint::mod() + l.val() - r.val()) *
irot.val();
;
}
if (s + 1 != (1 << (len - 1)))
irot *= info.irate2[countr_zero(~(unsigned int)(s))];
}
len--;
}
else {
// 4-base
int p = 1 << (h - len);
mint irot = 1,iimag = info.iroot[2];
for (int s = 0; s < (1 << (len - 2)); s++) {
mint irot2 = irot * irot;
mint irot3 = irot2 * irot;
int offset = s << (h - len + 2);
for (int i = 0; i < p; i++) {
auto a0 = 1ULL * a[i + offset + 0 * p].val();
auto a1 = 1ULL * a[i + offset + 1 * p].val();
auto a2 = 1ULL * a[i + offset + 2 * p].val();
auto a3 = 1ULL * a[i + offset + 3 * p].val();
auto a2na3iimag =
1ULL *
mint((mint::mod() + a2 - a3) * iimag.val()).val();
a[i + offset] = a0 + a1 + a2 + a3;
a[i + offset + 1 * p] =
(a0 + (mint::mod() - a1) + a2na3iimag) * irot.val();
a[i + offset + 2 * p] =
(a0 + a1 + (mint::mod() - a2) + (mint::mod() - a3)) *
irot2.val();
a[i + offset + 3 * p] =
(a0 + (mint::mod() - a1) + (mint::mod() - a2na3iimag)) *
irot3.val();
}
if (s + 1 != (1 << (len - 2)))
irot *= info.irate3[countr_zero(~(unsigned int)(s))];
}
len -= 2;
}
}
}
template <class mint,internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution_naive(const std::vector<mint>& a,
const std::vector<mint>& b) {
int n = int(a.size()),m = int(b.size());
std::vector<mint> ans(n + m - 1);
if (n < m) {
for (int j = 0; j < m; j++) {
for (int i = 0; i < n; i++) {
ans[i + j] += a[i] * b[j];
}
}
}
else {
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
ans[i + j] += a[i] * b[j];
}
}
}
return ans;
}
template <class mint,internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution_fft(std::vector<mint> a,std::vector<mint> b) {
int n = int(a.size()),m = int(b.size());
int z = (int)internal::bit_ceil((unsigned int)(n + m - 1));
a.resize(z);
internal::butterfly(a);
b.resize(z);
internal::butterfly(b);
for (int i = 0; i < z; i++) {
a[i] *= b[i];
}
internal::butterfly_inv(a);
a.resize(n + m - 1);
mint iz = mint(z).inv();
for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
return a;
}
} // namespace internal
template <class mint,internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(std::vector<mint>&& a,std::vector<mint>&& b) {
int n = int(a.size()),m = int(b.size());
if (!n || !m) return {};
int z = (int)internal::bit_ceil((unsigned int)(n + m - 1));
assert((mint::mod() - 1) % z == 0);
if (std::min(n,m) <= 60) return convolution_naive(a,b);
return internal::convolution_fft(a,b);
}
template <unsigned int mod = 998244353,
class T,
std::enable_if_t<internal::is_integral<T>::value>* = nullptr>
std::vector<T> convolution(const std::vector<T>& a,const std::vector<T>& b) {
int n = int(a.size()),m = int(b.size());
if (!n || !m) return {};
using mint = static_modint<mod>;
int z = (int)internal::bit_ceil((unsigned int)(n + m - 1));
assert((mint::mod() - 1) % z == 0);
std::vector<mint> a2(n),b2(m);
for (int i = 0; i < n; i++) {
a2[i] = mint(a[i]);
}
for (int i = 0; i < m; i++) {
b2[i] = mint(b[i]);
