#925504 (C++17) No.2527 H and W

提出ソース
結果

問題	No.2527 H and W
ユーザー	hamamu
提出日時	2023-11-03 21:47:56
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	18 ms / 2,000 ms
コード長	50,581 bytes
コンパイル時間	5,755 ms
コンパイル使用メモリ	300,984 KB
実行使用メモリ	19,024 KB
最終ジャッジ日時	2024-09-25 19:57:01
合計ジャッジ時間	6,924 ms
ジャッジサーバーID （参考情報）	judge1 / judge3
このコードへのチャレンジ
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テストケース

テストケース表示
入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 6,812 KB
testcase_01	AC	2 ms 6,816 KB
testcase_02	AC	17 ms 18,964 KB
testcase_03	AC	2 ms 6,944 KB
testcase_04	AC	17 ms 18,964 KB
testcase_05	AC	17 ms 18,976 KB
testcase_06	AC	18 ms 19,004 KB
testcase_07	AC	2 ms 6,940 KB
testcase_08	AC	18 ms 18,880 KB
testcase_09	AC	17 ms 19,012 KB
testcase_10	AC	18 ms 18,956 KB
testcase_11	AC	17 ms 18,876 KB
testcase_12	AC	17 ms 19,024 KB
testcase_13	AC	17 ms 18,948 KB
testcase_14	AC	16 ms 18,808 KB
testcase_15	AC	18 ms 18,872 KB
testcase_16	AC	18 ms 18,996 KB
testcase_17	AC	18 ms 19,024 KB
testcase_18	AC	17 ms 19,024 KB
testcase_19	AC	12 ms 12,592 KB
testcase_20	AC	13 ms 14,160 KB
testcase_21	AC	18 ms 18,864 KB
testcase_22	AC	17 ms 18,880 KB
testcase_23	AC	18 ms 19,008 KB
testcase_24	AC	13 ms 13,296 KB
testcase_25	AC	15 ms 16,484 KB
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ソースコード

raw source code
#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 !defined(_MSC_VER) && __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#endif
using namespace std;
using     ll=long long;     using   dd=double;     
using    vll=vector<   ll>; using  vdd=vector< dd>;
using   vvll=vector<  vll>; using vvdd=vector<vdd>;
using  vvvll=vector< vvll>; using vvvdd=vector<vvdd>;
using vvvvll=vector<vvvll>;
using   pll=pair<ll,ll>;  using   tll=tuple<ll,ll,ll>; using   qll=tuple<ll,ll,ll,ll>;
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 namespace chrono;
constexpr ll INF = 1001001001001001001;
struct Fast{ Fast(){ cin.tie(0); ios::sync_with_stdio(false); cout<<fixed<<setprecision(numeric_limits<double>::max_digits10); } } fast;
#define REPS(i, S, E) for (ll i = (S); i <= (E); i++)
#define REP(i, N) REPS(i, 0, (N)-1)
#define DEPS(i, S, E) for (ll i = (E); i >= (S); i--)
#define DEP(i, N) DEPS(i, 0, (N)-1)
#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 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,_,_)(__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 each2(e,v) for (auto && e:v)
#define each3(a,b,v) for (auto &&[a,b]:v)
#define each4(a,b,c,v) for (auto &&[a,b,c]:v)
#define each5(a,b,c,d,v) for (auto &&[a,b,c,d]:v)
#define each(...) EXPAND(overload5(__VA_ARGS__,each5,each4,each3,each2,_)(__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 all ALL
#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__))
#define rall RALL
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 T MaxE(vector<T>&v,ll S,ll E){ T m=v[S]; rep(i,S,E)chmax(m,v[i]); return m; }
template<class T> inline T MinE(vector<T>&v,ll S,ll E){ T m=v[S]; rep(i,S,E)chmin(m,v[i]); return m; }
template<class T> inline T MaxE(vector<T> &v) { return MaxE(v,0,(ll)v.size()-1); }
template<class T> inline T MinE(vector<T> &v) { return MinE(v,0,(ll)v.size()-1); }
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> inline T Sum(vector<T> &v,ll S,ll E){ T s=T(); rep(i,S,E)s+=v[i]; return s; }
template<class T> inline T Sum(vector<T> &v) { return Sum(v,0,v.size()-1); }
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

