結果

問題 No.1463 Hungry Kanten
ユーザー hamamuhamamu
提出日時 2021-04-03 00:26:02
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 236 ms / 2,000 ms
コード長 46,112 bytes
コンパイル時間 4,982 ms
コンパイル使用メモリ 281,748 KB
実行使用メモリ 28,160 KB
最終ジャッジ日時 2024-06-06 09:29:51
合計ジャッジ時間 5,547 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
このコードへのチャレンジ
（要ログイン）

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 1 ms
6,940 KB
testcase_02 AC 8 ms
6,940 KB
testcase_03 AC 68 ms
6,940 KB
testcase_04 AC 2 ms
6,944 KB
testcase_05 AC 236 ms
28,160 KB
testcase_06 AC 2 ms
6,940 KB
testcase_07 AC 2 ms
6,940 KB
testcase_08 AC 2 ms
6,940 KB
testcase_09 AC 2 ms
6,940 KB
testcase_10 AC 2 ms
6,944 KB
testcase_11 AC 2 ms
6,940 KB
testcase_12 AC 2 ms
6,940 KB
testcase_13 AC 2 ms
6,944 KB
testcase_14 AC 4 ms
6,940 KB
testcase_15 AC 2 ms
6,940 KB
testcase_16 AC 9 ms
6,944 KB
testcase_17 AC 25 ms
6,944 KB
testcase_18 AC 8 ms
6,944 KB
testcase_19 AC 127 ms
15,872 KB
testcase_20 AC 174 ms
18,432 KB
testcase_21 AC 2 ms
6,940 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

using namespace std;
#if !defined(INCLUDED_MAIN)
#define INCLUDED_MAIN
#include __FILE__


template<class T> struct SET{
	set<T> s;
	typename set<T>::iterator it;
	bool empty() const { return s.empty(); }
	ll size() const { return (ll)s.size(); }
	void clear() { return s.clear(); }
	bool insert(const T &x){ bool r; tie(it,r)=s.insert(x); return r; }
	template <class It> void insert(It b,It e){ s.insert(b,e); }
	void erase(const T &x){ s.erase(x); }
	void eraseit(){ s.erase(it); }
	void swap(SET &b){ s.swap(b.s); }
	bool contains(const T &x){ find(x); return it != s.end(); }
	void find(const T &x){ it=s.find(x); }
	T next() { return *(++it); }
	T prev() { return *(--it); }
	pair<T,bool> Next(){
		if (it!=s.end()) it++;
		if (it!=s.end()) return {*it,true};
		else return {T(),false};
	}
	pair<T,bool> Prev(){
		if (it!=s.begin()) return {*(--it), true};
		else return {T(),false};
	}
	T front() const{ return *s.begin(); }
	T back() const{ return *(--s.end()); }
	void pop_front(){ s.erase(s.begin()); }
	void pop_back(){ s.erase(--s.end()); }
	void push_front(const T &x){ it=s.insert(s.begin(),x); }
	void push_back(const T &x){ it=s.insert(s.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(); }
#ifdef _DEBUG
	void dump(){
		each(e,s) cout << e << " ";
		cout << '\n';
	}
#endif
};
/*
front(), back(), pop_front(), pop_back(), contains(x),
push_front(x), push_back(x)
ある要素の次、前を連続して得る機能 find(x), next(), Next(), prev(), Prev()
*/

struct bll{ //第0～62bitまで対応
	ll s;
	bll(ll s_=0): s(s_){}
	struct ref {
		bll &b; const ll msk;
		ref(bll &b_,ll pos):b(b_),msk(1LL<<pos){}
		operator bool() const { return b.s&msk; }
		ref &operator=(bool x){ if (x) b.s|=msk; else b.s&=~msk; return *this; }
	};
	ref operator[](ll pos){ return ref(*this,pos); }
	bool operator[](ll pos) const { return (s>>pos)&1; }
	bll &on(ll l,ll r){ s|= rangemask(l,r); return *this; }
	bll &off(ll l,ll r){ s&=~rangemask(l,r); return *this; }
	bll &flip(ll l,ll r){ s^= rangemask(l,r); return *this; }
	static ll rangemask(ll l,ll r){ return (1LL<<(r+1))-(1LL<<l); }
	ll msbit()const{
		for (ll o=63,x=-1;;){
			ll m=(o+x)/2;
			if (s < (1LL<<m)) o=m; else x=m;
			if (o-x==1) return x;
		}
	}
	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(); }
	vll idxes()const{
		vll v;
		for (ll i=0,t=s; t; t>>=1,i++) if (t&1)v.push_back(i);
		return v;
	}
};
/*
bll b(s);
b[3]=1;                        //第3bitを1に
b.on(4,7).off(9,59).flip(0,3); //第4~7bitを1に、等
b.s+=10;                       //普通に数値として扱いたい時
					 //0000001000101100 b
ll c=b.msb();        //0000001000000000 b.msb()
ll c=b.msbit();      //      ^第9bit    b.msbit()
ll c=b.lsb();        //0000000000000100 b.lsb()
ll c=b.lsbit();      //       第2bit^   b.lsbit()
ll c=b.count();      //1の数 (4個)
vll idxes=b.idxes(); //1のidxのvll  {2,3,5,9}
*/