}
auto c2 = convolution(std::move(a2),std::move(b2));
std::vector<T> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
c[i] = c2[i].val();
}
return c;
}
} // namespace atcoder
using atcoder::convolution;
namespace fpsspace{
using Int = long long;
using ll = long long;
constexpr int inf=int(1e9);
/********* utility関数 *********/
template<class T> T POW(T a,ll n){//a^n n負も可
if (n<0) a=T(1)/a,n=-n;
T r=1;
for (; n>0; n>>=1,a*=a) if (n&1)r*=a;
return r;
}
ll LimitMul(ll a,ll b,ll l=ll(9e18)){//min(a*b,l) a,b≧0
return (b==0 || a<=l/b) ? a*b : l;
}
/*---- 1/i列挙 i=1~d ----*/
template<int Kind> struct Wrap{};//オーバロード解決用にKindを型に変換
template<class T,int Kind,class=enable_if_t<Kind==1 || Kind==2>>
std::vector<T> &Invs(int d,Wrap<Kind>){//Kind=1 or 2(modint系)の時
static std::vector<T> invs(2,T(1));
int MOD = T::mod();
for (int i=(int)invs.size(); i<=d; ++i) invs.push_back(-invs[MOD%i]*T(MOD/i));
return invs;
}
template<class T> std::vector<T> &Invs(int d,Wrap<0>){//その他の時
static std::vector<T> invs(1);
for (int i=(int)invs.size(); i<=d; ++i) invs.push_back(T(1)/i);
return invs;
}
template<class T> std::vector<T> &Fact(int d){// i!列挙 i=0~d
static std::vector<T> fact(1,T(1));
for (int i=(int)fact.size(); i<=d; ++i) fact.push_back(fact.back()*T(i));
return fact;
}
template<class T,int Kind> std::vector<T> &FInv(int d){// 1/i!列挙 i=0~d
static std::vector<T> finv(1,T(1));
const std::vector<T> &invs=Invs<T>(d,Wrap<Kind>{});
for (int i=(int)finv.size(); i<=d; ++i) finv.push_back(finv.back()*invs[i]);
return finv;
}
// Berlekamp Massey法 2L-1次までのA(x)からA=P/QのQをL次で復元 Kind=1,2のみ
template <class T> std::vector<T> BerlekampMassey(const std::vector<T> &a){
std::vector<T> C={1},B={1};//C:求める数列、B:1つ前のCの状態を保存
int m=1; //ポインタ？っぽいもの
T b=T(1); //前回のdの値
auto C_update=[](std::vector<T> &C,T d,T b,std::vector<T> &B,int m){
T d_b=d/b;
int M=(int)B.size();
if ((int)C.size()<M+m) C.resize(M+m);
for (int i=0; i<M; ++i) C[i+m]-=d_b*B[i];
};
for (int n=0; n<(int)a.size(); ++n){
T d=T(0);
for (int k=0; k<(int)C.size(); ++k) d+=C[k]*a[n-k]; //dを計算
if (d!=T(0)){//①d=0なら、現在のCでAnを求める漸化式は成り立っている,そうでないなら調整
if (2*((int)C.size()-1) <= n){
std::vector<T> tmp=C;
C_update(C,d,b,B,m); //C -= d/b * (Bをmだけ右シフトしたもの)
B.swap(tmp); b=d; m=0;
}
else C_update(C,d,b,B,m); //C -= d/b * (Bをmだけ右シフトしたもの)
}
m++;
}
return C;
}
template<class FPS,class SPFPS,class T=typename FPS::value_type,class S>
FPS de_sparse( //a*F'=b*Fを満たすF
const SPFPS &a_,const SPFPS &b_,S f0,Int dmx_,const std::vector<T> &invs_=std::vector<T>())
{
assert(a_.lowdeg()<=b_.lowdeg());
int dmx=(int)dmx_;
const std::vector<T> &invs = invs_.size() ? invs_ : Invs<T>(dmx,Wrap<FPS::kind>{});
SPFPS a=a_.shift(-a_.lowdeg()),b=b_.shift(-a_.lowdeg());
T a0inv=T(1)/a.co(0);
a*=a0inv,b*=a0inv;
a.erase(a.begin());
FPS f({T(f0)},dmx);
for (int d=1; d<=dmx; ++d){
for (auto [bb,i]:b){
if (d-1-i>=0) f.at(d)+=bb*f[d-1-i];
}
for (auto [aa,i]:a){
if (d-i>=0) f.at(d)-=aa*f[d-i]*(d-i);
