結果
| 問題 | No.2952 Invision of Multiples |
| ユーザー |
 hamamu
|
| 提出日時 | 2024-10-26 03:34:15 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 3,667 ms / 4,000 ms |
| コード長 | 49,786 bytes |
| コンパイル時間 | 7,061 ms |
| コンパイル使用メモリ | 328,088 KB |
| 実行使用メモリ | 268,332 KB |
| 最終ジャッジ日時 | 2024-10-26 03:35:57 |
| 合計ジャッジ時間 | 100,263 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge3 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
6,820 KB |
| testcase_01 | AC | 2 ms
6,820 KB |
| testcase_02 | AC | 3 ms
6,816 KB |
| testcase_03 | AC | 47 ms
6,816 KB |
| testcase_04 | AC | 47 ms
6,820 KB |
| testcase_05 | AC | 45 ms
6,816 KB |
| testcase_06 | AC | 44 ms
6,816 KB |
| testcase_07 | AC | 45 ms
6,820 KB |
| testcase_08 | AC | 45 ms
6,816 KB |
| testcase_09 | AC | 1,812 ms
96,784 KB |
| testcase_10 | AC | 1,780 ms
88,252 KB |
| testcase_11 | AC | 2,191 ms
157,084 KB |
| testcase_12 | AC | 2,203 ms
159,884 KB |
| testcase_13 | AC | 1,503 ms
88,696 KB |
| testcase_14 | AC | 2,466 ms
155,836 KB |
| testcase_15 | AC | 3,075 ms
162,496 KB |
| testcase_16 | AC | 3,075 ms
162,460 KB |
| testcase_17 | AC | 3,636 ms
263,428 KB |
| testcase_18 | AC | 3,667 ms
268,332 KB |
| testcase_19 | AC | 2,551 ms
162,496 KB |
| testcase_20 | AC | 2,537 ms
162,480 KB |
| testcase_21 | AC | 2,615 ms
162,224 KB |
| testcase_22 | AC | 2,627 ms
162,360 KB |
| testcase_23 | AC | 2,663 ms
162,336 KB |
| testcase_24 | AC | 2,649 ms
162,692 KB |
| testcase_25 | AC | 2,660 ms
162,504 KB |
| testcase_26 | AC | 2,668 ms
162,336 KB |
| testcase_27 | AC | 3,130 ms
162,464 KB |
| testcase_28 | AC | 3,113 ms
162,616 KB |
| testcase_29 | AC | 3,127 ms
162,464 KB |
| testcase_30 | AC | 3,107 ms
162,464 KB |
| testcase_31 | AC | 3,114 ms
162,336 KB |
| testcase_32 | AC | 3,113 ms
162,464 KB |
| testcase_33 | AC | 2,264 ms
162,444 KB |
| testcase_34 | AC | 2,269 ms
162,600 KB |
| testcase_35 | AC | 2,303 ms
162,472 KB |
| testcase_36 | AC | 2,754 ms
162,448 KB |
| testcase_37 | AC | 2,831 ms
162,412 KB |
| testcase_38 | AC | 2,809 ms
162,488 KB |
| testcase_39 | AC | 2,279 ms
162,564 KB |
| testcase_40 | AC | 2,304 ms
162,472 KB |
| testcase_41 | AC | 2,274 ms
162,564 KB |
| testcase_42 | AC | 2,279 ms
162,620 KB |
| testcase_43 | AC | 2,282 ms
162,572 KB |
ソースコード
#if !defined(MYLOCAL)//提出時用テンプレート
#pragma GCC optimize("Ofast")
#if defined(NDEBUG)
#undef NDEBUG
#endif
#include "bits/stdc++.h"
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#endif
using namespace std;
using ll=long long;
using dd=long double;
using pll=pair<ll,ll>;
using tll=tuple<ll,ll,ll>;
using qll=tuple<ll,ll,ll,ll>;
using ll2=array<ll,2>;
using ll3=array<ll,3>;
using ll4=array<ll,4>;
using namespace chrono;
constexpr ll INF = 1201001001001001001;
struct Fast{ Fast(){ cin.tie(0); ios::sync_with_stdio(false); cout<<fixed<<setprecision(numeric_limits<double>::max_digits10); } } fast;
#define EXPAND( x ) x//VS用おまじない
#define overload3(_1,_2,_3,name,...) name
#define overload4(_1,_2,_3,_4,name,...) name
#define overload5(_1,_2,_3,_4,_5,name,...) name
#define rep1(N) for (ll dmyi = 0; dmyi < (N); dmyi++)
#define rep2(i, N) for (ll i = 0; i < (N); i++)
#define rep3(i, S, E) for (ll i = (S); i <= (E); i++)
#define rep4(i, S, E, t) for (ll i = (S); i <= (E); i+=(t))
#define rep(...) EXPAND(overload4(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__))
#define dep3(i, E, S) for (ll i = (E); i >= (S); i--)
#define dep4(i, E, S, t) for (ll i = (E); i >= (S); i-=(t))
#define dep(...) EXPAND(overload4(__VA_ARGS__, dep4, dep3,_,_)(__VA_ARGS__))
#define ALL1(v) (v).begin(), (v).end()
#define ALL2(v,E) (v).begin(), (v).begin()+((E)+1)
#define ALL3(v,S,E) (v).begin()+(S), (v).begin()+((E)+1)
#define all(...) EXPAND(overload3(__VA_ARGS__, ALL3, ALL2, ALL1)(__VA_ARGS__))
#define RALL1(v) (v).rbegin(), (v).rend()
#define RALL2(v,E) (v).rbegin(), (v).rbegin()+((E)+1)
#define RALL3(v,S,E) (v).rbegin()+(S), (v).rbegin()+((E)+1)
#define rall(...) EXPAND(overload3(__VA_ARGS__, RALL3, RALL2, RALL1)(__VA_ARGS__))
template<class T> inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; }return false; }
template<class T> inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; }return false; }
template<class T> inline auto maxe(T &&v,ll S,ll E){ return *max_element(all(v,S,E)); }
template<class T> inline auto maxe(T &&v){ return *max_element(all(v)); }
template<class T> inline auto mine(T &&v,ll S,ll E){ return *min_element(all(v,S,E)); }
template<class T> inline auto mine(T &&v){ return *min_element(all(v)); }
template<class T,class U=typename remove_reference<T>::type::value_type>