//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; }

template<class T,size_t S,class R> struct view1d;
template<class T,size_t S,class R> struct view1dIter{
	view1d<T,S,R> *vw=nullptr;
	ll idx=INF;
	view1dIter(){}
	view1dIter(view1d<T,S,R> *vw_,ll idx_):vw(vw_),idx(idx_){}
	view1dIter(const view1dIter<T,S,R> &it):vw(it.vw),idx(it.idx){}
	R &operator*()          { return (*vw)[idx]; }
	R &operator*()     const{ return (*vw)[idx]; }
	R &operator[](ll i)     { return (*vw)[idx+i]; }
	R &operator[](ll i)const{ return (*vw)[idx+i]; }
	auto &operator++(){ idx++; return *this; }
	auto &operator--(){ idx--; return *this; }
	auto operator++(int){ auto it=*this; idx++; return it; }
	auto operator--(int){ auto it=*this; idx--; return it; }
	auto &operator+=(ll n){ idx+=n; return *this; }
	auto &operator-=(ll n){ idx-=n; return *this; }
	auto operator+(ll n){ auto it=*this; return it+=n; }
	auto operator-(ll n){ auto it=*this; return it-=n; }
	ll   operator- (const view1dIter<T,S,R> &it)const{ return idx- it.idx; }
	bool operator< (const view1dIter<T,S,R> &it)const{ return idx< it.idx; }
	bool operator> (const view1dIter<T,S,R> &it)const{ return idx> it.idx; }
	bool operator<=(const view1dIter<T,S,R> &it)const{ return idx<=it.idx; }
	bool operator>=(const view1dIter<T,S,R> &it)const{ return idx>=it.idx; }
	bool operator!=(const view1dIter<T,S,R> &it)const{ return idx!=it.idx; }
	bool operator==(const view1dIter<T,S,R> &it)const{ return idx==it.idx; }
	using iterator_category = random_access_iterator_tag;
	using value_type = R;
	using difference_type = ll;
	using pointer = R*;
	using reference = R&;
};
template<class T,size_t S,class R> struct view1d{
	using Sll=array<ll,S>;
	T &data; //参照先データ
	Sll dsize; //参照先データ各軸のサイズ
	Sll s=Sll(); //view先頭
	Sll d=Sll(); //view方向
	ll len; //view長さ
	R &dummy; //範囲外の値参照
	R dummyj=R(); //範囲外の値実体
	/*---- コンストラクタ ----*/
	view1d(T &v): data(v),dummy(dummyj){
		SetDsize(v,dsize);
		d[S-1]=1;
		len=dsize[S-1];
	}
	//このコンストラクタは、マイナス座標指定を末尾にしない(暫定)
	//代入時Array<ll,2>{...}等と書くため、使い勝手悪い。将来廃止するかも。
	view1d(T &v,Sll s,Sll e,Sll d): data(v),s(s),d(d),len(Len(s,e,d)),dummy(dummyj){
		SetDsize(v,dsize);
	}
	view1d(T &v,Sll s,Sll d,ll len,R &dmy_): data(v),s(s),d(d),len(len),dummy(dmy_){
		SetDsize(v,dsize);
	}

	/*---- 演算 ----*/
	template<class Q> auto &operator =(const Q &b){ rep(i,0,len-1) (*this)[i] =b; return *this; }
	template<class Q> auto &operator+=(const Q &b){ rep(i,0,len-1) (*this)[i]+=b; return *this; }
	template<class Q> auto &operator-=(const Q &b){ rep(i,0,len-1) (*this)[i]-=b; return *this; }
	template<class Q> auto &operator*=(const Q &b){ rep(i,0,len-1) (*this)[i]*=b; return *this; }
	template<class Q> auto &operator/=(const Q &b){ rep(i,0,len-1) (*this)[i]/=b; return *this; }
	template<class Q> auto &operator%=(const Q &b){ rep(i,0,len-1) (*this)[i]%=b; return *this; }
	auto &operator =(const string &b){ return CpSeq(b); }
	template<size_t Q> auto &operator =(const char (&b)[Q]){ return *this=string(b); }
	template<class Q> auto &operator =(const vector<Q> &b){ return CpSeq(b); }
	template<class Q> auto &operator+=(const vector<Q> &b){ return PlSeq(b); }
	template<class Q> auto &operator-=(const vector<Q> &b){ return MnSeq(b); }
	template<class Q> auto &operator*=(const vector<Q> &b){ return PrSeq(b); }
	template<class Q> auto &operator/=(const vector<Q> &b){ return DvSeq(b); }
	template<class Q> auto &operator%=(const vector<Q> &b){ return RmSeq(b); }
	template<class Q,size_t P,class O> auto &operator =(const view1d<Q,P,O> &b){ return CpSeq(b); }
	template<class Q,size_t P,class O> auto &operator+=(const view1d<Q,P,O> &b){ return PlSeq(b); }
	template<class Q,size_t P,class O> auto &operator-=(const view1d<Q,P,O> &b){ return MnSeq(b); }
	template<class Q,size_t P,class O> auto &operator*=(const view1d<Q,P,O> &b){ return PrSeq(b); }
	template<class Q,size_t P,class O> auto &operator/=(const view1d<Q,P,O> &b){ return DvSeq(b); }
	template<class Q,size_t P,class O> auto &operator%=(const view1d<Q,P,O> &b){ return RmSeq(b); }
	template<class Q> auto &CpSeq(const Q &b){ rep(i,0,min(sz(b),len)-1) (*this)[i] =b[i]; return *this; }
	template<class Q> auto &PlSeq(const Q &b){ rep(i,0,min(sz(b),len)-1) (*this)[i]+=b[i]; return *this; }
	template<class Q> auto &MnSeq(const Q &b){ rep(i,0,min(sz(b),len)-1) (*this)[i]-=b[i]; return *this; }
	template<class Q> auto &PrSeq(const Q &b){ rep(i,0,min(sz(b),len)-1) (*this)[i]*=b[i]; return *this; }
	template<class Q> auto &DvSeq(const Q &b){ rep(i,0,min(sz(b),len)-1) (*this)[i]/=b[i]; return *this; }
	template<class Q> auto &RmSeq(const Q &b){ rep(i,0,min(sz(b),len)-1) (*this)[i]%=b[i]; return *this; }
	//template<class Q,class P> static bool eq(const Q &a,const P &b){
	//	return equals(ALL(a),ALL(b));
	//}
	template<class Q,class P> static bool eq(const Q &a,const P &b){
		if ((ll)a.size()!=(ll)b.size()) return false;
		rep(i,0,(ll)a.size()-1){
			if (a[i]!=b[i]) return false;
		}
		return true;
	}
	template<class Q,class P> static bool lt(const Q &a,const P &b){
		ll n=min((ll)a.size(),(ll)b.size());
		rep(i,0,n-1){
			if (a[i]<b[i])return true;
			if (a[i]>b[i])return false;
		}
		return (ll)a.size()<(ll)b.size();
	}
	template<class Q,size_t P,class O> bool operator==(           const view1d<Q,P,O> &b){ return eq(*this,b); }
	template<class Q>                  bool operator==(           const             Q &b){ return eq(*this,b); }
	template<class Q> friend           bool operator==(const Q &a,const view1d<T,S,R> &b){ return eq(    a,b); }
	template<size_t Q>                 bool operator==(           const     char (&b)[Q]){ return eq(*this,string(b)); }
	template<class Q,size_t P,class O> bool operator!=(           const view1d<Q,P,O> &b){ return !(*this==b); }
	template<class Q>                  bool operator!=(           const             Q &b){ return !(*this==b); }
	template<class Q> friend           bool operator!=(const Q &a,const view1d<T,S,R> &b){ return !(    a==b); }
	template<class Q,size_t P,class O> bool operator< (           const view1d<Q,P,O> &b){ return lt(*this,b); }
	template<class Q>                  bool operator< (           const             Q &b){ return lt(*this,b); }
	template<class Q> friend           bool operator< (const Q &a,const view1d<T,S,R> &b){ return lt(    a,b); }
	template<class Q,size_t P,class O> bool operator> (           const view1d<Q,P,O> &b){ return lt(b,*this); }
	template<class Q>                  bool operator> (           const             Q &b){ return lt(b,*this); }
	template<class Q> friend           bool operator> (const Q &a,const view1d<T,S,R> &b){ return lt(b,a    ); }
	template<class Q,size_t P,class O> bool operator<=(           const view1d<Q,P,O> &b){ return !(*this>b); }
	template<class Q>                  bool operator<=(           const             Q &b){ return !(*this>b); }
	template<class Q> friend           bool operator<=(const Q &a,const view1d<T,S,R> &b){ return !(    a>b); }
	template<class Q,size_t P,class O> bool operator>=(           const view1d<Q,P,O> &b){ return !(*this<b); }
	template<class Q>                  bool operator>=(           const             Q &b){ return !(*this<b); }
	template<class Q> friend           bool operator>=(const Q &a,const view1d<T,S,R> &b){ return !(    a<b); }

