結果

問題 No.5006 Hidden Maze
ユーザー hamamu
提出日時 2022-06-12 20:22:56
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 171 ms / 2,000 ms
コード長 46,759 bytes
コンパイル時間 4,784 ms
実行使用メモリ 22,716 KB
スコア 88,944
平均クエリ数 111.56
最終ジャッジ日時 2022-06-12 20:23:10
合計ジャッジ時間 12,938 ms
ジャッジサーバーID
（参考情報） 		judge14 / judge12
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ファイルパターン 結果
other AC * 100
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ソースコード

diff #
プレゼンテーションモードにする

·#if defined(MYLOCAL)
#   include "mylocal.h"
using namespace atcoder;
#else
#   pragma GCC optimize("Ofast")
#   include "bits/stdc++.h"
#   if __has_include(<atcoder/all>)
#       include <atcoder/all>
using namespace atcoder;
#   endif
#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;
struct{
    system_clock::time_point st = system_clock::now();
    ll operator()()const{return duration_cast<microseconds>(system_clock::now()-st).count()/1000;}
} timeget;
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 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,const vector<T> &b){ 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,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<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, d = 1;
        rep(i,0,b-1) c *= a-i;
        rep(i,0,b-1) d *= i+1;
        return c/d;
    }
    enum{modll=MOD};
};
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>;
};
#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>;
//////////////////////////////////////////
#if defined(_DEBUG)
ll dumpW = 5;
template<class T> void dump(vector<T> &v){
    rep(i,0,sz(v)-1) { cerr << ((i==0)?"[":" ") << setw(dumpW) << v[i]; }  cerr << "]";
}
void dump(vll &v){
    rep(i,0,sz(v)-1) {
        cerr << ((i==0)?"[":" ") << setw(dumpW);
        if (v[i] == INF) cerr << "INF";
        else if (v[i] == -INF) cerr << "-INF";
        else                   cerr << v[i];
    }  cerr << "]";
}
template<class T> void dump(vector<vector<T>> &v){
    ll N=(ll)v.size();  string d[2][2]={{" ", "["},  {"\n", "]\n"}};
    rep(i,0,N-1) { cerr << d[0][i==0];  dump(v[i]);  cerr << d[1][i==N-1]; }
}
template<class T> void dump(vector<vector<vector<T>>> &v){
    ll N=(ll)v.size();  string d[2]={"  <", "[ <"};
    rep(i,0,N-1) { cerr << d[i==0] << i << ">\n"; dump(v[i]); }  cerr << "]\n";
}
template<class T> void dump(vector<vector<vector<vector<T>>>> &v){
    ll N=(ll)v.size();  string d[2]={"  ---<", "[ ---<"};
    rep(i,0,N-1) { cerr << d[i==0] << i << ">---\n"; dump(v[i]); }  cerr << "]\n";
}
template<class T> void dump(vector<vector<vector<vector<vector<T>>>>> &v){
    ll N=(ll)v.size();  string d[2]={"  ======<", "[ ======<"};
    rep(i,0,N-1) { cerr << d[i==0] << i << ">======\n"; dump(v[i]); }  cerr << "]\n";
}
template<class T,class S> void dump(map<T,S> &m){
    for (auto e: m) cout << e.first << " : " << e.second << '\n';
}
#else
template<class T> void dump(T &v){}
#endif
struct rndutil{
    mt19937 mt;
    rndutil():mt(0){}
    ll val(ll a,ll b){ return mt()%(b-a+1)+a; }//[a,b]の乱数
    vll ary(ll n,ll a,ll b){//長さnの配列、要素[a,b]内、重複可
        vll v(n);
        for (ll i=0;i<n;++i) v[i]=this->val(a,b);
        return v;
    }
    vll sample(ll n,ll a,ll b){//長さnの配列、要素[a,b]内、重複無
        ll len=b-a+1;