#ifdef _MSC_VER
#include <intrin.h>
#endif
struct lll{
	using ull = unsigned long long;
	using vull = vector<ull>;
	using cull = const vull;
	vull d; //d[i]:2^64進法の第i桁 d[0]が最下位
	static vull buf,buf2; //計算用バッファ
	static lll tmp; //計算用lll

	lll(ll v=0):d(1,(ull)v) {} //コンストラクタll
	lll &operator=(ll b){ d.assign(1,(ull)b); return *this; } //代入ll
	lll(const string &s){ fromStr(s); } //コンストラクタ from string
	lll &operator=(const string &s){ fromStr(s); return *this; } //代入string

	ll LL() const{ return (ll)d[0]; }//要件:値がllに収まること
	bool operator< (ll b) const { return (d.size()==1U && d[0]< (ull)b); }
	bool operator<=(ll b) const { return (d.size()==1U && d[0]<=(ull)b); }
	bool operator> (ll b) const { return (d.size()>=2U || d[0]> (ull)b); }
	bool operator>=(ll b) const { return (d.size()>=2U || d[0]>=(ull)b); }
	bool operator==(ll b) const { return (d.size()==1U && d[0]==(ull)b); }
	bool operator!=(ll b) const { return !(*this==b); }
	bool operator< (const lll &b) const { return lt(d,0,b.d,0); }
	bool operator<=(const lll &b) const { return le(d,0,b.d,0); }
	bool operator> (const lll &b) const { return gt(d,0,b.d,0); }
	bool operator>=(const lll &b) const { return ge(d,0,b.d,0); }
	bool operator==(const lll &b) const { return d==b.d; }
	bool operator!=(const lll &b) const { return !(*this==b); }
	friend ostream &operator<<(ostream &os,const lll &a) { return os << a.tostr(); }
	lll operator+(ll b) const { lll c=*this; return c+=b; }
	lll operator-(ll b) const { lll c=*this; return c-=b; }
	lll operator*(ll b) const { lll c=*this; return c*=b; }
	lll operator/(ll b) const { lll c=*this; return c/=b; }
	lll operator%(ll b) const { lll c=*this; return c%=b; }
	lll operator+(const lll &b) const { lll c=*this; return c+=b; }
	lll operator-(const lll &b) const { lll c=*this; return c-=b; }
	lll operator*(const lll &b) const { lll c=*this; return c*=b; }
	lll operator/(const lll &b) const { lll c=*this; return c/=b; }
	lll operator%(const lll &b) const { lll c=*this; return c%=b; }
	lll &operator+=(ll b){
		if (d.size()==1U){//高速化のため別処理
			if ((d[0]+=b) < (ull)b) d.push_back(1);
		}
		else AddSub(d,0,(ull)b);
		return *this;
	}
	lll &operator-=(ll b){
		if (d.size()==1U) d[0]-=b; //高速化のため別処理
		else{
			SubSub(d,0,(ull)b);
			DelZero(d);
		}
		return *this;
	}
	lll &operator*=(ll b){
		if (d.size()==1U){//高速化のため別処理
			ull upper,lower;  tie(upper,lower) = Prod64(d[0],b);
			d[0]=lower;
			if (upper>=1) d.push_back(upper);
		}
		else{
			buf.assign(d.size()+1U,0);
			ProdSub((ull)b,buf,0);
			DelZero(buf);
			d.swap(buf);
		}
		return *this;
	}
#if 0//実装するまでコメントアウト
	lll &operator/=(ll b){
		if (d.size()==1U) d[0]/=b; //高速化のため別処理
		else{
			////////////////////////////DivSubll(d,b);
			////
			/////商をdとswapして完了
			////
		}
		return *this;
	}
#endif
	lll &operator+=(const lll &b){
		d.resize(max(d.size(),b.d.size()),0);
		rep(i,0,(ll)b.d.size()-1) AddSub(d,i,b.d[i]);
		return *this;
	}
	lll &operator-=(const lll &b){ //this<bはNG
		rep(i,0,(ll)b.d.size()-1) SubSub(d,i,b.d[i]);
		DelZero(d);
		return *this;
	}
	lll &operator*=(const lll &b){
		buf.assign(d.size()+b.d.size(),0);
		rep(i,0,(ll)b.d.size()-1) ProdSub(b.d[i],buf,i);
		DelZero(buf);
		d.swap(buf);
		return *this;
	}
	lll &operator/=(const lll &b){
		DivSublll(b);
		d.swap(buf2);
		return *this;
	}
	lll &operator%=(const lll &b){
		DivSublll(b);
		return *this;
	}
	inline void DivSublll(const lll &b){//商buf2 余りthis->d
		ll N=(ll)d.size();
		ll M=(ll)b.d.size();
		if (N<M){
			buf2.assign(1,0);
			return;
		}
		buf2.resize(N-M+1);//結果格納先
		dep(i,N-M,0){
			//-- 商第i桁を探す
			ull ok=0,ng=(ull)-1;//ullの最大値 通常のngより1小さいことに注意
			while (ng-ok>0){
				ull x = ok + (ng-ok)/2 + 1; //オーバーフローを避ける計算方法
				tmp=b;
				tmp*=x;
				if (le(tmp.d,0,d,i)) ok=x; else ng=x-1;
			}
			buf2[i]=ok;
			if (ok==0) continue;
			//-- dの第i桁からb*okを引く
			tmp=b;
			tmp*=ok;
			rep(j,0,(ll)tmp.d.size()-1) SubSub(d,i+j,tmp.d[j]);
			DelZero(d);
		}
		DelZero(buf2);
	}
	string tostr() const {
		ll dLen=(ll)d.size();
		vull dd(dLen*2); //32bitごとに分解
		rep(i,0,dLen-1){
			dd[i*2]  =d[i]&0xffffffff;
			dd[i*2+1]=d[i]>>32;
		}
		if (dd.back()==0) dd.pop_back();