	/*---- getter ----*/
	ll size() const { return len; }
	R &operator[](ll i){ return const_cast<R&>(OrgAt(s+d*i)); }
	const R &operator[](ll i) const { return OrgAt(s+d*i); }
	R &at(ll i){ if(i<0)i+=len; return (*this)[i]; }
	//vector<R> tov(){ vector<R> vvv(len);  rep(i,0,len-1) vvv[i]=(*this)[i];  return vvv; }
	operator vector<R>(){ vector<R> v(len);  rep(i,0,len-1) v[i]=(*this)[i];  return v; }
	bool contains(R a){ rep(i,0,len-1) if((*this)[i]==a)return true;  return false; }
	auto begin(){ return view1dIter<T,S,R>(this,0); }
	auto end(){ return view1dIter<T,S,R>(this,len); }
	/*---- view設定 ----*/
	view1d<T,S,R> &dmy(R dmy_) { dummy=dmy_; return *this; }//ダミー値セット
	template<class...Q> view1d<T,S,R> &st(Q... s_){//始点set 負は末尾からの位置
		this->s=RevIfNeg(SllD(s_...));
		this->len=AutoLen(this->s,this->d,this->dsize);
		return *this;
	}
	template<class...Q> view1d<T,S,R> &en(Q... e_){//終了条件再設定 負は末尾から
		this->len=Len(s, RevIfNeg(SllD(e_...)), d);
		return *this;
	}
	template<class...Q> view1d<T,S,R> &dir(Q... d_){//方向set、長さはdata端まで
		this->d=SllD(d_...);
		this->len=AutoLen(this->s,this->d,this->dsize);
		return *this;
	}
	template<class...Q>
	view1d<T,S,R> &mv(Q... s_){ this->s+=SllD(s_...); return *this; }//平行移動
	view1d<T,S,R> &size(ll len_) { len=len_; return *this; }//長さset
	template<class Q> view1d<T,S,R> &size(Q &v){ len=(ll)v.size(); return *this; }//長さset
	view1d<T,S,R> &rev() { s+=d*(len-1); d*=-1; return *this; }//反転