        assert(n<=len);
        vll v(len);
        iota(v.begin(),v.end(),a);
        for (ll i=0;i<n;++i) swap(v[i],v[this->val(i,len-1)]);
        v.resize(n);
        return v;
    }
    pll range(ll a,ll b,ll m=1){ //[a,b]内閉区間長さm以上
        while (true){
            ll l=this->val(a,b+1),r=this->val(a,b+1);
            if (r-l<m)continue;
            return {l,r-1};
        }
    }
    pair<ll,vpll> graph(ll n){ //単純連結無向グラフ 木に近いものが多め
        while (true){
            vpll uv;
            UnionFindTree uft(n);
            for (ll v=0;v<n;++v) for (ll u=v+1;u<n;++u){
                if (this->val(1,n*(n-1)/2)>=n)continue;//各辺確率n/Mで採用(M:総辺数n(n-1)/2)
                uv.emplace_back(v,u);
                uft.Unite(v,u);
            }
            if (uft.grpnm()==1) return {(ll)uv.size(),uv};
        }
    }
    vpll tree(ll n){ //木
        vpll uv;
        UnionFindTree uft(n);
        while (uft.grpnm()>1){
            ll u=this->val(0,n-1),v=this->val(0,n-1);
            if (uft.Same(u,v)) continue;
            if (u>v)swap(u,v);
            uft.Unite(u,v);
            uv.emplace_back(u,v);
        }
        return uv;
    }
    struct UnionFindTree{
        vll par,rank,size;
        ll g;
        UnionFindTree(ll num): par(num),rank(num),size(num,1),g(num){
            rep(i,0,num-1) par[i] = i;
        }
        bool Same(ll x,ll y) { return Root(x) == Root(y); }
        ll Root(ll x) { return (par[x] == x) ? x : par[x]=Root(par[x]); }
        ll Size(ll x){ return size[Root(x)]; }
        ll grpnm() { return g; }
        void Unite(ll x,ll y){
            x = Root(x);
            y = Root(y);
            if (x == y) return;
            if (rank[x] < rank[y]) par[x] = y;
            else                   par[y] = x;
            if (rank[x] == rank[y]) rank[x]++;
            size[x] = size[y] = size[x] + size[y];
            g--;
        }
    };
};
/*
rndutil ru;
.  ↓スカラ   ↓区間[a,b]内
ll x=ru.val(a,b);
.  ↓配列重複有 ↓長さn、各要素が区間[a,b]内
vll v=ru.ary(n,a,b);
.  ↓配列重複無 ↓長さn、各要素が区間[a,b]内
vll v=ru.sample(n,a,b);
.  ↓範囲1つ        ↓[a,b]に含まれ、区間長1以上
auto[l,r]=ru.range(a,b);
.  ↓範囲1つ        ↓[a,b]に含まれ、区間長m以上
auto[l,r]=ru.range(a,b,m);
.  ↓木        ↓頂点数
vpll vu=ru.tree(n);
.  ↓単純連結無向グラフ(辺数m)
auto[m,vu]=ru.graph(n);
.      ↑vpll       ↑頂点数
*/
rndutil ru;
template<class T> struct graphwrap{
    vvll to;
    bool isdirected;
    map<T,ll> v2imap;
    vector<T> i2vvec;
    graphwrap(bool isDirected):isdirected(isDirected){}
    ll size() const { return (ll)to.size(); }//node数
    vvll &get(){ return to; }
    void addedge(T v,T u){
        ll vv=V2i(v),uu=V2i(u);
        to[vv].push_back(uu);
        if (!isdirected) to[uu].push_back(vv);
    }
    void addnode(T v){
        if (v2imap.count(v)!=0) return;
        v2imap[v]=(ll)i2vvec.size();
        i2vvec.push_back(v);
        to.emplace_back();
    }
    ll v2i(T  v){ return v2imap[v]; }
    T  i2v(ll i){ return i2vvec[i]; }
    ll V2i(T v){ addnode(v); return v2i(v); }//発番込み
};
/*
.         ↓頂点の型 ↓false:無向、true:有向
graphwrap<pll> g(false);
.            ↓頂点(i,j)-頂点(ii,jj)間 辺追加 (頂点も自動追加)
g.addedge({i,j},{ii,jj});
.           ↓頂点(i,j)追加
g.addnode({i,j});
.     ↓グラフ取り出し
vvll &to=g.get();
ll n=g.size(); //頂点数
ll v=g.v2i({i,j}); //頂点(i,j)の頂点番号v