}
f.at(d)*=invs[d];
}
return f;
}
/********* 疎FPSクラス *********/
template<class T> struct sparseFps: std::vector<pair<T,Int>>{
using std::vector<pair<T,Int>>::vector; //親クラスのコンストラクタの隠蔽を回避
sparseFps &Norm(){//d昇順、同一dのco加算、co=0を削除
sort(this->begin(),this->end(),
[](const auto &x,const auto &y){return x.second<y.second; });
int j=-1;
for (int i=0; i<this->size(); ++i){
if (j>=0 && deg(j)==deg(i)){
co(j)+=co(i);
}
else{
if (!(j>=0 && co(j)==T(0))) ++j;
(*this)[j]=(*this)[i];
}
}
if (j>=0 && co(j)==T(0)) --j;
this->resize(j+1);
return *this;
}
/*---- I/F ----*/
template<class S,class R>
void set(S co,R deg){ this->emplace_back(T(co),Int(deg)); }
Int deg()const{ return this->empty() ? -1 : this->back().second; }//最高次数
T co(Int i)const{ return (*this)[i].first; }//(*this)[i]の係数
T &co(Int i) { return (*this)[i].first; }
Int deg(Int i)const{ return (*this)[i].second; }//(*this)[i]の次数
Int °(Int i) { return (*this)[i].second; }
Int lowdeg()const{ return this->empty() ? inf : this->front().second; }
sparseFps &operator+=(const sparseFps &sg){
this->insert(this->end(),sg.begin(),sg.end());
return Norm();
}
sparseFps operator+(const sparseFps &sg)const{ return sparseFps(*this)+=sg; }
sparseFps &operator*=(T b){ for (auto&&[c,_]:*this) c*=b; return *this; }
sparseFps operator*(T b)const{ return sparseFps(*this)*=b; }
sparseFps &operator*=(const sparseFps &sg){ return *this=*this*sg; }
sparseFps operator*(const sparseFps &sg)const{
sparseFps ret;
for (auto&&[cf,df]:*this) for (auto&&[cg,dg]:sg) ret.set(cf*cg,df+dg);
return ret.Norm();
}
sparseFps shift(Int k)const{ // *x^k
sparseFps ret;
for (auto&&[co,d]:*this) if (d+k>=0) ret.set(co,d+k);
return ret;
}
sparseFps diff()const{
sparseFps ret;
for (auto&&[co,d]:*this) if (d>0) ret.set(co*d,d-1);
return ret;
}
template<class FPS> FPS exp(Int dmx)const{
assert(lowdeg()!=0); //定数項=0必須
return de_sparse<FPS>(sparseFps{{1,0},},diff(),1,dmx);
}
template<class FPS>
FPS pow(ll k,Int dmx,const std::vector<T> &invs_=std::vector<T>())const{
assert(!(k<0 && lowdeg()>0));//k負なら定数項必須
if (k==0) return FPS({1},dmx);
//-- 計算後最高次数d：k<0ならdmx、k>0ならmin(dmx,deg()*k)まで
int d = (k<0 || LimitMul(deg(),k)>(ll)dmx) ? int(dmx) : int(deg()*k);
//-- invs[i]=1/iをi=1~dまで計算(計算済み分は再利用、足りない分だけ計算)
const std::vector<T> &invs = invs_.size() ? invs_ : Invs<T>(d,Wrap<FPS::kind>{});
//-- 最低次数関連処理
int s=(int)lowdeg();//計算前最低次数
if (k>0 && LimitMul(s,k)>(ll)dmx) return FPS(dmx);//計算後all0の時
//-- 漸化式で計算
T f0inv=T(1)/co(0);
FPS g({POW(co(0),k)},dmx);
for (int i=1; i<=d-s*k; ++i){ //k負の時必ずs=0なのでOK
for (int j=1; j<(int)this->size(); ++j){
auto [c,dg]=(*this)[j];
int b=int(dg)-s;
if (i-b<0)break;
g.at(i)+=c*g.at(i-b)*(T(k)*b-i+b);
}
g.at(i)*=f0inv*invs[i];
}
return g.shift(Int(s*k));
}
};
/********* FPSクラス *********/
template<
class T, //係数の型
int Kind //係数の種類 0:その他、1:NTTfriendly mod、2:任意mod
>
struct Fps: std::vector<T>{
static_assert(0<=Kind && Kind<=3);