inline U sum(T &&v,ll S,ll E) {return accumulate(all(v,S,E),U());}
template<class T> inline auto sum(T &&v) {return sum(v,0,v.end()-v.begin()-1);}
template<class T> inline ll sz(T &&v){ return (ll)v.size(); }
inline ll Ceil(ll a,ll b){ return (a<0) ? -(-a/b) : (a+b-1)/b; } //負もOK
inline ll Floor(ll a,ll b){ return -Ceil(-a,b); } //負もOK
inline ll Floormod(ll a,ll m){ return Floor(a,m)*m; } //負もOK
inline ll Ceilmod(ll a,ll m){ return Ceil(a,m)*m; } //負もOK
inline ll Mod(ll a,ll m){ ll r=a%m; if(r<0)r+=m; return r; } //負もOK
template<class T> inline T Pow(T a,ll n){ T r=1; for(; n>0; n>>=1,a*=a){ if(n&1)r*=a; } return r; }
inline ll Pow(int a,ll n){ return Pow((ll)a,n); }
inline ll limitmul(ll a,ll b,ll u){ return b==0||a<=u/b ? a*b : u; }//min(a*b,u) a,b,u≧0
//pair用テンプレート
template<class T,class S> inline pair<T,S>& operator+=(pair<T,S> &a,const pair<T,S> &b){ a.first+=b.first; a.second+=b.second; return a; }
template<class T,class S> inline pair<T,S>& operator-=(pair<T,S> &a,const pair<T,S> &b){ a.first-=b.first; a.second-=b.second; return a; }
template<class T,class S> inline pair<T,S>& operator*=(pair<T,S> &a,const pair<T,S> &b){ a.first*=b.first; a.second*=b.second; return a; }
template<class T,class S> inline pair<T,S>& operator/=(pair<T,S> &a,const pair<T,S> &b){ a.first/=b.first; a.second/=b.second; return a; }
template<class T,class S> inline pair<T,S>& operator%=(pair<T,S> &a,const pair<T,S> &b){ a.first%=b.first; a.second%=b.second; return a; }
template<class T,class S,class R> inline pair<T,S>& operator+=(pair<T,S> &a,R b){ a.first+=b; a.second+=b; return a; }
template<class T,class S,class R> inline pair<T,S>& operator-=(pair<T,S> &a,R b){ a.first-=b; a.second-=b; return a; }
template<class T,class S,class R> inline pair<T,S>& operator*=(pair<T,S> &a,R b){ a.first*=b; a.second*=b; return a; }
template<class T,class S,class R> inline pair<T,S>& operator/=(pair<T,S> &a,R b){ a.first/=b; a.second/=b; return a; }
template<class T,class S,class R> inline pair<T,S>& operator%=(pair<T,S> &a,R b){ a.first%=b; a.second%=b; return a; }
template<class T,class S,class R> inline pair<T,S> operator+(const pair<T,S> &a,R b){ pair<T,S> c=a; return c+=b; }
template<class T,class S,class R> inline pair<T,S> operator-(const pair<T,S> &a,R b){ pair<T,S> c=a; return c-=b; }
template<class T,class S,class R> inline pair<T,S> operator*(const pair<T,S> &a,R b){ pair<T,S> c=a; return c*=b; }
template<class T,class S,class R> inline pair<T,S> operator/(const pair<T,S> &a,R b){ pair<T,S> c=a; return c/=b; }
template<class T,class S,class R> inline pair<T,S> operator%(const pair<T,S> &a,R b){ pair<T,S> c=a; return c%=b; }
template<class T,class S,class R> inline pair<T,S> operator-(R b,const pair<T,S> &a){ pair<T,S> c=-a; return c+=b; }
template<class T,class S> inline pair<T,S> operator-(const pair<T,S> &a,const pair<T,S> &b){ pair<T,S> c=a; return c-=b; }
template<class T,class S> inline pair<T,S> operator-(const pair<T,S> &a){ pair<T,S> c=a; return c*=(-1); }
template<class T,class S> inline ostream &operator<<(ostream &os,const pair<T,S> &a){ return os << a.first << ' ' << a.second; }
//tuple用テンプレート 出力用のみ
template<class T,class S,class R> inline ostream &operator<<(ostream &os,const tuple<T,S,R> &a){ return os << get<0>(a) << ' ' << get<1>(a) << ' ' << get<2>(a); }
template<class T,class S,class R,class Q> inline ostream &operator<<(ostream &os,const tuple<T,S,R,Q> &a){ return os << get<0>(a) << ' ' << get<1>(a) << ' ' << get<2>(a) << ' ' << get<3>(a); }
//vector用テンプレート
template<class T> inline ostream &operator<<(ostream &os,const vector<T> &a){ for (ll i=0; i<(ll)a.size(); i++) os<<(i>0?" ":"")<<a[i]; return os; }
//array用テンプレート
template<class T,size_t S> inline array<T,S>& operator+=(array<T,S> &a,const array<T,S> &b){ for (ll i=0; i<(ll)S; i++) a[i]+=b[i]; return a; }
template<class T,size_t S> inline array<T,S>& operator-=(array<T,S> &a,const array<T,S> &b){ for (ll i=0; i<(ll)S; i++) a[i]-=b[i]; return a; }
template<class T,size_t S> inline array<T,S>& operator*=(array<T,S> &a,const array<T,S> &b){ for (ll i=0; i<(ll)S; i++) a[i]*=b[i]; return a; }
template<class T,size_t S> inline array<T,S>& operator/=(array<T,S> &a,const array<T,S> &b){ for (ll i=0; i<(ll)S; i++) a[i]/=b[i]; return a; }
template<class T,size_t S> inline array<T,S>& operator%=(array<T,S> &a,const array<T,S> &b){ for (ll i=0; i<(ll)S; i++) a[i]%=b[i]; return a; }
template<class T,size_t S,class R> inline array<T,S>& operator+=(array<T,S> &a,R b){ for (T &e: a) e+=b; return a; }
