結果
| 問題 |
No.3172 三角関数べき乗のフーリエ級数展開
|
| ユーザー |
 hamamu
|
| 提出日時 | 2025-06-06 22:05:25 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 662 ms / 2,000 ms |
| コード長 | 60,966 bytes |
| コンパイル時間 | 9,349 ms |
| コンパイル使用メモリ | 353,920 KB |
| 実行使用メモリ | 17,792 KB |
| 最終ジャッジ日時 | 2025-06-06 22:05:39 |
| 合計ジャッジ時間 | 12,027 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 15 |
ソースコード
#if !defined(MYLOCAL)//提出時用テンプレート
#pragma GCC optimize("Ofast")
#if defined(NDEBUG)
#undef NDEBUG
#endif
#include "bits/stdc++.h"
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#endif
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 ll2=array<ll,2>;
using ll3=array<ll,3>;
using ll4=array<ll,4>;
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__))
#define RALL1(v) (v).rbegin(), (v).rend()
#define RALL2(v,E) (v).rbegin(), (v).rbegin()+((E)+1)
#define RALL3(v,S,E) (v).rbegin()+(S), (v).rbegin()+((E)+1)
#define rall(...) EXPAND(overload3(__VA_ARGS__, RALL3, RALL2, RALL1)(__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> 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(); }
inline ll Ceil(ll a,ll b){ return (a<0) ? -(-a/b) : (a+b-1)/b; } //負もOK
inline ll Floor(ll a,ll b){ return -Ceil(-a,b); } //負もOK
inline ll Floormod(ll a,ll m){ return Floor(a,m)*m; } //負もOK
inline ll Ceilmod(ll a,ll m){ return Ceil(a,m)*m; } //負もOK
inline ll Mod(ll a,ll m){ ll r=a%m; if(r<0)r+=m; return r; } //負もOK
template<class T> inline T Pow(T a,ll n){ T r=1; for(; n>0; n>>=1,a*=a){ if(n&1)r*=a; } return r; }
inline ll Pow(int a,ll n){ return Pow((ll)a,n); }
inline ll limitmul(ll a,ll b,ll u){ return b==0||a<=u/b ? a*b : u; }//min(a*b,u) a,b,u≧0
//pair用テンプレート
template<class T,class S> inline pair<T,S>& operator+=(pair<T,S> &a,const pair<T,S> &b){ a.first+=b.first; a.second+=b.second; return a; }
template<class T,class S> inline pair<T,S>& operator-=(pair<T,S> &a,const pair<T,S> &b){ a.first-=b.first; a.second-=b.second; return a; }
template<class T,class S> inline pair<T,S>& operator*=(pair<T,S> &a,const pair<T,S> &b){ a.first*=b.first; a.second*=b.second; return a; }
template<class T,class S> inline pair<T,S>& operator/=(pair<T,S> &a,const pair<T,S> &b){ a.first/=b.first; a.second/=b.second; return a; }
template<class T,class S> inline pair<T,S>& operator%=(pair<T,S> &a,const pair<T,S> &b){ a.first%=b.first; a.second%=b.second; return a; }
template<class T,class S,class R> inline pair<T,S>& operator+=(pair<T,S> &a,R b){ a.first+=b; a.second+=b; return a; }
template<class T,class S,class R> inline pair<T,S>& operator-=(pair<T,S> &a,R b){ a.first-=b; a.second-=b; return a; }
template<class T,class S,class R> inline pair<T,S>& operator*=(pair<T,S> &a,R b){ a.first*=b; a.second*=b; return a; }
template<class T,class S,class R> inline pair<T,S>& operator/=(pair<T,S> &a,R b){ a.first/=b; a.second/=b; return a; }
template<class T,class S,class R> inline pair<T,S>& operator%=(pair<T,S> &a,R b){ a.first%=b; a.second%=b; return a; }
template<class T,class S,class R> inline pair<T,S> operator+(const pair<T,S> &a,R b){ pair<T,S> c=a; return c+=b; }
template<class T,class S,class R> inline pair<T,S> operator-(const pair<T,S> &a,R b){ pair<T,S> c=a; return c-=b; }