static constexpr int kind=Kind;
int dMx=int(1e6); //次数上限(x^dMxより上は保持しない)
using vT = std::vector<T>;
/*---- utility ----*/
int isize()const{ return (int)std::vector<T>::size(); }
int NormSize()const{//leading zeroを除いたサイズ const用
int sv=isize();
while (sv>0 && (*this)[sv-1]==T(0)) --sv;
return sv;
}
int Deg()const{ return NormSize()-1; } //最高次数 const用
Fps &Cut(){ return cut(dMx); }
Fps &ZeroExtend(){
int anm=max(0,dMx-isize()+1);
vT::insert(vT::end(),anm,T(0));
return *this;
}
int MinD(const Fps &g)const{ return min(dMx,g.dMx); }
void MergeD(const Fps &g){ dMx=MinD(g); Cut(); }
template <int Sign> Fps &Add(const Fps &g){
MergeD(g);
for (int i=min(dMx,g.Deg()); i>=0; --i) at(i)+=Sign*g[i];
return *this;
}
Fps ProdSparse(const sparseFps<T> &g,int d)const{//f*疎g mod x^(d+1)
Fps ret(d);
for (auto&&[co,dg]:g) for (int i=0; i<(int)isize(); ++i){
if (dg+i>d) break;
ret.at(dg+i)+=co*(*this)[i];
}
return ret;
}
Fps InvSparse(const sparseFps<T> &g,int d)const{//f/疎g mod x^(d+1) g0≠0
assert(!g.empty() && g.deg(0)==0 && g.co(0)!=0);
//-- g定数項を1にする
T c0inv=T(1)/g.co(0);
Fps ret=((*this)*c0inv).setdmx(d);
if (g.size()==1u) return ret;
sparseFps<T> gg=g*c0inv;
//-- 配るDP計算
for (int i=0; i+(int)gg.deg(1)<=d; ++i){
for (int j=1; j<(int)gg.size(); ++j){
auto [co,dg]=gg[j];
int ii=i+(int)dg;
if (d<ii)break;
ret.at(ii)-=ret.at(i)*co;
}
}
return ret;
}
Fps &LogSparse( //f+=log(疎g^k),g=1+ax^b
const sparseFps<T> &g,ll k,const std::vector<T> &invs_=std::vector<T>())
{
assert(g.size()==2U && g.co(0)==T(1) && g.deg(0)==0);
const std::vector<T> &invs = invs_.size() ? invs_ : Invs<T>(dMx,Wrap<Kind>{});
int b=(int)g.deg(1);
T c=g.co(1)*k;
for (int i=1; i*b<=dMx; ++i,c*=-g.co(1)) at(i*b)+=c*invs[i];
return *this;
}
/*---- コンストラクタ ----*/
explicit Fps(Int dmx=int(1e6)): dMx(int(dmx)){}
Fps(initializer_list<T> i,Int dmx=int(1e6)):
vT(i.begin(),i.end()),dMx(int(dmx)){
Cut();
}
template <class It,class=typename iterator_traits<It>::iterator_category>
Fps(It l,It r,Int dmx=int(1e6)) : vT(l,r),dMx(int(dmx)){ Cut(); }
Fps(std::vector<T> &&v,Int dmx=int(1e6)): vT(move(v)),dMx(int(dmx)){}
Fps(const sparseFps<T> &sf,Int dmx=int(1e6)):dMx(int(dmx)){ //疎f → f
for (auto&&[co,deg]:sf) if (deg<=dmx) at(deg)=co;
}
/*---- I/F ----*/
sparseFps<T> tosparse()const{ //f → 疎f
sparseFps<T> ret;
for (int i=0; i<isize(); ++i){
if ((*this)[i]!=T(0)) ret.set((*this)[i],i);
}
return ret;
}
Int size()const{ return (Int)std::vector<T>::size(); }
Int deg(){ fit(); return size()-1; }
Int lowdeg()const{
for (int i=0; i<isize(); ++i){
if ((*this)[i]!=T(0)) return i;
}
return inf;
}
Fps &setdmx(Int dmx){ dMx=(int)dmx; return Cut(); }
T at(Int i)const{ return size()<=i ? T(0) : (*this)[i]; }
T &at(Int i){
if (size()<=i) this->resize(i+1);
return (*this)[i];
}
Fps &fit(){
this->resize(NormSize());
return *this;
}
Fps &operator+=(const Fps &g){ return Add<1>(g); }
Fps &operator-=(const Fps &g){ return Add<-1>(g); }