	/*---- utility ----*/
	template<class Q> inline static ll sz(Q &v){ return (ll)v.size(); }
	Sll RevIfNeg(Sll pos){//!< 負なら末尾からの位置に変換
		rep(i,0,S-1)  if (pos[i]<0) pos[i]+=dsize[i];
		return pos;
	}
	static ll AutoLen(Sll s_,Sll d_,Sll dsz){//位置s_から方向d_ではみ出すまでの長さ
		Sll e=dsz-1;
		rep(i,0,S-1) e[i] *= (d_[i]>=0);//方向が負の軸を0にする
		return Len(s_,e,d_);
	}
	/*---- 先頭位置s、方向d、終了条件eから長さlen計算 ----*/
	//template<size_t Q> static ll Len(array<ll,Q> s,array<ll,Q> e,array<ll,Q> d){
	//	ll ret=INF;
	//	rep(i,0,Q-1) chmin(ret, Len1(s[i],e[i],d[i]));
	//	return ret;
	//}
	static ll Len(Sll s,Sll e,Sll d){
		ll ret=INF;
		rep(i,0,S-1) chmin(ret, Len1(s[i],e[i],d[i]));
		return ret;
	}
	static ll Len1(ll s,ll e,ll d){
		if (d==0) return INF;
		if (d<0){ s=-s; e=-e; d=-d; }
		if (s>e) return 0;
		return (e-s)/d+1;
	}
	/*---- 可変長引数をSllに変換 ----*/
	template<class...Q> static Sll SllD(Q... args){ return SllRec(0,args...); }
	template<class...Q> static Sll SllRec(ll i,ll first,Q... rest) {
		Sll sll = (i==S-1) ? Sll() : SllRec(i+1,rest...);
		sll[i]=first;
		return sll;
	}
	static Sll SllRec(ll i){ return Sll(); }
	/*---- dataの位置posの値取得 ----*/
	const R &OrgAt(Sll pos) const {
		rep(i,0,S-1){
			if (pos[i]<0 || dsize[i]<=pos[i]) return dummy;
		}
		return OrgAt_(data,pos);
	}
	template<class Q> using V   = vector<Q>;
	template<class Q> using VV  = V<V<Q>>;
	template<class Q> using VVV = V<V<V<Q>>>;
	using Vs  = V<string>;
	using VVs = VV<string>;
	using ll1 = array<ll,1>;
	using ll2 = array<ll,2>;
	using ll3 = array<ll,3>;
	auto &OrgAt_(V<R>   &dat,ll1 pos)const{ auto [i]    =pos; return dat[i]; }
	auto &OrgAt_(string &dat,ll1 pos)const{ auto [i]    =pos; return dat[i]; }
	auto &OrgAt_(VV<R>  &dat,ll2 pos)const{ auto [i,j]  =pos; return dat[i][j]; }
	auto &OrgAt_(Vs     &dat,ll2 pos)const{ auto [i,j]  =pos; return dat[i][j]; }
	auto &OrgAt_(VVV<R> &dat,ll3 pos)const{ auto [i,j,k]=pos; return dat[i][j][k]; }
	auto &OrgAt_(VVs    &dat,ll3 pos)const{ auto [i,j,k]=pos; return dat[i][j][k]; }
	/*---- dataの各軸size取得 ----*/
	static void SetDsize(V<R>   &dat,ll1 &dsz){ dsz={sz(dat)}; }
	static void SetDsize(string &dat,ll1 &dsz){ dsz={sz(dat)}; }
	static void SetDsize(VV<R>  &dat,ll2 &dsz){ dsz={sz(dat),sz(dat[0])}; }
	static void SetDsize(Vs     &dat,ll2 &dsz){ dsz={sz(dat),sz(dat[0])}; }
	static void SetDsize(VVV<R> &dat,ll3 &dsz){ dsz={sz(dat),sz(dat[0]),sz(dat[0][0])}; }
	static void SetDsize(VVs    &dat,ll3 &dsz){ dsz={sz(dat),sz(dat[0]),sz(dat[0][0])}; }
	typedef view1dIter<T,S,R> iterator;
	using value_type = R;
};
template<class Q> using V   = vector<Q>;
template<class Q> using VV  = V<V<Q>>;
template<class Q> using VVV = V<V<V<Q>>>;
template<class T>         view1d(    VVV<T>      ) -> view1d<    VVV<T>,3,T>;
template<class T>         view1d(     VV<T>      ) -> view1d<     VV<T>,2,T>;
template<class T>         view1d(      V<T>      ) -> view1d<      V<T>,1,T>;
;                         view1d(VV<string>      ) -> view1d<VV<string>,3,char>;
;                         view1d( V<string>      ) -> view1d< V<string>,2,char>;
;                         view1d(   string       ) -> view1d<   string ,1,char>;
template<class T,class S> view1d(    VVV<T>,S,S,S) -> view1d<    VVV<T>,3,T>;
template<class T,class S> view1d(     VV<T>,S,S,S) -> view1d<     VV<T>,2,T>;
template<class T,class S> view1d(      V<T>,S,S,S) -> view1d<      V<T>,1,T>;
template<class S>         view1d(VV<string>,S,S,S) -> view1d<VV<string>,3,char>;
template<class S>         view1d( V<string>,S,S,S) -> view1d< V<string>,2,char>;
template<class S>         view1d(   string ,S,S,S) -> view1d<   string ,1,char>;