template<class T,class S,class R> inline pair<T,S> operator*(const pair<T,S> &a,R b){ pair<T,S> c=a; return c*=b; }
template<class T,class S,class R> inline pair<T,S> operator/(const pair<T,S> &a,R b){ pair<T,S> c=a; return c/=b; }
template<class T,class S,class R> inline pair<T,S> operator%(const pair<T,S> &a,R b){ pair<T,S> c=a; return c%=b; }
template<class T,class S,class R> inline pair<T,S> operator-(R b,const pair<T,S> &a){ pair<T,S> c=-a; return c+=b; }
template<class T,class S> inline pair<T,S> operator-(const pair<T,S> &a,const pair<T,S> &b){ pair<T,S> c=a; return c-=b; }
template<class T,class S> inline pair<T,S> operator-(const pair<T,S> &a){ pair<T,S> c=a; return c*=(-1); }
template<class T,class S> inline ostream &operator<<(ostream &os,const pair<T,S> &a){ return os << a.first << ' ' << a.second; }
//tuple用テンプレート 出力用のみ
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); }
//vector用テンプレート
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; }
//array用テンプレート
template<class T,size_t S> inline array<T,S>& operator+=(array<T,S> &a,const array<T,S> &b){ for (ll i=0; i<(ll)S; i++) a[i]+=b[i]; return a; }
template<class T,size_t S> inline array<T,S>& operator-=(array<T,S> &a,const array<T,S> &b){ for (ll i=0; i<(ll)S; i++) a[i]-=b[i]; return a; }
template<class T,size_t S> inline array<T,S>& operator*=(array<T,S> &a,const array<T,S> &b){ for (ll i=0; i<(ll)S; i++) a[i]*=b[i]; return a; }
template<class T,size_t S> inline array<T,S>& operator/=(array<T,S> &a,const array<T,S> &b){ for (ll i=0; i<(ll)S; i++) a[i]/=b[i]; return a; }
template<class T,size_t S> inline array<T,S>& operator%=(array<T,S> &a,const array<T,S> &b){ for (ll i=0; i<(ll)S; i++) a[i]%=b[i]; return a; }
template<class T,size_t S,class R> inline array<T,S>& operator+=(array<T,S> &a,R b){ for (T &e: a) e+=b; return a; }
template<class T,size_t S,class R> inline array<T,S>& operator-=(array<T,S> &a,R b){ for (T &e: a) e-=b; return a; }
template<class T,size_t S,class R> inline array<T,S>& operator*=(array<T,S> &a,R b){ for (T &e: a) e*=b; return a; }
template<class T,size_t S,class R> inline array<T,S>& operator/=(array<T,S> &a,R b){ for (T &e: a) e/=b; return a; }
template<class T,size_t S,class R> inline array<T,S>& operator%=(array<T,S> &a,R b){ for (T &e: a) e%=b; return a; }
template<class T,size_t S,class R> inline array<T,S> operator+(const array<T,S> &a,R b){ array<T,S> c=a; return c+=b; }
template<class T,size_t S,class R> inline array<T,S> operator-(const array<T,S> &a,R b){ array<T,S> c=a; return c-=b; }
template<class T,size_t S,class R> inline array<T,S> operator*(const array<T,S> &a,R b){ array<T,S> c=a; return c*=b; }
template<class T,size_t S,class R> inline array<T,S> operator/(const array<T,S> &a,R b){ array<T,S> c=a; return c/=b; }
template<class T,size_t S,class R> inline array<T,S> operator%(const array<T,S> &a,R b){ array<T,S> c=a; return c%=b; }
template<class T,size_t S,class R> inline array<T,S> operator-(R b,const array<T,S> &a){ array<T,S> c=-a; return c+=b; }
template<class T,size_t S> inline array<T,S> operator-(const array<T,S> &a,const array<T,S> &b){ array<T,S> c=a; return c-=b; }