Fps &operator*=(const Fps &g){ return *this=*this*g; }
Fps &operator/=(const Fps &g){ return *this=*this/g; }
Fps &operator*=(const sparseFps<T> &g){ return *this=*this*g; }
Fps &operator/=(const sparseFps<T> &g){ return *this=*this/g; }
Fps &operator+=(T c){ at(0)+=c; return *this; }
Fps &operator-=(T c){ at(0)-=c; return *this; }
Fps &operator*=(T c){ for (auto&& e: *this) e*=c; return *this; }
Fps &operator/=(T c){ return (*this)*=T(1)/c; }
Fps operator+(const Fps &g)const{ return Fps(*this)+=g; }
Fps operator-(const Fps &g)const{ return Fps(*this)-=g; }
Fps operator*(const Fps &g)const{ return Prod(*this,g,MinD(g)); }
Fps operator/(const Fps &g)const{ return InvSparse(g.tosparse(),MinD(g)); }
Fps operator*(const sparseFps<T> &g)const{ return ProdSparse(g,dMx); }
Fps operator/(const sparseFps<T> &g)const{ return InvSparse(g,dMx); }
Fps operator+(T c)const{ return Fps(*this)+=c; }
Fps operator-(T c)const{ return Fps(*this)-=c; }
Fps operator*(T c)const{ return Fps(*this)*=c; }
Fps operator/(T c)const{ return Fps(*this)/=c; }
Fps operator-()const{ return Fps(*this)*=T(-1); }
friend Fps operator+(T c,const Fps &f){ return f+c; }
friend Fps operator-(T c,const Fps &f){ return -f+c; }
friend Fps operator*(T c,const Fps &f){ return f*c; }
T prod1(const Fps &g,Int k_)const{ //[x^k]f*g
int df=Deg(),dg=g.Deg(),k=(int)k_;
if (MinD(g)<k) return T(0);
T ret=T(0);
for (int i=max(0,k-dg),j=k-i; i<=df&&j>=0; ++i,--j) ret+=(*this)[i]*g[j];
return ret;
}
T bostanmori(const Fps &g,ll k)const{ //[x^k]f/g
assert(g.at(0)!=0);
Fps P=Fps(*this).setdmx(inf),Q=Fps(g).setdmx(inf);
for (; k>0; k>>=1){
Fps Q1=Q;
for (int i=1; i<Q1.isize(); i+=2) Q1[i]*=-1; //Q1=(Qの奇数項を正負反転)
Fps PQ=P*Q1,QQ=Q*Q1;
P.clear(),Q.clear();
for (int i=k&1; i<PQ.isize(); i+=2) P.push_back(PQ[i]);//P=(PQの奇or偶数項)
for (int i=0; i<QQ.isize(); i+=2) Q.push_back(QQ[i]);//Q=(QQの偶数項)
}
return P.at(0)/Q[0];
}
Fps berlekamp_massey(Int d)const{ //f=P/QのQを得る x^d(d奇数)までの係数から推定
assert(d%2==1);
std::vector<T> f;
for (int i=0; i<=d; ++i) f.push_back(at(i));
std::vector<T> Q=BerlekampMassey(f);
Int dmx=Int(Q.size()-1);
return Fps(move(Q),dmx);
}
T nthterm(Int d,ll k)const{ //[x^k]f 線形漸化式を仮定しx^d(d奇数)までから推定
Fps Q=berlekamp_massey(d);
Fps P=Prod(*this,Q,Q.dMx-1).fit();
return P.bostanmori(Q,k);
}
Fps &estimate(Int d,Int dmx=-1){ //dmx次まで推定 線形漸化式を仮定しx^d(d奇数)までから推定
if (dmx==-1) dmx=dMx;
Fps Q=berlekamp_massey(d);
Fps P=Prod(*this,Q,Q.dMx-1).fit().setdmx(dmx);
return *this=(Q.setdmx(dmx).inv()*P).ZeroExtend();
}
Fps &cut(Int d){ //x^dまでにする
if (d+1<size()) vT::resize(size_t(d+1));
return *this;
}
Fps &mod(Int n){ return cut(n-1); } //mod x^n
[[nodiscard]] Fps shift(Int k_)const{ // *x^k
Fps ret(dMx);
const int k=(int)k_,m=min(isize()+k,dMx+1); //変換後長さ
if (m<=0 || dMx<k) return ret; //空になる時
for (int i=m-1-k; i>=max(0,-k); --i) ret.at(i+k)=(*this)[i];
return ret;
}
T eval(T x)const{ //f(c)
T ret=T(0);
for (int i=isize()-1; i>=0; --i) ret*=x,ret+=(*this)[i];