template<class VIEW2D> struct view2dIter{
	VIEW2D *vw=nullptr;
	ll idx=INF;
	view2dIter(){}
	view2dIter(VIEW2D *vw_,ll idx_):vw(vw_),idx(idx_){}
	view2dIter(const view2dIter &it):vw(it.vw),idx(it.idx){}
	auto &operator*()          { return (*vw)[x(idx)][y(idx)]; }
	auto &operator*()     const{ return (*vw)[x(idx)][y(idx)]; }
	auto &operator[](ll i)     { return (*vw)[x(idx+i)][y(idx+i)]; }
	auto &operator[](ll i)const{ return (*vw)[x(idx+i)][y(idx+i)]; }
	auto &operator++(){ idx++; return *this; }
	auto &operator--(){ idx--; return *this; }
	auto operator++(int){ auto it=*this; idx++; return it; }
	auto operator--(int){ auto it=*this; idx--; return it; }
	auto &operator+=(ll n){ idx+=n; return *this; }
	auto &operator-=(ll n){ idx-=n; return *this; }
	auto operator+(ll n){ auto it=*this; return it+=n; }
	auto operator-(ll n){ auto it=*this; return it-=n; }
	ll   operator- (const view2dIter &it)const{ return idx- it.idx; }
	bool operator< (const view2dIter &it)const{ return idx< it.idx; }
	bool operator> (const view2dIter &it)const{ return idx> it.idx; }
	bool operator<=(const view2dIter &it)const{ return idx<=it.idx; }
	bool operator>=(const view2dIter &it)const{ return idx>=it.idx; }
	bool operator!=(const view2dIter &it)const{ return idx!=it.idx; }
	bool operator==(const view2dIter &it)const{ return idx==it.idx; }
	ll x(ll i)const{ return i/vw->leny(); }
	ll y(ll i)const{ return i%vw->leny(); }
	using iterator_category = random_access_iterator_tag;
	using value_type = typename VIEW2D::value_type;
	using difference_type = ll;
	using pointer = value_type*;
	using reference = value_type&;
};


template<class T,size_t S,class R> struct view2d{
	using Sll=array<ll,S>;
	T &data; //参照先データ
	Sll dsize; //参照先データ各軸のサイズ
	Sll s=Sll(); //view始点
	Sll dx=Sll(); //view x軸方向
	Sll dy=Sll(); //view y軸方向
	ll xl; //view x軸長さ
	ll yl; //view y軸長さ
	R dummy=R(); //範囲外の値
	/*---- コンストラクタ ----*/
	view2d(T &v): data(v){
		view1d<T,S,R>::SetDsize(v,dsize);
		dx[S-2]=1;
		dy[S-1]=1;
		xl=dsize[S-2];
		yl=dsize[S-1];
	}
	/*---- 演算 ----*/
	//template<class Q> auto &operator =(const Q &b){ rep(i,0,xl-1) (*this)[i] =b; return *this; }
	//template<class Q,size_t P,class O> auto &operator+=(const view2d<Q,P,O> &b){
	//	rep(i,0,xl-1) (*this)[i]
	//	return PlSeq(b); }
	/*---- getter ----*/
	ll size() const { return xl; }
	array<ll,2> shape() const { return {xl,yl}; }
	ll lenx() const { return xl; }
	ll leny() const { return yl; }
	///pll shape() const { return {xl,yl}; }
	view1d<T,S,R> operator[](ll i){ return view1d(data,s+dx*i,dy,yl,dummy); }
	const view1d<T,S,R> operator[](ll i) const { return view1d(data,s+dx*i,dy,yl,dummy); }
	R &at(ll i,ll j){ if(i<0)i+=xl;  if(j<0)j+=yl;  return (*this)[i][j]; }
	//vector<vector<R>> tovv(){
	//	vector<vector<R>> vvv(xl);
	//	///rep(i,0,xl-1) vvv[i]=(*this)[i].tov();  return vvv;
	//	rep(i,0,xl-1) vvv[i]=(*this)[i];  return vvv;
	//}
	operator vector<vector<R>>(){
		vector<vector<R>> v(xl);
		rep(i,0,xl-1) v[i]=(*this)[i];  return v;
	}
	auto begin(){ return view2dIter(this,0); }
	auto end(){ return view2dIter(this,xl*yl); }
#if defined(_DEBUG)
	void dump(){ ::dump(tovv()); }
#endif
	/*---- view設定 ----*/
	view2d<T,S,R> &dmy(R dmy_) { dummy=dmy_; return *this; }//ダミー値セット
	template<class...Q> view2d<T,S,R> &st(Q... s_){//始点set 負は末尾からの位置
		this->s=RevIfNeg(view1d<T,S,R>::SllD(s_...));
		this->xl=view1d<T,S,R>::AutoLen(this->s,this->dx,this->dsize);
		this->yl=view1d<T,S,R>::AutoLen(this->s,this->dy,this->dsize);
		return *this;
	}
	template<class...Q> view2d<T,S,R> &dirx(Q... d_){//x軸set、長さはdata端まで
		this->dx=view1d<T,S,R>::SllD(d_...);
		this->xl=view1d<T,S,R>::AutoLen(this->s,this->dx,this->dsize);
		return *this;
	}
	template<class...Q> view2d<T,S,R> &diry(Q... d_){//y軸set、長さはdata端まで
		this->dy=view1d<T,S,R>::SllD(d_...);
		this->yl=view1d<T,S,R>::AutoLen(this->s,this->dy,this->dsize);
		return *this;
	}
	template<class...Q> view2d<T,S,R> &mv(Q... s_){//平行移動
		this->s += view1d<T,S,R>::SllD(s_...);
		return *this;
	}
	view2d<T,S,R> &lenx(ll xl_) { xl=xl_; return *this; }
	view2d<T,S,R> &leny(ll yl_) { yl=yl_; return *this; }
	view2d<T,S,R> &shape(ll xl_,ll yl_) { xl=xl_; yl=yl_; return *this; }
	template<class Q> view2d<T,S,R> &shape(Q &v) { xl=v.lenx(); yl=v.leny(); return *this; }
	view2d<T,S,R> &rot90 () { s+=dx*(xl-1); swap(xl,yl); swap(dx,dy); dy*=-1; return *this; }
	view2d<T,S,R> &rot270() { s+=dy*(yl-1); swap(xl,yl); swap(dx,dy); dx*=-1; return *this; }
	view2d<T,S,R> &rot180() { s+=dx*(xl-1)+dy*(yl-1); dx*=-1; dy*=-1; return *this; }
	view2d<T,S,R> &revx() { s+=dx*(xl-1); dx*=-1; return *this; }
	view2d<T,S,R> &revy() { s+=dy*(yl-1); dy*=-1; return *this; }
	view2d<T,S,R> &swapxy() { swap(xl,yl); swap(dx,dy); return *this; }//xy軸入替