template<class T,size_t S,class R> inline array<T,S>& operator-=(array<T,S> &a,R b){ for (T &e: a) e-=b; return a; }
template<class T,size_t S,class R> inline array<T,S>& operator*=(array<T,S> &a,R b){ for (T &e: a) e*=b; return a; }
template<class T,size_t S,class R> inline array<T,S>& operator/=(array<T,S> &a,R b){ for (T &e: a) e/=b; return a; }
template<class T,size_t S,class R> inline array<T,S>& operator%=(array<T,S> &a,R b){ for (T &e: a) e%=b; return a; }
template<class T,size_t S,class R> inline array<T,S> operator+(const array<T,S> &a,R b){ array<T,S> c=a; return c+=b; }
template<class T,size_t S,class R> inline array<T,S> operator-(const array<T,S> &a,R b){ array<T,S> c=a; return c-=b; }
template<class T,size_t S,class R> inline array<T,S> operator*(const array<T,S> &a,R b){ array<T,S> c=a; return c*=b; }
template<class T,size_t S,class R> inline array<T,S> operator/(const array<T,S> &a,R b){ array<T,S> c=a; return c/=b; }
template<class T,size_t S,class R> inline array<T,S> operator%(const array<T,S> &a,R b){ array<T,S> c=a; return c%=b; }
template<class T,size_t S,class R> inline array<T,S> operator-(R b,const array<T,S> &a){ array<T,S> c=-a; return c+=b; }
template<class T,size_t S> inline array<T,S> operator-(const array<T,S> &a,const array<T,S> &b){ array<T,S> c=a; return c-=b; }
template<class T,size_t S> inline array<T,S> operator-(const array<T,S> &a){ array<T,S> c=a; return c*=(-1); }
template<class T,size_t S> inline ostream &operator<<(ostream &os,const array<T,S> &a){ for (ll i=0; i<(ll)S; i++) os<<(i>0?" ":"")<<a[i]; return os; }
inline struct{
system_clock::time_point st = system_clock::now();
ll operator()()const{return duration_cast<microseconds>(system_clock::now()-st).count()/1000;}
} timeget;
struct cinutil{
template<class T> static void cin1core(T &a){ cin>>a; }
template<class T,class S> static void cin1core(pair<T,S> &a){
cin1core(a.first), cin1core(a.second);
}
template<class... Args> static void cin1core(tuple<Args...> &a){
cinTplRec<tuple<Args...>,sizeof...(Args)-1>()(a);
}
template<class T,size_t N>
static void cin1core(array<T,N> &a){for(int i=0;i<(int)N;++i) cin>>a[i];}
private:
template<class Tpl,int i> struct cinTplRec{
void operator()(Tpl &a){ cinTplRec<Tpl,i-1>()(a); cin1core(get<i>(a)); }
};
template<class Tpl> struct cinTplRec<Tpl,0>{
void operator()(Tpl &a){ cin1core(get<0>(a)); }
};
};
template<class T> T cin1(){ T a; cinutil::cin1core(a); return a; }
template<class... Args> tuple<Args...> cins(){ return cin1<tuple<Args...>>(); }
template<long long MOD> struct mll_{
using Int = long long;
using ll = long long;
ll val_=0;
/*---- utility ----*/
mll_ &norm(){ return normR().normS(); }//正規化
mll_ &normR(){ val_%=MOD; return *this; }//剰余正規化のみ
mll_ &normS(){ if (val_<0) val_+=MOD; return *this; }//正負正規化のみ
mll_ &normP(){ if (val_>=MOD) val_-=MOD; return *this; }//加算時正規化
mll_ &invsg(){ val_=-val_; return normS(); }//正負反転
ll modinv(int a){//a^-1 mod MOD
int ypre=0,y=1,apre=MOD;
while (a>1){
int t=apre/a;
apre-=a*t,swap(a,apre);
ypre-=y*t,swap(y,ypre);
}
return y<0 ? y+MOD: y;
}
/*---- I/F ----*/
mll_(){}
mll_(ll v): val_(v){ norm(); }
mll_(ll v,bool b): val_(v){} //正規化無のコンストラクタ
Int val()const{ return (Int)val_; }
bool isnone() const { return val_==-1; } //true:値なし
mll_ &none() { val_=-1; return *this; } //値なしにする
mll_ &inv(){ val_=modinv((int)val_); return *this; }
mll_ &operator+=(mll_ b){ val_+=b.val_; return normP(); }
mll_ &operator-=(mll_ b){ val_-=b.val_; return normS(); }
mll_ &operator*=(mll_ b){ val_*=b.val_; return normR(); }
mll_ &operator/=(mll_ b){ return *this*=b.inv(); }
mll_ &operator+=(ll b){ return *this+=mll_(b); }
mll_ &operator-=(ll b){ return *this-=mll_(b); }
mll_ &operator*=(ll b){ return *this*=mll_(b); }
mll_ &operator/=(ll b){ return *this/=mll_(b); }
mll_ &operator--(int){ return *this-=1; }
mll_ &operator++(int){ return *this+=1; }
mll_ operator-()const{ return mll_(*this).invsg(); }
mll_ operator+(mll_ b)const{ return mll_(*this)+=b; }
mll_ operator-(mll_ b)const{ return mll_(*this)-=b; }
mll_ operator*(mll_ b)const{ return mll_(*this)*=b; }
mll_ operator/(mll_ b)const{ return mll_(*this)/=b; }
mll_ operator+(ll b)const{ return mll_(*this)+=b; }
mll_ operator-(ll b)const{ return mll_(*this)-=b; }
mll_ operator*(ll b)const{ return mll_(*this)*=b; }
mll_ operator/(ll b)const{ return mll_(*this)/=b; }
friend mll_ operator+(ll a,mll_ b){ return b+a; }
friend mll_ operator-(ll a,mll_ b){ return -b+a; }
friend mll_ operator*(ll a,mll_ b){ return b*a; }
friend mll_ operator/(ll a,mll_ b){ return mll_(a)/b; }
bool operator==(mll_ b)const{ return val_==b.val_; }