auto[i,j]=g.i2v(v); //頂点番号vの頂点名
*/
template<class T> struct SET: set<T>{
    using P=set<T>;
    typename P::iterator it=P::end();
    template<class...Args> SET(Args...args): P(args...){}
    SET(initializer_list<T> a): P(a.begin(),a.end()){}
    ll size() const { return (ll)P::size(); }
    bool insert(const T &x){ bool r; tie(it,r)=P::insert(x); return r; }
    template <class It> void insert(It st,It en){ P::insert(st,en); }
    void insert(initializer_list<T> a){ P::insert(a.begin(),a.end()); }
    template<class...A> bool emplace(A&&...a){ bool r; tie(it,r)=P::emplace(a...); return r; }
    void eraseit(){ it=P::erase(it); }
    void find(const T &x){ it=P::find(x); }
    bool contains(const T &x){ return P::count(x)==1; }
    void lower_bound(const T &x){ it=P::lower_bound(x); }
    void upper_bound(const T &x){ it=P::upper_bound(x); }
    bool isend() { return it==P::end(); }
    T getit() { return *it; }
    T next() { return *(++it); }
    T prev() { return *(--it); }
    bool nextok() { return !isend() && it!=--P::end(); }
    bool prevok() { return it!=P::begin(); }
    T front() { return *(it=P::begin()); }
    T back()  { return *(it=--P::end()); }
    void pop_front(){ front(); eraseit(); }
    void pop_back(){ back(); eraseit(); }
    void push_front(const T &x){ it=P::insert(P::begin(),x); }
    void push_back(const T &x){ it=P::insert(P::end(),x); }
    void push_out(SET &b){ b.push_front(back()); pop_back(); }
    void pull_in(SET &b){ push_back(b.front()); b.pop_front(); }
};
/*
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(), prev(), nextok(), prevok()
*/
ll H,W,P;
/*
dir
　１
０┼２
　３
*/
//            左     上     右    下
pll dxy[4]={{0,-1},{-1,0},{0,1},{1,0},};
string dirchar="LURD";
inline ll dxy2dir(pll dxy){ return dxy.first+dxy.second+1+abs(dxy.first); }
inline pll rot90 (pll &a){ return {-a.second, a.first }; }
inline pll rot180(pll &a){ return {-a.first, -a.second}; }
inline pll rot270(pll &a){ return { a.second,-a.first }; }
inline pll xyof(ll v){ return {v/W,v%W}; }
inline ll vof(pll xy){ return xy.first*W+xy.second; }
inline ll uof(ll v,ll dir){ return v + ((dir&2)-1)*((dir&1)*(W-1)+1); }
inline ll uof(pll eg){ return uof(eg.first,eg.second); }
inline ll rev(ll dir){ return dir^2ll; }//dir反転
inline pll rev(pll eg){ return {uof(eg),rev(eg.second)}; }//辺反転
inline pll normalizeEdge(pll eg){ return (eg.second&2) ? rev(eg) : eg; } //辺をdir=0,1のみで表す
inline pll nds(pll eg){ return {eg.first,uof(eg)}; }
inline ll inner(pll a,pll b){ return a.first*b.first+a.second*b.second; }
inline ll norm1(pll v){ return abs(v.first)+abs(v.second); }
inline ll manD(pll v,pll u){ return norm1(v-u); }
inline pll edir(pll dv){ return dv/norm1(dv); }//縦/横方向vecから単位vecを得る
ll char2dir(char c){
    if (c=='L') return 0;
    if (c=='U') return 1;
    if (c=='R') return 2;
    /*if (c=='D')*/ return 3;
}
bool outHW(pll xy){
    auto [x,y]=xy;
    return x<0 or H<=x or y<0 or W<=y;
}
ll coutcin(string &outstr){
    cout << outstr << endl;
    //cerr << outstr << endl;
    ll nm;
    cin >> nm;
    return nm;
}
using pdl=pair<dd,ll>;
using vpdl=vector<pdl>;
dd Prob(map<pll,dd> &wallp,pll xy,ll dir){
    ll v=vof(xy);
    if (wallp.count({v,dir})==1) return wallp[{v,dir}];