	/*---- utility ----*/
	Sll RevIfNeg(Sll pos){//!< 負なら末尾からの位置に変換
		rep(i,0,S-1)  if (pos[i]<0) pos[i]+=dsize[i];
		return pos;
	}
	using value_type = R;
};
template<class T> view2d(    VVV<T>) -> view2d<    VVV<T>,3,T>;
template<class T> view2d(     VV<T>) -> view2d<     VV<T>,2,T>;
;                 view2d(VV<string>) -> view2d<VV<string>,3,char>;
;                 view2d( V<string>) -> view2d< V<string>,2,char>;



/*
zipは参照のpairを返す。それをさらに参照するのはまずいので、コピーする。
*/
template<class ZIP> struct zipIter{
	ZIP *z=nullptr;
	ll idx=INF;
	zipIter(){}
	zipIter(ZIP *z_,ll idx_):z(z_),idx(idx_){}
	zipIter(const zipIter<ZIP> &it):z(it.z),idx(it.idx){}
	auto operator*()          { return (*z)[idx]; }//参照ではなく値戻し
	auto operator*()     const{ return (*z)[idx]; }//同上
	auto operator[](ll i)     { return (*z)[idx+i]; }//同上
	auto operator[](ll i)const{ return (*z)[idx+i]; }//同上
	auto &operator++(){ idx++; return *this; }
	auto &operator--(){ idx--; return *this; }
	auto operator++(int){ auto it=*this; idx++; return it; }
	auto operator--(int){ auto it=*this; idx--; return it; }
	auto &operator+=(ll n){ idx+=n; return *this; }
	auto &operator-=(ll n){ idx-=n; return *this; }
	auto operator+(ll n){ auto it=*this; return it+=n; }
	auto operator-(ll n){ auto it=*this; return it-=n; }
	ll   operator- (const zipIter<ZIP> &it)const{ return idx- it.idx; }
	bool operator< (const zipIter<ZIP> &it)const{ return idx< it.idx; }
	bool operator> (const zipIter<ZIP> &it)const{ return idx> it.idx; }
	bool operator<=(const zipIter<ZIP> &it)const{ return idx<=it.idx; }
	bool operator>=(const zipIter<ZIP> &it)const{ return idx>=it.idx; }
	bool operator!=(const zipIter<ZIP> &it)const{ return idx!=it.idx; }
	bool operator==(const zipIter<ZIP> &it)const{ return idx==it.idx; }
	using iterator_category = random_access_iterator_tag;
	using value_type = typename ZIP::value_type;
	using difference_type = ll;
	using pointer = value_type*;
	using reference = value_type&;
};

template<class T,class S> struct zip2{
	T &t; S &s;
	zip2(T &t_,S &s_):t(t_),s(s_){}
	ll size() const { return t.end()-t.begin(); }
	auto operator[](ll i)     { return make_pair(ref(t.begin()[i]),ref(s.begin()[i])); }
	auto operator[](ll i)const{ return make_pair(ref(t.begin()[i]),ref(s.begin()[i])); }
	auto begin(){ return zipIter(this,0); }
	auto end(){ return zipIter(this,size()); }
	using value_type = pair<typename T::value_type,typename S::value_type>;
};
template<class T,class S,class R> struct zip3{
	T &t; S &s; R &r;
	zip3(T &t_,S &s_,R &r_):t(t_),s(s_),r(r_){}
	ll size() const { return t.end()-t.begin(); }
	auto operator[](ll i)     { return make_tuple(ref(t.begin()[i]),ref(s.begin()[i]),ref(r.begin()[i])); }
	auto operator[](ll i)const{ return make_tuple(ref(t.begin()[i]),ref(s.begin()[i]),ref(r.begin()[i])); }
	auto begin(){ return zipIter(this,0); }
	auto end(){ return zipIter(this,size()); }
	using value_type = tuple<typename T::value_type,typename S::value_type,typename R::value_type>;
};
#endif//テンプレートend

#if defined(_MSC_VER) && __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#endif
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 };
};
#if 0
template<long long MOD> struct mll_{
	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
	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;
	}
	enum{ modll=MOD };
};
#endif
#if 0
#define MODLL (1000000007LL)
#else
#define MODLL (998244353LL)
#endif
using mll = mll_<MODLL>;
using vmll    = std::vector<mll>;
using vvmll   = std::vector<vmll>;
using vvvmll  = std::vector<vvmll>;
using vvvvmll = std::vector<vvvmll>;