bool operator!=(mll_ b)const{ return val_!=b.val_; }
bool operator==(ll b)const{ return *this==mll_(b); }
bool operator!=(ll b)const{ return *this!=mll_(b); }
friend bool operator==(ll a,mll_ b){ return mll_(a)==b; }
friend bool operator!=(ll a,mll_ b){ return mll_(a)!=b; }
friend ostream &operator<<(ostream &os,mll_ a){ return os << a.val_; }
friend istream &operator>>(istream &is,mll_ &a){ return is >> a.val_; }
mll_ pow(ll k)const{
mll_ ret(1,false),a(*this);
for (; k>0; k>>=1,a*=a) if (k&1)ret*=a;
return ret;
}
static constexpr int mod() { return MOD; }
//enum{ modll=MOD };
};
struct bll{
ll s=0;
bll(ll s_=0): s(s_){}
bll(int s_): s(s_){}
bll(const string &bitstr): s(str2val(bitstr)){}
bll(const char *bitstr): s(str2val(bitstr)){}
struct ref {
bll &b; const ll msk;
ref(bll &b_,ll pos):b(b_),msk(1LL<<pos){}
operator ll() const { return (b.s&msk)!=0; }
ref &operator=(bool x){ if(x) b.s|=msk; else b.s&=~msk; return *this; }
};
ref operator[](ll pos){ return ref(*this,pos); }
ll operator[](ll pos) const { return (s>>pos)&1; }
bll &operator=(int b){ s=b; return *this; }
bll &operator=(ll b){ s=b; return *this; }
bll &operator=(const string &bitstr){ s=str2val(bitstr); return *this; }
bll &operator=(const char *bitstr){ s=str2val(bitstr); return *this; }
bll operator++(int){ bll b(*this); s++; return b; }
bll operator--(int){ bll b(*this); s--; return b; }
operator ll() const noexcept { return s; }
bll &operator&=(ll b){ s&=b; return *this; }
bll &operator|=(ll b){ s|=b; return *this; }
bll &operator^=(ll b){ s^=b; return *this; }
bll &operator+=(ll b){ s+=b; return *this; }
bll &operator-=(ll b){ s-=b; return *this; }
bll &operator<<=(ll i){ s<<=i; return *this; }
bll &operator>>=(ll i){ s>>=i; return *this; }
bll operator&(ll b)const{ return s&b; }
bll operator|(ll b)const{ return s|b; }
bll operator^(ll b)const{ return s^b; }
bll operator+(ll b)const{ return s+b; }
bll operator-(ll b)const{ return s-b; }
bll operator<<(ll i)const{ return s<<i; }
bll operator>>(ll i)const{ return s>>i; }
bll operator&(int b)const{ return s&b; }
bll operator|(int b)const{ return s|b; }
bll operator^(int b)const{ return s^b; }
bll operator+(int b)const{ return s+b; }
bll operator-(int b)const{ return s-b; }
bll operator<<(int i)const{ return s<<i; }
bll operator>>(int i)const{ return s>>i; }
bll operator~()const{ return ~s; }
bll &oneq (bll msk){ s|= msk.s; return *this; }
bll &offeq (bll msk){ s&=~msk.s; return *this; }
bll &flipeq(bll msk){ s^= msk.s; return *this; }
bll on (bll msk)const{ return bll(s).oneq (msk); }
bll off (bll msk)const{ return bll(s).offeq (msk); }
bll flip (bll msk)const{ return bll(s).flipeq(msk); }
bool any0(bll msk)const{ return ~s&msk.s; }
bool any1(bll msk)const{ return s&msk.s; }
bool all0(bll msk)const{ return !any1(msk); }
bool all1(bll msk)const{ return !any0(msk); }
bll &oneq (ll l,ll r){ return oneq (rngmsk(l,r)); }
bll &offeq (ll l,ll r){ return offeq (rngmsk(l,r)); }
bll &flipeq(ll l,ll r){ return flipeq(rngmsk(l,r)); }
bll on (ll l,ll r)const{ return on (rngmsk(l,r)); }
bll off (ll l,ll r)const{ return off (rngmsk(l,r)); }
bll flip (ll l,ll r)const{ return flip(rngmsk(l,r)); }
bool any0(ll l,ll r)const{ return any0(rngmsk(l,r)); }
bool any1(ll l,ll r)const{ return any1(rngmsk(l,r)); }
bool all0(ll l,ll r)const{ return all0(rngmsk(l,r)); }
bool all1(ll l,ll r)const{ return all1(rngmsk(l,r)); }
bll &maskeq(ll l,ll r){ s&=rngmsk(l,r); return *this; }
bll mask(ll l,ll r)const{ return bll(s).maskeq(l,r); }
bll &oneq (ll i){ s|= (1LL<<i); return *this; }
bll &offeq (ll i){ s&=~(1LL<<i); return *this; }
bll &flipeq(ll i){ s^= (1LL<<i); return *this; }
bll on (ll i)const{ return s| (1LL<<i); }
bll off (ll i)const{ return s&~(1LL<<i); }
bll flip(ll i)const{ return s^ (1LL<<i); }
bool contains(ll b)const{ return (s&b)==b; }
bll substr(ll l,ll r)const{ return (s&rngmsk(l,r))>>r; }
static bll rngmsk(ll l,ll r){ return (1LL<<(l+1))-(1LL<<r); }
ll msbit()const{
for(ll x=63,o=-1;;){
ll m=(x+o)/2;
if((1LL<<m)<=s) o=m; else x=m;
if(x-o==1) return o;
}
}
ll lsbit()const{ return bll(lsb()).msbit(); }
ll msb()const{ ll pos=msbit(); return (pos<0) ? 0LL : 1LL<<pos; }
ll lsb()const{ return s&-s; }
ll count()const{ return bitset<64>(s).count(); }
ll count(bll msk)const{ return (msk&s).count(); }
ll count(ll l,ll r)const{ return mask(l,r).count(); }
vector<ll> idxes()const{
vector<ll> v;
for(ll i=0,t=s; t; t>>=1,i++) if(t&1)v.push_back(i);
return v;
}
string to_string(ll wd=-1)const{
wd=max({wd,msbit()+1,1LL});
string ret;
for(ll i=wd-1;i>=0;--i) ret += '0'+char((s>>i)&1);
return ret;
}
private:
ll str2val(const string &bitstr){
ll val=0, len=(ll)bitstr.size();
for(ll i=0;i<len;++i) val|=ll(bitstr[i]-'0')<<(len-1-i);
return val;
}
};
template<class T> struct SET: set<T>{
using P=set<T>;
typename P::iterator it=P::end();
template<class...Args> SET(Args...args): P(args...){}
SET(initializer_list<T> a): P(a.begin(),a.end()){}
ll size() const { return (ll)P::size(); }
bool insert(const T &x){ bool r; tie(it,r)=P::insert(x); return r; }
template <class It> void insert(It st,It en){ P::insert(st,en); }
void insert(initializer_list<T> a){ P::insert(a.begin(),a.end()); }
template<class...A> bool emplace(A&&...a){ bool r; tie(it,r)=P::emplace(a...); return r; }
void eraseit(){ it=P::erase(it); }
void find(const T &x){ it=P::find(x); }
bool contains(const T &x){ return P::count(x)==1; }
void lower_bound(const T &x){ it=P::lower_bound(x); }
void upper_bound(const T &x){ it=P::upper_bound(x); }
bool isend() { return it==P::end(); }
T getit() { return *it; }
T next() { return *(++it); }
T prev() { return *(--it); }
bool nextok() { return !isend() && it!=--P::end(); }
bool prevok() { return it!=P::begin(); }
T front() { return *(it=P::begin()); }
T back() { return *(it=--P::end()); }
void pop_front(){ front(); eraseit(); }
void pop_back(){ back(); eraseit(); }
void push_front(const T &x){ it=P::insert(P::begin(),x); }
void push_back (const T &x){ it=P::insert(P::end(),x); }
void push_out(SET &b){ b.push_front(back()); pop_back(); }
void pull_in(SET &b){ push_back(b.front()); b.pop_front(); }
};
template<class T> struct cumulativesum{
using Int = long long;
using ll = long long;
ll n=0; vector<T> c;
cumulativesum():c(1){}
template<class S> cumulativesum(S &&v): n((ll)v.size()),c(n+1) { Ini(v); }
template<class S> void init(S &&v){ n=(ll)v.size(); c.resize(n+1); Ini(v); }
void add(T x) { n++; c.push_back(c.back()+x); }
T operator()(Int l,Int r){ return c[max(min(n,r+1),0LL)]-c[min(max(0LL,l),n)]; }
pair<Int,T> group(T i){
ll g=upper_bound(c.begin(),c.end(),i)-c.begin()-1;
T r = g>=0 ? i-c[g] : i;
return {g,r};
}
T mx(){//区間和max
T mn=T(),samx=0;
for(ll i=1;i<=n;++i){
chmax(samx,c[i]-mn);
chmin(mn,c[i]);
}
return samx;
}
template<class S> void Ini(S &&v) { for(ll i=0;i<n;++i) c[i+1]=c[i]+v[i]; }
};
template<class S> cumulativesum(S) -> cumulativesum<typename remove_reference<S>::type::value_type>;
template<class T> vector<T> powers(T m,ll n){
vector<T> ret(n+1,1);
for(ll i=1;i<=n;++i) ret[i]=ret[i-1]*m;
return ret;
}
template <class T> auto runlength(T &&v){
vector<pair<typename remove_reference<T>::type::value_type,ll>> ret;
for(auto&&e:v){
if(ret.empty() or ret.back().first!=e) ret.emplace_back(e,1);
else ret.back().second++;
}
return ret;
}
inline vector<ll> str2num(string &s,char base,const string &etc){
vector<ll> v(s.size());
for(ll i=0;i<(ll)s.size();++i){
size_t pos=etc.find(s[i]);
if(pos==etc.npos) v[i]=s[i]-(ll)base;
else v[i]=-((ll)pos+1);
}
return v;
}
template<class T> struct combination{
vector<T> f,g; ll mxN=0;
combination(){}
combination(ll maxN): f(maxN+1,1),g(maxN+1),mxN(maxN) {
for (ll i=1;i<=mxN;++i) { f[i]=f[i-1]*i; }
g[mxN]=1/f[mxN];
for (ll i=mxN;i>=1;--i) { g[i-1]=g[i]*i; }
}
T P(ll n,ll r){ return (n<0 || r<0 || n<r) ? T(0) : f[n]*g[n-r]; } //nPr
T H(ll n,ll r){ return operator()(n+r-1,n-1); }//nHr
T inv(ll n) { return f[n-1] * g[n]; } //1/n
T fact(ll n) { return f[n]; } //n!
T finv(ll n) { return g[n]; } //1/n!
T operator()(ll n,ll r){
if (r<0) return 0;
if (n<0) return operator()(-n+r-1,r) * ((r&1)?-1:1); //-nＣr = (-1)^r * n+r-1Ｃr
if (n<r) return 0;
if (n<=mxN) return f[n]*g[n-r]*g[r]; //通常
//n巨大、rかn-r小
if (n-r<r) r=n-r;
T bunsi=1,bunbo=1;
for (ll i=0;i<r;++i) bunsi*=n-i;
for (ll i=0;i<r;++i) bunbo*=i+1;
return bunsi/bunbo;
}
template<class SP>
vector<T> CnLnR(long long nL,long long nR,long long r,SP sp){
if (nR-nL+1<=0) return vector<T>();
if (r<0) return vector<T>(nR-nL+1,0);
vector<T> v=sp(nL-r+1,nR-r+1,r);
for (T& e: v) e*=finv(r);
return v;
}
template<class SP>
vector<T> HrLrR(long long n,long long rL,long long rR,SP sp){//r<0不可
return CnLnR(n-1+rL,n-1+rR,n-1,sp);
}
};
template<class T> struct wrapVector1d{
using S=typename T::value_type;
using Int = long long;
const T *v;
S Ini;
wrapVector1d(const T &v_,S ini_=S()):v(&v_),Ini(ini_){}
S operator[](Int i)const{ return (i<0 || (Int)v->size()<=i) ? Ini : (*v)[i]; }
};
template<class T> struct wrapVector2d{
using S=typename T::value_type;
using Int = long long;
const vector<T> *v;
S Ini;
T dmy;
wrapVector2d(const vector<T> &v_,S ini_=S()):v(&v_),Ini(ini_){}
wrapVector1d<T> operator[](ll i)const{
return (i<0 || (Int)v->size()<=i) ?