return ret;
}
Fps diff()const{ //微分
Fps ret(dMx-1);
for (int i=Deg(); i>=1; --i) ret.at(i-1)=(*this)[i]*i;
return ret;
}
Fps integ()const{ //積分
Fps ret(dMx+1);
for (int i=min(Deg(),dMx); i>=0; --i) ret.at(i+1)=(*this)[i]/(i+1);
return ret;
}
T integrange(T l,T r)const{ //定積分 ∫_l^r f dx
Fps itg=integ();
return itg.eval(r)-itg.eval(l);
}
Fps inv()const{
assert(at(0)!=0);//定数項≠0
Fps g{T(1)/at(0)};
for (int i=1; i<dMx+1; i*=2){//i:項数
g.setdmx(min(i*2-1,dMx));
g = g+g-g*g*(*this);
}
return g;
}
Fps log()const{ //log f
assert(at(0)==T(1));//定数項=1
return (diff()*inv()).integ();
}
Fps exp()const{ //exp f
assert(at(0)==T(0));//定数項=0
Fps g{1};
for (int i=1; i<dMx+1; i*=2){//i:項数
g.setdmx(min(i*2-1,dMx));
g = g*(T(1)-g.log()+(*this));
}
return g;
}
Fps pow(ll k)const{ //f^k k<0は未対応
if (k==0) return Fps({1},dMx);
if (k==1) return *this;
int z=(int)lowdeg();
if (z==inf || z>int(dMx/k)) return Fps(dMx);//f(x)=0か結果=0の時
int m=int(dMx+1-z*k); //最終は先頭にゼロがz*k個→計算はdMx+1-z*k項でok
Fps g=shift(-z).setdmx(m-1)/at(z); //定数項1にする変換
Fps gk=(g.log()*k).exp(); //g^k
Fps ret=(gk*POW(at(z),k)).setdmx(dMx).shift(Int(z*k)); //変換を戻す
return ret;
}
Fps powdbl(ll k)const{ //f^k
Fps ret({1},dMx),g=*this;
for (; k>0; k>>=1,g*=g) if (k&1)ret*=g;
return ret;
}
Fps powsparse(ll k,const std::vector<T> &invs=std::vector<T>())const{ //疎f^k
return tosparse().template pow<Fps>(k,dMx,invs);
}
pair<Fps,Fps> div(const Fps &g)const{ //多項式f/g,f%g
const Fps &f=*this;
int na=f.NormSize(),nb=g.NormSize();
assert(nb>0);
int n=na-nb+1;//商の項数
if (n<=0) return {Fps(dMx),f};
int nu=f.isize(),nv=g.isize();
Fps aR(f.rbegin()+nu-na,f.rbegin()+min(nu-na+n,nu),n-1);
Fps bR(g.rbegin()+nv-nb,g.rbegin()+min(nv-nb+n,nv),n-1);
Fps qR=bR.inv()*aR;
qR.resize(n);
reverse(qR.begin(),qR.end());
qR.fit().setdmx(dMx);
Fps r=(f-Prod(qR,g,dMx)).fit();
return {move(qR),move(r)};
}
};
/********* 積をNTTmod畳み込み、任意mod畳み込み、畳み込み不使用から選択 *********/
template<class T> //f*g mod x^(d+1) 畳み込み不使用
Fps<T,0> Prod(const Fps<T,0> &f,const Fps<T,0> &g,int d){
return f.ProdSparse(g.tosparse(),d);
}
template<class T> //f*g mod x^(d+1) NTTmod畳み込み
Fps<T,1> Prod(const Fps<T,1> &f,const Fps<T,1> &g,int d){
int nf=min(d+1,f.NormSize()),ng=min(d+1,g.NormSize());
std::vector<ll> ff,gg;
ff.reserve(nf),gg.reserve(ng);
for (int i=0; i<nf; ++i) ff.push_back(f[i].val());
for (int i=0; i<ng; ++i) gg.push_back(g[i].val());
std::vector<ll> hh=convolution<T::mod()>(ff,gg);
if ((int)hh.size()>d+1) hh.resize(d+1);
return Fps<T,1>(hh.begin(),hh.end(),d);
}
template<class T> //f*g mod x^(d+1) 任意mod畳み込み
Fps<T,2> Prod(const Fps<T,2> &f,const Fps<T,2> &g,int d){
static constexpr int m0 = 167772161; //m0<m1<m2必須
static constexpr int m1 = 469762049;
static constexpr int m2 = 754974721;
static constexpr int m01 = 104391568;// 1/m0(mod m1)
static constexpr int m12 = 399692502;// 1/m1(mod m2)
static constexpr int m012 = 190329765;// 1/m0m1(mod m2)