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,T s,T d){ iota(n,s,d); }
	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-()const{ return Vector(*this)*=-1; }
	template<class S> friend Vector operator-(S x,const Vector &a){ return -a+=x; }
	Int size()const{ return (Int)vT::size(); }
	Vector &push_back(cT& x){ vT::push_back(x); return *this; }
	Vector &pop_back(){ vT::pop_back(); return *this; }
	Vector &push_front(cT& x){ insert(begin(),x); return *this; }
	Vector &pop_front(){ erase(0); return *this; }
	Vector &insert(Int i,cT& x){ insert(it(i),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){ insert(end(),b.begin(),b.end()); return *this; }
	Vector &concat(cvT &b,Int n){ for (int i=0;i<n;++i) concat(b); return *this; }
	Vector &repeat(Int n){ concat(vT(*this),n-1); return *this; }
	Vector &reverse(){ std::reverse(begin(),end()); return *this; }
	Vector &sort(){ std::sort(begin(),end()); return *this; }
	Vector &rsort(){ std::sort(vT::rbegin(),vT::rend()); return *this; }
	template<class Pr> Vector &sort(Pr pr){ std::sort(begin(),end(),pr); return *this; }
	Vector &uniq(){ erase(unique(begin(),end()),end()); return *this; }
	Vector &sortq(){ return sort().uniq(); }
	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 Int(std::count(begin(),end(),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 Int(count_if(begin(),end(),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 Int(std::find(begin(),end(),x)-begin()); }
	Int find(Int l,Int r,cT& x)const{ return Int(std::find(it(l),it(r+1),x)-begin()); }
	template<class Pr> Int findif(Pr pr)const{ return Int(find_if(begin(),end(),pr)-begin()); }
	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; }
};
/*
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  //∀i a[i]にxを演算
a.push_front(x);
a.push_back(x);
a.pop_front();
a.pop_back();
a.insert(i,x); //a[i]にx挿入
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
a.concat(b,n); //aにbをn回結合
a.repeat(n);   //aをn回繰り返す
a.reverse(); //反転
a.sort();    //ソート
a.rsort();   //逆順ソート
p.sort([&](pll x,pll y){return x.second<y.second;});//比較関数指定ソート
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
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
- -------- 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
*/



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   vpll=vector<  pll>; using    vtll=vector<   tll>; using  vqll=vector< qll>;
using  vvpll=vector< vpll>; using   vvtll=vector<  vtll>; using vvqll=vector<vqll>;



struct combination{
	vmll 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; }
	}
	mll P(ll n,ll r){ return (n<0 || r<0 || n<r) ? mll(0) : f[n]*g[n-r]; } //nPr
	mll H(ll n,ll r){ return operator()(n+r-1,r); }//nHr
	mll inv(ll n) { return f[n-1] * g[n]; } //1/n
	mll fact(ll n) { return f[n]; } //n!
	mll finv(ll n) { return g[n]; } //1/n!
	mll 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;
		mll 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;
	}
};
/*
combination cmb(n+10);
mll v=cmb(n,r);    // nCr 負も可、n<rも可、n巨大も愚直計算
mll v=cmb.P(n,r);  // nPr
mll v=cmb.H(n,r);  // nHr  x1+…+xn=rの個数  初期化時cmb(n+r-1)以上必要
mll v=cmb.inv(n);  // nの逆数
mll v=cmb.finv(n); // n!の逆数
mll v=cmb.fact(n); // n!
*/