template<class T,size_t S> inline array<T,S> operator-(const array<T,S> &a){ array<T,S> c=a; return c*=(-1); }
template<class T,size_t S> inline ostream &operator<<(ostream &os,const array<T,S> &a){ for (ll i=0; i<(ll)S; 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;
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...>>(); }
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 ----*/
constexpr mll_(){}
mll_(ll v): val_(v){ norm(); }
constexpr 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--(int){ return *this-=1; }
mll_ &operator++(int){ return *this+=1; }
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 };
};
struct bll{
ll s=0;
bll(ll s_=0): s(s_){}
bll(int s_): s(s_){}
bll(const string &bitstr): s(str2val(bitstr)){}
bll(const char *bitstr): s(str2val(bitstr)){}
struct ref {
bll &b; const ll msk;
ref(bll &b_,ll pos):b(b_),msk(1LL<<pos){}
operator ll() const { return (b.s&msk)!=0; }
ref &operator=(bool x){ if(x) b.s|=msk; else b.s&=~msk; return *this; }
};
ref operator[](ll pos){ return ref(*this,pos); }
ll operator[](ll pos) const { return (s>>pos)&1; }
bll &operator=(int b){ s=b; return *this; }
bll &operator=(ll b){ s=b; return *this; }
bll &operator=(const string &bitstr){ s=str2val(bitstr); return *this; }
bll &operator=(const char *bitstr){ s=str2val(bitstr); return *this; }
bll operator++(int){ bll b(*this); s++; return b; }
bll operator--(int){ bll b(*this); s--; return b; }
operator ll() const noexcept { return s; }
bll &operator&=(ll b){ s&=b; return *this; }
bll &operator|=(ll b){ s|=b; return *this; }
bll &operator^=(ll b){ s^=b; return *this; }
bll &operator+=(ll b){ s+=b; return *this; }
bll &operator-=(ll b){ s-=b; return *this; }
bll &operator<<=(ll i){ s<<=i; return *this; }
bll &operator>>=(ll i){ s>>=i; return *this; }
bll operator&(ll b)const{ return s&b; }
bll operator|(ll b)const{ return s|b; }
bll operator^(ll b)const{ return s^b; }
bll operator+(ll b)const{ return s+b; }
bll operator-(ll b)const{ return s-b; }
bll operator<<(ll i)const{ return s<<i; }
bll operator>>(ll i)const{ return s>>i; }
bll operator&(int b)const{ return s&b; }
bll operator|(int b)const{ return s|b; }
bll operator^(int b)const{ return s^b; }
bll operator+(int b)const{ return s+b; }
bll operator-(int b)const{ return s-b; }
bll operator<<(int i)const{ return s<<i; }
bll operator>>(int i)const{ return s>>i; }
bll operator~()const{ return ~s; }
bll &oneq (bll msk){ s|= msk.s; return *this; }
bll &offeq (bll msk){ s&=~msk.s; return *this; }
bll &flipeq(bll msk){ s^= msk.s; return *this; }
bll on (bll msk)const{ return bll(s).oneq (msk); }
bll off (bll msk)const{ return bll(s).offeq (msk); }
bll flip (bll msk)const{ return bll(s).flipeq(msk); }
bool any0(bll msk)const{ return ~s&msk.s; }
bool any1(bll msk)const{ return s&msk.s; }
bool all0(bll msk)const{ return !any1(msk); }
bool all1(bll msk)const{ return !any0(msk); }
bll &oneq (ll l,ll r){ return oneq (rngmsk(l,r)); }
bll &offeq (ll l,ll r){ return offeq (rngmsk(l,r)); }
bll &flipeq(ll l,ll r){ return flipeq(rngmsk(l,r)); }