		vull buf10;
		for (ll j=0; !dd.empty(); j++){ //10^9進法の下の桁から求めるループ
			ll r=0;
			dep(i,(ll)dd.size()-1,0){
				dd[i]+=(r<<32);
				ull y=dd[i]/1000000000;
				r=dd[i]-y*1000000000; //r=dd[i]%1000000000を高速化
				dd[i]=y;
			}
			buf10.push_back(r);
			if (dd.back()==0) dd.pop_back();
		}
		ostringstream ss;
		ss << buf10.back(); //最上位のみ0無
		for (ll i=(ll)buf10.size()-2; i>=0; i--){
			ss << setw(9) << setfill('0') << buf10[i];
		}
		return ss.str();
	}
	void fromStr(const string &s){
		d.clear();
		const ll N=9,M=1000000000;
		ll ddLen=(s.size()+N-1)/N;
		vull dd(ddLen);//10^9ごとに分解
		rep(i,0,(ll)s.size()-1){
			ll ii=(ll)s.size()-1-i;
			dd[ii/N] = dd[ii/N]*10 + (s[i]-'0');
		}
		while (dd.back()==0 && dd.size()>1) dd.pop_back();//先頭0削除

		for (ll j=0; !dd.empty(); j++){ //32bit進法の下の桁から求めるループ
			ll r=0;
			dep(i,(ll)dd.size()-1,0){
				dd[i]+=r*M;
				r=dd[i]&((1LL<<32)-1);
				dd[i]>>=32;
			}
			if (j%2==0) d.push_back(r);
			else d.back()+=r<<32;
			while (!dd.empty() && dd.back()==0) dd.pop_back();//先頭0削除
		}
	}