    else return 15./76;
}
void setprob(map<pll,dd> &wallp,pll xy,ll dir,dd prob){
    ll v=vof(xy);
    wallp[{v,dir}]=prob;
    pll uxy=xy+dxy[dir];
    ll u=vof(uxy);
    wallp[{u,rev(dir)}]=prob;
}
vpll Dijkstra(map<pll,dd> &wallp){
    ll s=0;
    ll N = H*W;
    dd inf=1e100;
    vdd dist(N,inf);
    priority_queue<pdl, vpdl, greater<pdl>> Q;
    Q.push(pdl(0., s));
    dist[s] = 0.;
    while (!Q.empty()){
        dd d; ll v; tie(d, v) = Q.top(); Q.pop();
        if (d > dist[v]) continue;
        rep(dir,0,4-1){
            pll xy=xyof(v);
            xy+=dxy[dir];
            if (outHW(xy))continue;
            ll u=vof(xy);
            dd r=Prob(wallp,xyof(v),dir);//壁がある確率
            dd t=(1-r)*(1-P/100.);//通れる確率
            dd c=-log(t);
            if (chmin(dist[u],dist[v]+c)){
                Q.push(pdl{dist[u],u});
            }
        }
    }
#if defined(_DEBUG)
    rep(x,0,H-1){
        rep(y,0,W-1){
            dd c=dist[x*W+y];
            printf("%f ",c);
        }printf("\n");
    }printf("\n");
#endif
    //パスを得る
    vpll path;
    path.emplace_back(H-1,W-1);
    while (path.back()!=pll{0,0}){
        pll xy=path.back();
        dd mn=inf;
        //pll mnxy;
        vector<pair<dd,pll>> bf;
        rep(dir,0,4-1){
            pll xxyy=xy+dxy[dir];
            if (outHW(xxyy))continue;
            dd r=Prob(wallp,xxyy,rev(dir));//壁がある確率
            dd t=(1-r)*(1-P/100.);//通れる確率
            dd c=-log(t);
            dd di=dist[vof(xxyy)]+c;
            bf.emplace_back(di,xxyy);
            //if (chmin(mn,di)) mnxy=xxyy;
        }
        sort(all(bf));
        {
            ll len=sz(bf);
            auto [d0,__]=bf[0];
            dep(i,len-1,1){
                auto [di,_]=bf[i];
                if (d0+0.1<di) bf.pop_back();
                else break;
            }
        }
        ll i=ru.val(0,sz(bf)-1);
        path.push_back(bf[i].second);
    }
    reverse(all(path));
    return path;
}
string path2outstr(vpll &path){
    string outstr;
    rep(i,1,sz(path)-1){
        pll dxy=path[i]-path[i-1];
        ll dir=dxy2dir(dxy);
        outstr.push_back(dirchar[dir]);
    }
    return outstr;
}
void cin2solve()
{
    cin >> H >> W >> P;
    map<pll,dd> wallp;//壁がある確率 初期値15/76
    rep(_,0,INF-1){
        vpll path=Dijkstra(wallp);
        string outstr=path2outstr(path);
        ll nm=coutcin(outstr); if (nm==-1)return;
        
        //壁更新 ないところ,確率=0にする
        rep(i,0,nm-1){
            pll xy  =path[i];
            pll xxyy=path[i+1];
            ll v=vof(xy);
            pll dxy=xxyy-xy;
            ll dir=dxy2dir(dxy);
            setprob(wallp,xy,dir,0.);
        }
        //壁候補のところ
        {
            pll xy  =path[nm];
            pll xxyy=path[nm+1];
            pll dxy=xxyy-xy;
            ll dir=dxy2dir(dxy);
            dd r=Prob(wallp,xy,dir);
            dd rr=r/(r+(1.-r)*P/100.);
            setprob(wallp,xy,dir,rr);
        }
    }
    return;
}
//////////////////////////////////////////
int main(){
#if 1
    cin2solve();
    //generand();
#else
    ll t;  cin >> t;
    rep(i,0,t-1){
        cin2solve();
        //generand();
    }
#endif
    cerr << timeget() <<"ms"<< '\n';
    return 0;
}
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