bll on (ll l,ll r)const{ return on (rngmsk(l,r)); }
bll off (ll l,ll r)const{ return off (rngmsk(l,r)); }
bll flip (ll l,ll r)const{ return flip(rngmsk(l,r)); }
bool any0(ll l,ll r)const{ return any0(rngmsk(l,r)); }
bool any1(ll l,ll r)const{ return any1(rngmsk(l,r)); }
bool all0(ll l,ll r)const{ return all0(rngmsk(l,r)); }
bool all1(ll l,ll r)const{ return all1(rngmsk(l,r)); }
bll &maskeq(ll l,ll r){ s&=rngmsk(l,r); return *this; }
bll mask(ll l,ll r)const{ return bll(s).maskeq(l,r); }
bll &oneq (ll i){ s|= (1LL<<i); return *this; }
bll &offeq (ll i){ s&=~(1LL<<i); return *this; }
bll &flipeq(ll i){ s^= (1LL<<i); return *this; }
bll on (ll i)const{ return s| (1LL<<i); }
bll off (ll i)const{ return s&~(1LL<<i); }
bll flip(ll i)const{ return s^ (1LL<<i); }
bool contains(ll b)const{ return (s&b)==b; }
bll substr(ll l,ll r)const{ return (s&rngmsk(l,r))>>r; }
static bll rngmsk(ll l,ll r){ return (1LL<<(l+1))-(1LL<<r); }
ll msbit()const{
for(ll x=63,o=-1;;){
ll m=(x+o)/2;
if((1LL<<m)<=s) o=m; else x=m;
if(x-o==1) return o;
}
}
ll lsbit()const{ return bll(lsb()).msbit(); }
ll msb()const{ ll pos=msbit(); return (pos<0) ? 0LL : 1LL<<pos; }
ll lsb()const{ return s&-s; }
ll count()const{ return bitset<64>(s).count(); }
ll count(bll msk)const{ return (msk&s).count(); }
ll count(ll l,ll r)const{ return mask(l,r).count(); }
vector<ll> idxes()const{
vector<ll> v;
for(ll i=0,t=s; t; t>>=1,i++) if(t&1)v.push_back(i);
return v;
}
string to_string(ll wd=-1)const{
wd=max({wd,msbit()+1,1LL});
string ret;
for(ll i=wd-1;i>=0;--i) ret += '0'+char((s>>i)&1);
return ret;
}
private:
ll str2val(const string &bitstr){
ll val=0, len=(ll)bitstr.size();
for(ll i=0;i<len;++i) val|=ll(bitstr[i]-'0')<<(len-1-i);
return val;
}
};
template<class T> struct SET: set<T>{
using P=set<T>;
typename P::iterator it=P::end();
template<class...Args> SET(Args...args): P(args...){}
SET(initializer_list<T> a): P(a.begin(),a.end()){}
ll size() const { return (ll)P::size(); }
bool insert(const T &x){ bool r; tie(it,r)=P::insert(x); return r; }
template <class It> void insert(It st,It en){ P::insert(st,en); }
void insert(initializer_list<T> a){ P::insert(a.begin(),a.end()); }
template<class...A> bool emplace(A&&...a){ bool r; tie(it,r)=P::emplace(a...); return r; }
void eraseit(){ it=P::erase(it); }
void find(const T &x){ it=P::find(x); }
bool contains(const T &x){ return P::count(x)==1; }
void lower_bound(const T &x){ it=P::lower_bound(x); }
void upper_bound(const T &x){ it=P::upper_bound(x); }
T floor(const T &x){ return *(it=--P::upper_bound(x)); }
T ceil (const T &x){ return *(it=P::lower_bound(x)); }
bool isend() { return it==P::end(); }
T getit() { return *it; }
T next() { return *(++it); }
T prev() { return *(--it); }
bool nextok() { return !isend() && it!=--P::end(); }
bool prevok() { return it!=P::begin(); }
T front() { return *(it=P::begin()); }
T back() { return *(it=--P::end()); }
void pop_front(){ front(); eraseit(); }
void pop_back(){ back(); eraseit(); }
void push_front(const T &x){ it=P::insert(P::begin(),x); }
void push_back (const T &x){ it=P::insert(P::end(),x); }
void push_out(SET &b){ b.push_front(back()); pop_back(); }