static int m0m1 = ll(m0)*m1 % T::mod();
int nf=min(d+1,f.NormSize()),ng=min(d+1,g.NormSize());
std::vector<ll> ff,gg;
ff.reserve(nf),gg.reserve(ng);
for (int i=0; i<nf; ++i) ff.push_back(f[i].val());
for (int i=0; i<ng; ++i) gg.push_back(g[i].val());
std::vector<ll> h0=convolution<m0>(ff,gg);
std::vector<ll> h1=convolution<m1>(ff,gg);
std::vector<ll> h2=convolution<m2>(ff,gg);
Fps<T,2> ret(d);
int nn=min(d+1,(int)h0.size());
ret.reserve(nn);
for (int i=0; i<nn; ++i){
ll r0=h0[i],r1=h1[i],r2=h2[i];
ll s0=r0;
ll s1=(r1+m1-s0)*m01%m1; //s0<m1のため正になる
ll s2=((r2+m2-s0)*m012+(m2-s1)*m12)%m2; //s0,s1<m2のため正になる
ret.emplace_back(s0+s1*m0+s2*m0m1);
}
return ret;
}
#if 0 //f*g mod x^(d+1) FFT畳み込み 使用時はFFTライブラリを貼った上で1にする
template<class T>
Fps<T,3> Prod(const Fps<T,3> &f,const Fps<T,3> &g,int d){
std::vector<T> ff(f.begin(),f.end()),gg(g.begin(),g.end());
std::vector<T> hh = ArbitraryModConvolution::CooleyTukey::multiply(ff,gg);
if ((int)hh.size()>d+1) hh.resize(d+1);
return Fps<T,3>(hh.begin(),hh.end(),d);
}
#endif
/********* I/F関数 *********/
template<class FPS,class T=typename FPS::value_type> FPS prodtwopow(//f^k*g^m
sparseFps<T> f_,ll k,sparseFps<T> g_,ll m,Int dmx,
const std::vector<T> &invs=std::vector<T>())
{
if (k==0) f_={{T(1),0},},k=1;
if (m==0) g_={{T(1),0},},m=1;
Int fz=f_.lowdeg(),gz=g_.lowdeg();
assert(!(fz==Int(1e9) && k<0) && !(gz==Int(1e9) && m<0));//f=0かつk>0はNG
if (fz==Int(1e9) || gz==Int(1e9)) return FPS(dmx);//f=0なら結果=0
ll z=fz*k+gz*m; //k,m巨大時のoverflowは未対応とする
assert(z>=0);
if (ll(dmx)<z) return FPS(dmx);
sparseFps<T> f=f_.shift(-fz),g=g_.shift(-gz);
Int dmx2=dmx-z;
sparseFps<T> a=f*g,b=f.diff()*g*k+f*g.diff()*m;
T h0=POW(f.co(0),k)*POW(g.co(0),m);
FPS h=de_sparse<FPS>(a,b,h0,dmx2,invs);
return h.setdmx(dmx).shift(Int(z));
}
}//namespace fpsspace
#if 0
using fpsT = dd;
using fps = fpsspace::Fps<fpsT,0>; //0:畳み込み不使用
#elif 1
using fpsT = mll;
using fps = fpsspace::Fps<fpsT,1>; //1:NTTfriendly mod
#elif 0
using fpsT = atcoder::modint;
using fps = fpsspace::Fps<fpsT,2>; //2:任意mod
#elif 0
using fpsT = dd;
using fps = fpsspace::Fps<fpsT,3>; //3:FFT
#endif
using spfps = fpsspace::sparseFps<fpsT>;
/*
- 各種演算の結果の次数上限は、一部例外を除きf,gの小さい方となる。
- 疎FPSクラスは次数昇順、係数≠0必須
- -------- コンストラクタ --------
fps f; //f(x)=0 次数上限1e6
fps f(d); // 〃 〃 d
fps f{2,3,4,}; //f(x)=2+3x+4x^2 次数上限1e6
fps f({2,3,4,},d); // 〃 〃 d
fps f(all(v)); //vll等のvをコピー 次数上限1e6
fps f(all(v),d); // 〃 〃 d
- -------- コンストラクタ疎版 -------- vector<pair>と同じ
spfps sf={{4,2},{-1,5}}; //f(x)=4x^2-x^5
sf.set(c,d); //c*x^dを末尾に追加
- -------- 演算子(fps同士) --------
f+=g f-=g f+g f-g -f 疎f+=疎g 疎f*=疎g 疎f+疎g 疎f*疎g
f*=g f*g //NTTmod,任意mod,愚直がテンプレートで切り替わる
f*=疎g f*疎g //愚直
f/=g f/=疎g f/g f/疎g //漸化式で愚直 g定数項≠0
- -------- 演算子(定数) --------
f+=c f-=c f*=c f/=c f+c f-c f*c f/c 疎f*=c 疎f*c
- -------- アクセス・操作 --------
f[i]=val; //直接操作
f.at(i)=val; //自動サイズ調整有
ll n=f.size(); //項数(次数+1) leading zero含む
ll d=f.deg(); //非0の最高次の次数 f(x)=0の時-1
ll d=f.lowdeg(); //非0の最低次の次数 f(x)=0の時1e9