	inline static void AddSub(vull &v,ll s,ull b){//vの第s桁にbを加算
		for (ll i=s; i<(ll)v.size() && b>0; i++){
			v[i]+=b;
			b=(v[i]<b);
		}
		if (b>0) v.push_back(b);
	}
	inline static void SubSub(vull &v,ll s,ull b){//vの第s桁からbを減算 負になるのはNG
		for (ll i=s; i<(ll)v.size() && b>0; i++){
			ull c=(v[i]<b);
			v[i]-=b;
			b=c;
		}
	}
	void ProdSub(ull b,vull &sm,ll offset){//d*bをsmの第offset桁以降に加算
		rep(i,0,(ll)d.size()-1){
			ull upper,lower;  tie(upper,lower) = Prod64(d[i],b);
			AddSub(sm,i+offset,lower); //smのi+offset  桁にlowerを加算
			AddSub(sm,i+offset+1,upper); //smのi+offset+1桁にupperを加算
		}
	}
	inline pair<ull,ull> Prod64(ull a,ull b){//a*bの<上位64bit,下位64bit>を計算
		ull upper,lower;
#ifdef _MSC_VER
		lower=_umul128(a,b,&upper);
#else
		unsigned __int128 tmp=(unsigned __int128)(a)*b;
		upper=tmp>>64;
		lower=tmp;
#endif
		return {upper,lower};
	}
	//第sv桁以降のv と 第su桁以降のu の比較
	inline static bool lt(cull &v,ll sv,cull &u,ll su) { return cmp(v,sv,u,su,true,false); }
	inline static bool le(cull &v,ll sv,cull &u,ll su) { return cmp(v,sv,u,su,true,true); }
	inline static bool gt(cull &v,ll sv,cull &u,ll su) { return cmp(u,su,v,sv,true,false); }
	inline static bool ge(cull &v,ll sv,cull &u,ll su) { return cmp(u,su,v,sv,true,true); }
	inline static bool eq(cull &v,ll sv,cull &u,ll su) { return cmp(v,sv,u,su,false,true); }
	//比較汎用関数 v<uの時l,v==uの時e,v>uの時falseを返す sv,su共に溢れた時は未定義
	inline static bool cmp(cull &v,ll sv,cull &u,ll su,bool l,bool e){
		ll szv=(ll)v.size()-sv;
		ll szu=(ll)u.size()-su;
		if (szv<szu) return true;
		if (szv>szu) return false;
		dep(i,szv-1,0){
			if (v[i+sv]<u[i+su]) return true;
			if (v[i+sv]>u[i+su]) return false;
		}
		return e;
	}
	inline static void DelZero(vull &v){//上位桁の0を削除 v[0]は0でも残す
		dep(i,(ll)v.size()-1,1){
			if (v[i]>0) break;
			v.pop_back();
		}
	}
};
vector<unsigned long long> lll::buf,lll::buf2;//計算用バッファ
lll lll::tmp; //計算用lll


void solve()
{
	ll n,k;
	cin >> n >> k;
	vector<ll> a;
	rep(i,0,n-1){ ll a__; cin>>a__; a.push_back(a__); }
	SET<lll> st;
	rep(s,0,(1LL<<n)-1){
		if (bll(s).count()<k)continue;

		ll sm=0;
		lll pr=1;
		rep(i,0,n-1){
			if (!(s&(1LL<<i)))continue;

			sm+=a[i];
			pr*=a[i];
		}
		st.insert(lll(sm));
		st.insert(pr);
	}
	cout << st.size() << '\n';


	return;
}



int main(){
#if 1
	solve();
	//cin2solve();
	//generand();
#else
	ll t;  cin >> t;
	rep(i, 0, t-1){
		solve();
		//cin2solve();
	}
#endif
	return 0;
}



#else //INCLUDED_MAIN

#include "bits/stdc++.h"
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#endif
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>;
constexpr ll INF = 1LL << 60;
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
using  vpll=vector< pll>;
using vvpll=vector<vpll>;
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){ 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; }