void pull_in(SET &b){ push_back(b.front()); b.pop_front(); }
};
template<class T> struct cumulativesum{
using Int = long long;
using ll = long long;
ll n=0; vector<T> c;
cumulativesum():c(1){}
template<class S> cumulativesum(S &&v): n((ll)v.size()),c(n+1) { Ini(v); }
template<class S> void init(S &&v){ n=(ll)v.size(); c.resize(n+1); Ini(v); }
void add(T x) { n++; c.push_back(c.back()+x); }
T operator()(Int l,Int r){ return c[max(min(n,r+1),0LL)]-c[min(max(0LL,l),n)]; }
pair<Int,T> group(T i){
ll g=upper_bound(c.begin(),c.end(),i)-c.begin()-1;
T r = g>=0 ? i-c[g] : i;
return {g,r};
}
T mx(){//区間和max
T mn=T(),samx=0;
for(ll i=1;i<=n;++i){
chmax(samx,c[i]-mn);
chmin(mn,c[i]);
}
return samx;
}
template<class S> void Ini(S &&v) { for(ll i=0;i<n;++i) c[i+1]=c[i]+v[i]; }
};
template<class S> cumulativesum(S) -> cumulativesum<typename remove_reference<S>::type::value_type>;
template<class T> vector<T> powers(T m,ll n){
vector<T> ret(n+1,1);
for(ll i=1;i<=n;++i) ret[i]=ret[i-1]*m;
return ret;
}
template <class T> auto runlength(T &&v){
vector<pair<typename remove_reference<T>::type::value_type,ll>> ret;
for(auto&&e:v){
if(ret.empty() or ret.back().first!=e) ret.emplace_back(e,1);
else ret.back().second++;
}
return ret;
}
inline vector<ll> str2num(string &s,char base,const string &etc){
vector<ll> v(s.size());
for(ll i=0;i<(ll)s.size();++i){
size_t pos=etc.find(s[i]);
if(pos==etc.npos) v[i]=s[i]-(ll)base;
else v[i]=-((ll)pos+1);
}
return v;
}
template<class T> struct combination{
vector<T> f,g; ll mxN=0;
combination(){}
combination(ll maxN): f(maxN+1,1),g(maxN+1),mxN(maxN) {
for (ll i=1;i<=mxN;++i) { f[i]=f[i-1]*i; }
g[mxN]=1/f[mxN];
for (ll i=mxN;i>=1;--i) { g[i-1]=g[i]*i; }
}
T P(ll n,ll r){ return (n<0 || r<0 || n<r) ? T(0) : f[n]*g[n-r]; } //nPr
T H(ll n,ll r){ return operator()(n+r-1,n-1); }//nHr
T inv(ll n) { return f[n-1] * g[n]; } //1/n
T fact(ll n) { return f[n]; } //n!
T finv(ll n) { return g[n]; } //1/n!
T operator()(ll n,ll r){
if (r<0) return 0;
if (n<0) return operator()(-n+r-1,r) * ((r&1)?-1:1); //-nＣr = (-1)^r * n+r-1Ｃr
if (n<r) return 0;
if (n<=mxN) return f[n]*g[n-r]*g[r]; //通常
//n巨大、rかn-r小
if (n-r<r) r=n-r;
T bunsi=1,bunbo=1;
for (ll i=0;i<r;++i) bunsi*=n-i;
for (ll i=0;i<r;++i) bunbo*=i+1;
return bunsi/bunbo;
}
template<class SP>
vector<T> CnLnR(long long nL,long long nR,long long r,SP sp){
if (nR-nL+1<=0) return vector<T>();
if (r<0) return vector<T>(nR-nL+1,0);
vector<T> v=sp(nL-r+1,nR-r+1,r);
for (T& e: v) e*=finv(r);
return v;
}
template<class SP>
vector<T> HrLrR(long long n,long long rL,long long rR,SP sp){//r<0不可
return CnLnR(n-1+rL,n-1+rR,n-1,sp);
}
};
template<class T> struct wrapVector1d{
using S=typename T::value_type;
using Int = long long;
const T *v;
S Ini;
wrapVector1d(const T &v_,S ini_=S()):v(&v_),Ini(ini_){}
S operator[](Int i)const{ return (i<0 || (Int)v->size()<=i) ? Ini : (*v)[i]; }
};
template<class T> struct wrapVector2d{
using S=typename T::value_type;
using Int = long long;
const vector<T> *v;
S Ini;
T dmy;
wrapVector2d(const vector<T> &v_,S ini_=S()):v(&v_),Ini(ini_){}
wrapVector1d<T> operator[](ll i)const{
return (i<0 || (Int)v->size()<=i) ?