wrapVector1d(dmy,Ini) : wrapVector1d((*v)[i],Ini);
}
};
namespace dumpstring{//dummy
struct args{
using Int = long long;
args(){}
args &wd(Int wd__){ (void)wd__; return *this; }
template<size_t DIM> args &rngs(array<array<Int,DIM>,2> rngs){ return *this; }
args &tr(vector<Int> tr__){ (void)tr__; return *this; }
args &tr(){ return *this; }
args &labels(vector<string> labels__){ (void)labels__; return *this; }
args &xrev(){ return *this; }
args &yrev(){ return *this; }
args &zrev(){ return *this; }
args &wrev(){ return *this; }
};
template<class NdT>
void dumpNd(const string &h,const NdT &fd,const args &p=args(),ostream &os=cerr){}
};
using dumpstring::args; using dumpstring::dumpNd;
#endif//テンプレートend
template<class T> struct Vector: vector<T>{
using Int = long long;
using vT=vector<T>;
using cvT=const vector<T>;
using cT=const T;
using vT::vT; //親クラスのコンストラクタの隠蔽を回避
using vT::begin,vT::end,vT::insert,vT::erase;
auto it(Int i){ return begin()+i; }
auto it(Int i)const{ return begin()+i; }
Vector(cvT& b):vT(b){}
Vector(vT&& b):vT(move(b)){}
Vector(int n,cT& x):vT(n,x){}// ┬ 型推論のためラッパー
Vector(long long n,cT& x):vT(n,x){}
template<class S> Vector(const Vector<S>& b):vT(b.begin(),b.end()){}
template<class S> Vector(const vector<S>& b):vT(b.begin(),b.end()){}
Vector(Int n,T s,T d){ iota(n,s,d); }
Vector(Int n,function<T(Int)> g):vT(n){ for(Int i=0;i<n;++i) (*this)[i]=g(i); }
Vector &operator+=(cvT &b){ assert(size()==b.size()); for(Int i=0;i<size();++i) (*this)[i]+=b[i]; return *this; }
Vector &operator-=(cvT &b){ assert(size()==b.size()); for(Int i=0;i<size();++i) (*this)[i]-=b[i]; return *this; }
Vector &operator*=(cvT &b){ assert(size()==b.size()); for(Int i=0;i<size();++i) (*this)[i]*=b[i]; return *this; }
Vector &operator/=(cvT &b){ assert(size()==b.size()); for(Int i=0;i<size();++i) (*this)[i]/=b[i]; return *this; }
Vector &operator%=(cvT &b){ assert(size()==b.size()); for(Int i=0;i<size();++i) (*this)[i]%=b[i]; return *this; }
Vector &operator+=(const Vector<T> &b){ return *this+=(cvT&)b; }
Vector &operator-=(const Vector<T> &b){ return *this-=(cvT&)b; }
Vector &operator*=(const Vector<T> &b){ return *this*=(cvT&)b; }
Vector &operator/=(const Vector<T> &b){ return *this/=(cvT&)b; }
Vector &operator%=(const Vector<T> &b){ return *this%=(cvT&)b; }
Vector operator+(cvT &b){ return Vector(*this)+=b; }
Vector operator-(cvT &b){ return Vector(*this)-=b; }
Vector operator*(cvT &b){ return Vector(*this)*=b; }
Vector operator/(cvT &b){ return Vector(*this)/=b; }
Vector operator%(cvT &b){ return Vector(*this)%=b; }
Vector operator+(const Vector<T> &b){ return Vector(*this)+=b; }
Vector operator-(const Vector<T> &b){ return Vector(*this)-=b; }
Vector operator*(const Vector<T> &b){ return Vector(*this)*=b; }
Vector operator/(const Vector<T> &b){ return Vector(*this)/=b; }
Vector operator%(const Vector<T> &b){ return Vector(*this)%=b; }
template<class S> Vector &operator+=(S x){ for(T &e: *this) e+=x; return *this; }
template<class S> Vector &operator-=(S x){ for(T &e: *this) e-=x; return *this; }
template<class S> Vector &operator*=(S x){ for(T &e: *this) e*=x; return *this; }
template<class S> Vector &operator/=(S x){ for(T &e: *this) e/=x; return *this; }
template<class S> Vector &operator%=(S x){ for(T &e: *this) e%=x; return *this; }
template<class S> Vector operator+(S x)const{ return Vector(*this)+=x; }
template<class S> Vector operator-(S x)const{ return Vector(*this)-=x; }
template<class S> Vector operator*(S x)const{ return Vector(*this)*=x; }
template<class S> Vector operator/(S x)const{ return Vector(*this)/=x; }
template<class S> Vector operator%(S x)const{ return Vector(*this)%=x; }
Vector &operator--(int){ return *this-=T(1); }
Vector &operator++(int){ return *this+=T(1); }
Vector operator-()const{ return Vector(*this)*=-1; }
template<class S> friend Vector operator-(S x,const Vector &a){ return -a+=x; }
Vector slice(Int l,Int r,Int d=1)const{
Vector ret;
for(Int i=l;(d>0&&i<=r)||(d<0&&r<=i);i+=d) ret.push_back((*this)[i]);
return ret;
}
Int size()const{ return (Int)vT::size(); }
Vector &push_back(cT& x,Int n=1){ for(Int i=0;i<n;++i){ vT::push_back(x); } return *this; }
Vector &pop_back(Int n=1){ for(Int i=0;i<n;++i){ vT::pop_back(); } return *this; }
Vector &push_front(cT& x,Int n=1){ this->insert(0,x,n); return *this; }
Vector &pop_front(Int n=1){ erase(0,n-1); return *this; }