#ifdef _MSC_VER
#include <intrin.h>
#endif
struct primefactorization{
	using ull = unsigned long long;
	ll fmax=0; //篩のmax
	vll mnpr; //最小素因数表
	vll primes; //素数リスト
	vpll pfact; //素因数分解結果 例:{<2,3>,<3,1>,<5,2>}→2^3×3^1×5^2
	vll divs; //約数列挙結果
	primefactorization(){} //篩無し
	primefactorization(ll fmx){ init(fmx); } //篩使用
	void init(ll fmx){ //エラトステネスの篩で最小素因数表+素数リストを作成
		fmax=fmx;
		mnpr.resize(fmx+1);
		primes.reserve(fmx/10+1);
		for (ll i=2; i<=fmax; i++){
			if (mnpr[i]) continue;
			primes.push_back(i);
			mnpr[i]=i;
			for (ll j=i*i; j<=fmax; j+=i) if (mnpr[j]==0) mnpr[j]=i;
		}
	}
	vll &primelist(){ return primes; }
	bool isprime(ll a){
		if (a<=fmax) return mnpr[a]==a;
		else return MillerRabin((ull)a);
	}
	vpll &operator()(ll a){//素因数分解
		return this->pfact=Factorization(a);
	}
	vll pfactlist(ll a){//素因数リスト(指数は返さない)
		(*this)(a);//素因数分解実行
		vll ret;
		for (auto&&[p,_]:this->pfact) ret.push_back(p);
		return ret;
	}
	/*!
	@brief   素因数分解結果pfactから約数列挙divsを得る
	@details e乗しても約数のもののみ raise=trueならe乗後を返す
	*/
	static void divisorCore(const vpll &pfact,vll &divs,ll e=1,bool raise=false){
		divs.assign(1,1);
		for (auto [p,nm]: pfact){
			ll prenm=(ll)divs.size();
			for (int i=0;i<prenm*(nm/e);++i) divs.push_back(divs[i]*p);
		}
		if (raise){ //e乗
			for (auto&& y: divs){
				for (ll i=1,yorg=y;i<e;++i) y*=yorg;
			}
		}
	}
	vll &divisor(ll a,ll e=1,bool raise=false){//約数列挙 e乗して約数のもの
		(*this)(a);//素因数分解実行
		divisorCore(this->pfact,this->divs,e,raise);//約数列挙コア
		return divs;
	}
	vpll Factorization(ll a){
		if (a<(1LL<<31)) return FactorizationCore((int)a);
		else             return FactorizationCore(a);
	}
	template<class T> vpll FactorizationCore(T a){//素因数分解
		vpll ret;
		if (a<=1) return ret;
		if (a<=fmax){//篩の範囲→osa_k法
			for (; mnpr[a]!=a; a/=(T)mnpr[a]) Add(ret,mnpr[a]);
			Add(ret,a);
			return ret;
		}
		if (MillerRabin((ull)a)){//素数の時
			ret.emplace_back(a,1);
			return ret;
		}
		//それ以外→ロー法で再帰
		ll y=RhoAlgorithm((ull)a);
		vpll ret1=Factorization(y);
		vpll ret2=Factorization(a/y);
		ll i=0,j=0,len1=(ll)ret1.size(),len2=(ll)ret2.size();
		while (i<len1 || j<len2){
			if (j==len2 || (i<len1 && ret1[i]<ret2[j])) AddBlock(ret,ret1[i++]);
			else                                        AddBlock(ret,ret2[j++]);
		}
		return ret;
	}
	bool MillerRabin(ull n){//true:素数 定数は http://miller-rabin.appspot.com/ より
		auto modpow=[&](ull a,ull b,ull m){ //a^b (mod m)
			ull r=1;
			for (; b>0; b>>=1,a=ModMul(a,a,m)) if (b&1) r=ModMul(r,a,m);
			return r;
			};
		auto f=[&](ull a){//true:素数かもしれない、false:合成数確定
			a%=n;
			if (a==0) return true;
			ull t=n-1,s=0;
			while (t%2==0) t>>=1,s++;
			ull x=modpow(a,t,n);
			if (x==1 || x==n-1) return true;
			for (ull r=1; r<s; ++r){
				if ((x=ModMul(x,x,n))==n-1) return true;
			}
			return false;
			};
		if (n<=1) return false;
		if (n==2) return true;
		if (n%2==0) return false;
		if (n<4759123141) return f(2)&&f(7)&&f(61);
		return f(2)&&f(325)&&f(9375)&&f(28178)&&f(450775)&&f(9780504)&&f(1795265022);
	}
	ll RhoAlgorithm(ull n){//約数の1つを返す 素数はNG(無限ループする)
		if ((n&1)==0) return 2;
		for (ull c=1,x=1;;++c){
			auto f=[&](ull x){ return (ModMul(x,x,n)+c)%n; };
			ull y=x,g=1;
			while (g==1){
				x=f(x);
				y=f(f(y));
				g=gcd(abs(ll(x-y)),n);
			}
			if (g<n) return (ll)g;
		}
	}
	void AddBlock(vpll &v,pll &p){
		if (!v.empty() and v.back().first==p.first) v.back().second+=p.second;
		else v.push_back(p);
	}
	void Add(vpll &v,ll x){
		if (!v.empty() and v.back().first==x) v.back().second++;
		else v.emplace_back(x,1);
	}
	inline ull ModMul(ull a,ull b,ull m){ //a*b%m
		if (a < 1ULL<<32 && b < 1ULL<<32) return a*b%m;
#ifdef _MSC_VER
		ull upper,lower,rem;
		lower=_umul128(a,b,&upper);
		_udiv128(upper,lower,m,&rem);
		return rem;
#else
		return (ull)((unsigned __int128)(a)*b%m);
#endif
	}
};
/*
- -------- 定義 -------- M:篩最大値
primefactorization pr;
primefactorization pr(M);
- -------- 素数判定 -------- 篩内なら使用、篩外ならミラーラビンで判定
bool b=pr.isprime(x);
- -------- 素数リスト --------  {2,3,5,7,11,…}
vll &primes=pr.primelist();
- -------- 素因数分解 --------
vpll &pfact=pr(x);
.      ↑例: x=1  → {}
.            x=2  → {<2,1>} //2^1の意味
.            x=600→ {<2,3>,<3,1>,<5,2>} //2^3×3^1×5^2 素因数昇順
- -------- 素因数分解(指数なし) -------- 例:x=600→{2,3,5} (600=2^3×3^1×5^2)
vll plist=pr.pfactlist(x);
- -------- 約数列挙 -------- 例:x=12→{1,2,4,3,6,12}＜未ソート＞
vll &div=pr.divisor(x);
vll &div=pr.divisor(x,e);      //e乗が約数のものを列挙
vll &div=pr.divisor(x,e,true); //約数でe乗数のものを列挙
*/


void cin2solve()
{
	ll H,W,K;
	cin >> H >> W >> K;

	combination cmb(max(H,W)+10);
	primefactorization pr;

	vll &div=pr.divisor(K);

	mll ans=0;
	for (auto&& y: div){
		ans+=cmb(H,y)*cmb(W,K/y);
	}
	cout << ans << '\n';

	return;
}


};//SolvingSpace

//////////////////////////////////////////


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;
}
yukicoder

結果

テストケース

ソースコード