wrapVector1d(dmy,Ini) : wrapVector1d((*v)[i],Ini);
}
};
namespace dumpstring{//dummy
inline string stringf(const char *format,...){
char bf[1000];
va_list ap;
va_start(ap,format);
vsprintf(bf,format,ap);
va_end(ap);
return string(bf);
}
template <class T> string stringfx(T x,int wd=1){ return ""; }
struct args{
using Int = long long;
args(){}
args &wd(Int wd__){ (void)wd__; return *this; }
args &sx(Int s){ (void)s; return *this; }
template<size_t DIM> args &rngs(array<array<Int,DIM>,2> rngs){ return *this; }
args &tr(vector<Int> tr__){ (void)tr__; return *this; }
args &tr(){ return *this; }
args &labels(vector<string> labels__){ (void)labels__; return *this; }
args &xrev(){ return *this; }
args &yrev(){ return *this; }
args &zrev(){ return *this; }
args &wrev(){ return *this; }
};
template<class NdT>
void dumpNd(const string &h,const NdT &fd,const args &p=args(),ostream &os=cerr){}
};
using dumpstring::stringf; using dumpstring::stringfx;
using dumpstring::args; using dumpstring::dumpNd;
#endif//テンプレートend
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; }
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(); }
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 &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; }
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; }
};
/*
vll a={9,8,7},b={1,2,3};
vpll p={{5,3},{7,8},{0,2},};
- -------- 操作系 --------
a+=x a-=x a*=x a/=x a%=x a+x a-x a*x a/x a%x -a x-a a++ a-- //∀i a[i]にxを演算
a+=b a-=b a*=b a/=b a%=b a+b a-b a*b a/b a%b //要素毎演算(同サイズ時)
a.push_front(x,n); //n個先頭追加 省略時1
a.push_back(x,n); //n個末尾追加 省略時1
a.pop_front(n); //n個先頭削除 省略時1
a.pop_back(n); //n個末尾削除 省略時1
ll x=a.pull_front(); //pop_front()と同時に値取得
ll x=a.pull_back(); //pop_back()と同時に値取得
a.insert(i,x,n); //a[i]にn個x挿入 n省略時1
a.insert(i,b); //a[i]にvll b挿入
a.erase(i); //a[i]削除
a.erase(l,r); //区間[l,r]削除
a.concat(b); //aにbを結合 b=a可
a.concat(b,n); //aにbをn回結合 b=a可
a.reverse(l,r); //[l,r]を反転 l,r省略可
a.rotate(m); //a[m]を先頭にするrotate
a.rotate(l,r,m); //a[m]を先頭にするrotate 範囲[l,r]
a.sort(l,r); //[l,r]をソート l,r省略可
a.rsort(l,r); //[l,r]を逆順ソート l,r省略可
p.sort(l,r,[&](pll x,pll y){return x.second<y.second;});//比較関数指定sort l,r省略可
a.uniq(); //連続同値を1つにする
a.sortq(); //ソートしてユニーク
a.fill(l,r,x); //[l,r]にx代入 l,r省略可
a.iota(n,s,d); //aを等差数列にする 長さn,初項s,公差d
vll a(n,s,d); //コンストラクタ版iota
vll b=a.slice(st,en,d); //a[st:en:d] d省略時1
vll b=a.repeat(n); //aをn回繰り返す
- -------- 検索系 --------
auto pr=[&](auto &x){ return x>0; }; //検索条件
ll m=a.count(x); //xの個数
ll m=a.count(l,r,x); //xの個数in[l,r]
ll m=a.countif(pr); //条件満たす個数
ll m=a.countif(l,r,pr); //条件満たす個数in[l,r]
ll i=a.find(x); //xの最左位置i ない時N(配列長)
ll i=a.find(l,r,x); //xの最左位置i in[l,r] ない時r+1
ll i=a.findif(pr); //条件満たす最左位置i ない時N(配列長)
ll i=a.findif(l,r,pr); //条件満たす最左位置i in[l,r] ない時r+1
vll is=a.findall(x); //xの位置i列挙
vll is=a.findall(l,r,x); //xの位置i列挙in[l,r]
vll is=a.findallif(pr); //条件満たす位置i列挙
vll is=a.findallif(l,r,pr); //条件満たす位置i列挙in[l,r]
- -------- 昇順sort済み配列用 --------
ll i=a.flooridx(x); //x以下の最近傍位置i ない時-1
ll i=a.ceilidx(x); //x以上の最近傍位置i ない時N(配列長)
ll m=a.leftnmof(x); //x以下の個数
ll m=a.rightnmof(x); //x以上の個数
bool b=a.contains(x); //xを含む
- -------- 比較関数prでsort済みの配列用 --------
auto pr=[&](auto &x,auto &y){ return x>y; }; //降順ソート時
ll i=a.flooridx(x,pr); //x以左の最近傍位置i ない時-1
ll i=a.ceilidx(x,pr); //x以右の最近傍位置i ない時N(配列長)
ll m=a.leftnmof(x,pr); //x以左の個数
ll m=a.rightnmof(x,pr); //x以右の個数
bool b=a.contains(x,pr); //xを含む
a.concat(b,n).pop_back().rsort().uniq(); //連続適用できる
auto aa=a.tostd(); //N次元VectorをN次元vectorに変換(N≦5)
*/
template<class T> struct wrapv: Vector<T>{
using Int = long long;
T def=T();
T defIF=T();
wrapv(const Vector<T> &b):Vector<T>(b){}
wrapv(Vector<T> &&b):Vector<T>(move(b)){}
wrapv(const std::vector<T> &b):Vector<T>(b){}
wrapv(std::vector<T> &&b):Vector<T>(move(b)){}
T &operator[](Int i){
return (i<0 || this->size()<=i) ? (defIF=def) : Vector<T>::operator[](i);
}
void setdef(const T& x){ def=x; }
};
/*
wrapv v=vll(N,0,1); //vllなどでコンストラクトしてから代入する