T pull_back(){ T x=move(vT::back()); vT::pop_back(); return x; }
T pull_front(){ T x=move(vT::front()); erase(0); return x; }
Vector &insert(Int i,cT& x,Int n=1){ insert(it(i),n,x); return *this; }
Vector &insert(Int i,cvT& b){ insert(it(i),b.begin(),b.end()); return *this; }
Vector &erase(Int i){ erase(it(i)); return *this; }
Vector &erase(Int l,Int r){ erase(it(l),it(r+1)); return *this; }
Vector &concat(cvT &b,Int n=1){
cvT B = (&b==this) ? *this : vT{};
for(int i=0;i<n;++i) this->insert(size(),(&b==this)?B:b);
return *this;
}
Vector repeat(Int n){ return Vector{}.concat(*this,n); }
Vector &reverse(Int l=0,Int r=-1){ r+=r<0?size():0; std::reverse(it(l),it(r+1)); return *this; }
Vector &rotate(Int m){ return rotate(0,size()-1,m); }
Vector &rotate(Int l,Int r,Int m){ std::rotate(it(l),it(m),it(r+1)); return *this; }
Vector &sort(Int l=0,Int r=-1){ r+=r<0?size():0; std::sort(it(l),it(r+1)); return *this; }
Vector &rsort(Int l=0,Int r=-1){ return sort(l,r).reverse(l,r); }
template<class Pr> Vector &sort(Pr pr){ return sort(0,size()-1,pr); }
template<class Pr> Vector &sort(Int l,Int r,Pr pr){ std::sort(it(l),it(r+1),pr); return *this; }
Vector &uniq(){ erase(unique(begin(),end()),end()); return *this; }
Vector &sortq(){ return sort().uniq(); }
Vector &fill(cT& x){ return fill(0,size()-1,x); }
Vector &fill(Int l,Int r,cT& x){ std::fill(it(l),it(r+1),x); return *this; }
template<class S=Int> Vector &iota(Int n,T s=0,S d=1){
vT::resize(n);
if(n==0) return *this;
(*this)[0]=s;
for(int i=1;i<n;++i) (*this)[i]=(*this)[i-1]+d;
return *this;
}
Int count(cT& x)const{ return count(0,size()-1,x); }
Int count(Int l,Int r,cT& x)const{ return Int(std::count(it(l),it(r+1),x)); }
template<class Pr> Int countif(Pr pr)const{ return countif(0,size()-1,pr); }
template<class Pr> Int countif(Int l,Int r,Pr pr)const{ return Int(count_if(it(l),it(r+1),pr)); }
Int find(cT& x)const{ return find(0,size()-1,x); }
Int find(Int l,Int r,cT& x)const{ return Int(std::find(it(l),it(r+1),x)-begin()); }
template<class Pr> Int findif(Pr pr)const{ return findif(0,size()-1,pr); }
template<class Pr> Int findif(Int l,Int r,Pr pr)const{ return Int(find_if(it(l),it(r+1),pr)-begin()); }
Vector<Int> findall(cT& x)const{ return findall(0,size()-1,x); }
Vector<Int> findall(Int l,Int r,cT& x)const{ return findallif(l,r,[&](cT& y){return y==x;}); }
template<class Pr> Vector<Int> findallif(Pr pr)const{ return findallif(0,size()-1,pr); }
template<class Pr> Vector<Int> findallif(Int l,Int r,Pr pr)const{
Vector<Int> ret;
for(Int i=l;i<=r;++i) if(pr((*this)[i])) ret.push_back(i);
return ret;
}
Int flooridx(cT& x)const{ return Int(upper_bound(begin(),end(),x)-begin()-1); }
Int ceilidx(cT& x)const{ return Int(lower_bound(begin(),end(),x)-begin()); }
Int leftnmof(cT& x)const{ return flooridx(x)+1; }
Int rightnmof(cT& x)const{ return size()-ceilidx(x); }
bool contains(cT& x)const{ Int i=flooridx(x); return i>=0 && (*this)[i]==x; }
template<class Pr> Int flooridx(cT& x,Pr pr)const{ return Int(upper_bound(begin(),end(),x,pr)-begin()-1); }
template<class Pr> Int ceilidx(cT& x,Pr pr)const{ return Int(lower_bound(begin(),end(),x,pr)-begin()); }
template<class Pr> Int leftnmof(cT& x,Pr pr)const{ return flooridx(x,pr)+1; }
template<class Pr> Int rightnmof(cT& x,Pr pr)const{ return size()-ceilidx(x,pr); }
template<class Pr> bool contains(cT& x,Pr pr)const{ Int i=flooridx(x,pr); return i>=0 && (*this)[i]==x; }
template<class S> using VV = Vector<Vector<S>>; template<class S> using sVV = vector<vector<S>>;
template<class S> using VVV = Vector<VV<S>>; template<class S> using sVVV = vector<sVV<S>>;
template<class S> using VVVV = Vector<VVV<S>>; template<class S> using sVVVV = vector<sVVV<S>>;
template<class S> using VVVVV = Vector<VVVV<S>>; template<class S> using sVVVVV = vector<sVVVV<S>>;
auto tostd()const{ return tov(*this); }
template <class S> static vector<S> tov(const Vector<S>&v){ return v; }
template <class S> static sVV<S> tov(const VV<S> &v){ sVV<S> ret; for(auto&& e:v) ret.push_back(e); return ret; }
template <class S> static sVVV<S> tov(const VVV<S> &v){ sVVV<S> ret; for(auto&& e:v) ret.push_back(e.tostd()); return ret; }
template <class S> static sVVVV<S> tov(const VVVV<S> &v){ sVVVV<S> ret; for(auto&& e:v) ret.push_back(e.tostd()); return ret; }