//vector用テンプレート
template<class T> inline vector<T>& operator+=(vector<T> &a,const vector<T> &b){ for (ll i=0; i<(ll)a.size(); i++) a[i]+=b[i];  return a; }
template<class T> inline vector<T>& operator-=(vector<T> &a,const vector<T> &b){ for (ll i=0; i<(ll)a.size(); i++) a[i]-=b[i];  return a; }
template<class T> inline vector<T>& operator*=(vector<T> &a,const vector<T> &b){ for (ll i=0; i<(ll)a.size(); i++) a[i]*=b[i];  return a; }
template<class T> inline vector<T>& operator/=(vector<T> &a,const vector<T> &b){ for (ll i=0; i<(ll)a.size(); i++) a[i]/=b[i];  return a; }
template<class T> inline vector<T>& operator%=(vector<T> &a,const vector<T> &b){ for (ll i=0; i<(ll)a.size(); i++) a[i]%=b[i];  return a; }
template<class T,class S> inline vector<T>& operator+=(vector<T> &a,S b){ for (T &e: a) e+=b;  return a; }
template<class T,class S> inline vector<T>& operator-=(vector<T> &a,S b){ for (T &e: a) e-=b;  return a; }
template<class T,class S> inline vector<T>& operator*=(vector<T> &a,S b){ for (T &e: a) e*=b;  return a; }
template<class T,class S> inline vector<T>& operator/=(vector<T> &a,S b){ for (T &e: a) e/=b;  return a; }
template<class T,class S> inline vector<T>& operator%=(vector<T> &a,S b){ for (T &e: a) e%=b;  return a; }
template<class T,class S> inline vector<T> operator+(const vector<T> &a,S b){ vector<T> c=a; return c+=b; }
template<class T,class S> inline vector<T> operator-(const vector<T> &a,S b){ vector<T> c=a; return c-=b; }
template<class T,class S> inline vector<T> operator*(const vector<T> &a,S b){ vector<T> c=a; return c*=b; }
template<class T,class S> inline vector<T> operator/(const vector<T> &a,S b){ vector<T> c=a; return c/=b; }
template<class T,class S> inline vector<T> operator%(const vector<T> &a,S b){ vector<T> c=a; return c%=b; }
template<class T,class S> inline vector<T> operator-(S b,const vector<T> &a){ vector<T> c=-a; return c+=b; }
template<class T> inline vector<T> operator-(const vector<T> &a){ vector<T> c=a; return c*=(-1); }
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){ 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<ll MOD> struct mll_{
	ll val;
	mll_(ll v = 0): val(v % MOD){ if (val < 0) val += MOD; }
	mll_ operator - () const { return -val; }
	mll_ operator + (const mll_ &b) const { return val + b.val; }
	mll_ operator - (const mll_ &b) const { return val - b.val; }
	mll_ operator * (const mll_ &b) const { return val * b.val; }
	mll_ operator / (const mll_ &b) const { return mll_(*this) /= b; }
	mll_ operator + (ll b) const { return *this + mll_(b); }
	mll_ operator - (ll b) const { return *this - mll_(b); }
	mll_ operator * (ll b) const { return *this * mll_(b); }
	friend mll_ operator + (ll a,const mll_ &b) { return b + a; }
	friend mll_ operator - (ll a,const mll_ &b) { return -b + a; }
	friend mll_ operator * (ll a,const mll_ &b) { return b * a; }
	friend mll_ operator / (ll a,const mll_ &b) { return mll_(a)/b; }
	mll_ &operator += (const mll_ &b) { val=(val+b.val)%MOD; return *this; }
	mll_ &operator -= (const mll_ &b) { val=(val+MOD-b.val)%MOD; return *this; }
	mll_ &operator *= (const mll_ &b) { val=(val*b.val)%MOD; return *this; }
	mll_ &operator /= (const mll_ &b) {
		ll c=b.val,d=MOD,u=1,v=0;
		while (d){
			ll t = c / d;
			c -= t * d; swap(c,d);
			u -= t * v; swap(u,v);
		}
		val = val * u % MOD;
		if (val < 0) val += MOD;
		return *this;
	}
	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); }
	bool operator == (const mll_ &b) const { return val == b.val; }
	bool operator != (const 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,const mll_ &b) { return mll_(a) == b.val; }
	friend bool operator != (ll a,const mll_ &b) { return mll_(a) != b.val; }
	friend ostream &operator << (ostream &os,const mll_ &a) { return os << a.val; }
	friend istream &operator >> (istream &is,mll_ &a) { return is >> a.val; }
	static mll_ Combination(ll a,ll b){
		chmin(b,a-b);
		if (b<0) return mll_(0);
		mll_ c = 1;
		rep(i,0,b-1) c *= a-i;
		rep(i,0,b-1) c /= i+1;
		return c;
	}
};
//using mll = mll_<1000000007LL>;
using mll = mll_<998244353LL>;
using vmll    = std::vector<mll>;
using vvmll   = std::vector<vmll>;
using vvvmll  = std::vector<vvmll>;
using vvvvmll = std::vector<vvvmll>;

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 //INCLUDED_MAIN
0