f.setdmx(d); //次数上限をx^dにセット ＆ mod x^(d+1) d≧0
f.fit(); //最高次≠0になるよう縮める
fps f(sf); //疎f→f 変換
fps f(sf,d); //疎f→f 変換 次数上限d
spfps sf=f.tosparse(); //f→疎f 変換
- -------- 演算 --------
mll c=f.prod1(g,k); //[x^k]f*g
mll c=f.bostanmori(g,k);//[x^k]f/g g定数項≠0 k巨大(10^18)でもOK
f.cut(d); //x^dまでにする
f.mod(n); //mod x^n
fps g=f.shift(k); //f*x^k k負も可
spfps sg=sf.shift(k); //疎f*x^k k負も可
mll val=f.eval(c); //f(c)
fps g=f.diff(); //微分
fps g=f.integ(); //積分
mll val=f.integrange(l,r); //定積分 ∫_l^r f dx
fps g=f.inv(); //1/f 定数項≠0
fps g=f.log(); //log f 定数項=1
fps g=f.exp(); //exp f 定数項=0
fps g=sf.exp<fps>(d); //exp 疎f 定数項=0
fps g=f.pow(k); //f^k k負は未対応
fps g=f.powdbl(k); //f^k doubling版
fps g=sf.pow<fps>(k,d); //疎f^k 次数上限d k負も可(定数項≠0必須)
fps g=f.powsparse(k); //疎f^k k負も可(定数項≠0必須)
auto[h,r]=f.div(g); //多項式の除算・剰余 h=f/g,r=f%g 次数上限はfの方
fps Q=f.berlekamp_massey(d); //f=P/QのQを復元 x^d(d奇数)までから推定
//Qの次数≦(d+1)/2 QのdmxはQの次数になる
mll c=f.nthterm(d,k); //[x^k]f k~10^18も可 x^d(d奇数)までから推定
f.estimate(d); //x^d(d奇数)までを使用し次数上限まで推定
f.estimate(d,k); //x^d(d奇数)までを使用しk次まで推定
fps F=fpsspace::de_sparse<fps>(sf,sg,F0,d); //微分方程式 疎f*F'=疎g*F 次数上限d
fps h=fpsspace::prodtwopow<fps>(sf,k,sg,m,d); //疎f^k*疎g^m 次数上限d k,m負も可
*/
namespace SolvingSpace{
template<class T> using vector = Vector<T>;
using vll=vector< ll>; using vmll=vector< mll>; using vdd=vector< dd>;
using vvll=vector< vll>; using vvmll=vector< vmll>; using vvdd=vector< vdd>;
using vvvll=vector< vvll>; using vvvmll=vector< vvmll>; using vvvdd=vector< vvdd>;
using vvvvll=vector<vvvll>; using vvvvmll=vector<vvvmll>; using vvvvdd=vector<vvvdd>;
using vpll=vector< pll>; using vtll=vector< tll>; using vqll=vector< qll>;
using vvpll=vector< vpll>; using vvtll=vector< vtll>; using vvqll=vector< vqll>;
using vss=vector<string>;
template<class T> vector<T> cinv(ll nm){ return vector<T>(nm,[](ll i){ (void)i; return cin1<T>(); }); }
template<class T> vector<vector<T>> cinvv(ll H,ll W){ return vector<vector<T>>(H,[&](ll i){ (void)i; return cinv<T>(W); }); }
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void cin2solve()
{
auto [N,M,K,L]=cins<ll,ll,ll,ll>();
mll ans=0;
rep(v,L,M){
ll ji=K*M-v;
mll Q,P;
{
spfps sf={{1,0},{-1,v+1}};
fps f=sf.pow<fps>(N-1,ji); //疎f^k 次数上限d k負も可(定数項≠0必須)
spfps sg={{1,0},{-1,1}};
fps g=sg.pow<fps>(-N+1,ji); //疎f^k 次数上限d k負も可(定数項≠0必須)
fps h=f*g;
Q=h.at(ji);
}
{
spfps sf={{1,0},{-1,M+1}};
fps f=sf.pow<fps>(N-1,ji); //疎f^k 次数上限d k負も可(定数項≠0必須)
spfps sg={{1,0},{-1,1}};
fps g=sg.pow<fps>(-N+1,ji); //疎f^k 次数上限d k負も可(定数項≠0必須)
fps h=f*g;
P=h.at(ji);
}
ans+=P-Q;
}
cout << ans << '\n';
return;
}
}//SolvingSpace
//////////////////////////////////////////
int main(){
#if defined(RANDOM_TEST)
SolvingSpace::cin2solve();
SolvingSpace::generand();
#else
#if 1
//SolvingSpace::labo();'
SolvingSpace::cin2solve();
#else
ll t; cin >> t;
rep(i,0,t-1){
SolvingSpace::cin2solve();
}
#endif
#endif
cerr << timeget() <<"ms"<< '\n';
return 0;
}