v.setdef(INF); //範囲外での値セット
*/
#if 0
#define MODLL (1000000007LL)
#else
#define MODLL (998244353LL)
#endif
using mll = mll_<MODLL>;
//using mll = fraction;
// １
//０┼２
// ３ 左 上 右 下
const vector<pll> dxys={{0,-1},{-1,0},{0,1},{1,0},};
const string lurd="LURD";
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>>
vector<T>& Invs(int d, Wrap<Kind>) {//Kind=1 or 2(modint系)の時
static 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> vector<T>& Invs(int d, Wrap<0>) {//その他の時
static vector<T> invs(1);
for (int i = (int)invs.size(); i <= d; ++i) invs.push_back(T(1) / i);
return invs;
}
template<class T> vector<T>& Fact(int d) {// i!列挙 i=0~d
static 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> vector<T>& FInv(int d) {// 1/i!列挙 i=0~d
static vector<T> finv(1, T(1));
const 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> vector<T> BerlekampMassey(const vector<T>& a) {
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 = [](vector<T>& C, T d, T b, 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) {
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 vector<T>& invs_ = vector<T>())
{
assert(a_.lowdeg() <= b_.lowdeg());
int dmx = (int)dmx_;
const 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 : vector<pair<T, Int>> {
using 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& deg(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 vector<T>& invs_ = 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 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 : 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 = vector<T>;
/*---- utility ----*/
int isize()const { return (int)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 vector<T>& invs_ = vector<T>())
{
assert(g.size() == 2U && g.co(0) == T(1) && g.deg(0) == 0);
const 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(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)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);
vector<T> f;
for (int i = 0; i <= d; ++i) f.push_back(at(i));
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 vector<T>& invs = 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());
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());
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());
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());
vector<ll> h0 = convolution<m0>(ff, gg);
vector<ll> h1 = convolution<m1>(ff, gg);
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) {
vector<T> ff(f.begin(), f.end()), gg(g.begin(), g.end());
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 vector<T>& invs = 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(); //f=P/QのQを復元 fは2d-1次、Qはd次 Qのdmx=d
mll c=f.nthterm(k); //[x^k]f 線形漸化式を仮定 k巨大(10^18)でもOK
f.estimate(); //次数上限まで推定 線形漸化式を仮定
f.estimate(d); //d次まで推定 線形漸化式を仮定
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 vll2=vector< ll2>; using vll3=vector< ll3>; using vll4=vector< ll4>;
using vvll2=vector< vll2>; using vvll3=vector< vll3>; using vvll4=vector< vll4>;
using vvvll2=vector<vvll2>; using vvvll3=vector< vvll3>; using vvvll4=vector<vvll4>;
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); }); }
void cin2solve()
{
auto N = cin1<ll>();
if (N == 0) {
cout << 1 << '\n'; return;
}
auto seki = [&](fps& f, fps&g) {
ll n = f.deg(), m = g.deg();
fps h = f * g;
reverse(all(g));
fps hh = f * g;
rep(i, 0, n+m) {
ll ji = abs(i - m);
h.at(ji) += hh.at(i);
}
return h;
};
deque<fps> fs(N, fps({ 0,1 }, N));
while (fs.size() > 1) {
fps f0 = move(fs.front()); fs.pop_front();
fps f1 = move(fs.front()); fs.pop_front();
fps h = seki(f0, f1);
fs.push_back(move(h));
}
fps &ans = fs[0];
ans *= 2;
cout << ans << '\n';
return;
}
}//SorvingSpace
//////////////////////////////////////////
int main(){
#if 1
//SolvingSpace::labo();
SolvingSpace::cin2solve();
//SolvingSpace::generand();
#else
ll t; cin >> t;
rep(i,0,t-1){
SolvingSpace::cin2solve();
//SolvingSpace::generand();
}
#endif
cerr << timeget() <<"ms"<< '\n';
return 0;
}