template <class S> static sVVVVV<S> tov(const VVVVV<S> &v){ sVVVVV<S> ret; for(auto&& e:v) ret.push_back(e.tostd()); return ret; }
};
/*
vll a={9,8,7},b={1,2,3};
vpll p={{5,3},{7,8},{0,2},};
- -------- 操作系 --------
a+=x a-=x a*=x a/=x a%=x a+x a-x a*x a/x a%x -a x-a a++ a-- //∀i a[i]にxを演算
a+=b a-=b a*=b a/=b a%=b a+b a-b a*b a/b a%b //要素毎演算(同サイズ時)
a.push_front(x,n); //n個先頭追加 省略時1
a.push_back(x,n); //n個末尾追加 省略時1
a.pop_front(n); //n個先頭削除 省略時1
a.pop_back(n); //n個末尾削除 省略時1
ll x=a.pull_front(); //pop_front()と同時に値取得
ll x=a.pull_back(); //pop_back()と同時に値取得
a.insert(i,x,n); //a[i]にn個x挿入 n省略時1
a.insert(i,b); //a[i]にvll b挿入
a.erase(i); //a[i]削除
a.erase(l,r); //区間[l,r]削除
a.concat(b); //aにbを結合 b=a可
a.concat(b,n); //aにbをn回結合 b=a可
a.reverse(l,r); //[l,r]を反転 l,r省略可
a.rotate(m); //a[m]を先頭にするrotate
a.rotate(l,r,m); //a[m]を先頭にするrotate 範囲[l,r]
a.sort(l,r); //[l,r]をソート l,r省略可
a.rsort(l,r); //[l,r]を逆順ソート l,r省略可
p.sort(l,r,[&](pll x,pll y){return x.second<y.second;});//比較関数指定sort l,r省略可
a.uniq(); //連続同値を1つにする
a.sortq(); //ソートしてユニーク
a.fill(l,r,x); //[l,r]にx代入 l,r省略可
a.iota(n,s,d); //aを等差数列にする 長さn,初項s,公差d
vll a(n,s,d); //コンストラクタ版iota
vll b=a.slice(st,en,d); //a[st:en:d] d省略時1
vll b=a.repeat(n); //aをn回繰り返す
- -------- 検索系 --------
auto pr=[&](auto &x){ return x>0; }; //検索条件
ll m=a.count(x); //xの個数
ll m=a.count(l,r,x); //xの個数in[l,r]
ll m=a.countif(pr); //条件満たす個数
ll m=a.countif(l,r,pr); //条件満たす個数in[l,r]
ll i=a.find(x); //xの最左位置i ない時N(配列長)
ll i=a.find(l,r,x); //xの最左位置i in[l,r] ない時r+1
ll i=a.findif(pr); //条件満たす最左位置i ない時N(配列長)
ll i=a.findif(l,r,pr); //条件満たす最左位置i in[l,r] ない時r+1
vll is=a.findall(x); //xの位置i列挙
vll is=a.findall(l,r,x); //xの位置i列挙in[l,r]
vll is=a.findallif(pr); //条件満たす位置i列挙
vll is=a.findallif(l,r,pr); //条件満たす位置i列挙in[l,r]
- -------- 昇順sort済み配列用 --------
ll i=a.flooridx(x); //x以下の最近傍位置i ない時-1
ll i=a.ceilidx(x); //x以上の最近傍位置i ない時N(配列長)
ll m=a.leftnmof(x); //x以下の個数
ll m=a.rightnmof(x); //x以上の個数
bool b=a.contains(x); //xを含む
- -------- 比較関数prでsort済みの配列用 --------
auto pr=[&](auto &x,auto &y){ return x>y; }; //降順ソート時
ll i=a.flooridx(x,pr); //x以左の最近傍位置i ない時-1
ll i=a.ceilidx(x,pr); //x以右の最近傍位置i ない時N(配列長)
ll m=a.leftnmof(x,pr); //x以左の個数
ll m=a.rightnmof(x,pr); //x以右の個数
bool b=a.contains(x,pr); //xを含む
a.concat(b,n).pop_back().rsort().uniq(); //連続適用できる
auto aa=a.tostd(); //N次元VectorをN次元vectorに変換(N≦5)
*/
template<class T> struct wrapv: Vector<T>{
using Int = long long;
T def=T();
T defIF=T();
wrapv(const Vector<T> &b):Vector<T>(b){}
wrapv(Vector<T> &&b):Vector<T>(move(b)){}
wrapv(const std::vector<T> &b):Vector<T>(b){}
wrapv(std::vector<T> &&b):Vector<T>(move(b)){}
T &operator[](Int i){
return (i<0 || this->size()<=i) ? (defIF=def) : Vector<T>::operator[](i);
}
void setdef(const T& x){ def=x; }
};
/*
wrapv v=vll(N,0,1); //vllなどでコンストラクトしてから代入する
v.setdef(INF); //範囲外での値セット
*/
struct fraction{
ll bunsi=0,bunbo=1;
/*---- utilty ----*/
fraction &norm(){//正規化(約分,分母正)
ll g=gcd(bunsi,bunbo);
bunsi/=g,bunbo/=g;
if(bunbo<0) bunsi*=-1,bunbo*=-1;
return *this;
}
fraction &invsg(){//正負反転
bunsi*=-1;
return *this;
}
/*---- I/F ----*/
fraction(){}
fraction(ll bunsi_,ll bunbo_):bunsi(bunsi_),bunbo(bunbo_){
norm();
}
fraction(ll b):bunsi(b){}//整数用コンストラクタ
fraction(ll bunsi_,ll bunbo_,bool)//正規化無のコンストラクタ
:bunsi(bunsi_),bunbo(bunbo_){}
fraction &operator+=(fraction b){
ll bo=bunbo*b.bunbo;
ll si=bunsi*b.bunbo + b.bunsi*bunbo;
bunsi=si,bunbo=bo;
return norm();
}
fraction &operator-=(fraction b){
return (*this)+=b.invsg();
}
fraction &operator*=(fraction b){
bunsi*=b.bunsi;
bunbo*=b.bunbo;
return norm();
}
fraction &operator/=(fraction b){
return (*this)*=b.inv();
}
fraction &operator+=(ll b){ bunsi+=bunbo*b; return *this; }
fraction &operator-=(ll b){ return (*this)+=-b; }
fraction &operator*=(ll b){ bunsi*=b; return norm(); }
fraction &operator/=(ll b){ bunbo*=b; return norm(); }
fraction operator-()const{ return {-bunsi,bunbo,0}; }
fraction operator+(const fraction &b)const{ return fraction(*this)+=b; }
fraction operator-(const fraction &b)const{ return fraction(*this)-=b; }
fraction operator*(const fraction &b)const{ return fraction(*this)*=b; }
fraction operator/(const fraction &b)const{ return fraction(*this)/=b; }
fraction operator+(ll b)const{ return fraction(*this)+=b; }
fraction operator-(ll b)const{ return fraction(*this)-=b; }
fraction operator*(ll b)const{ return fraction(*this)*=b; }
fraction operator/(ll b)const{ return fraction(*this)/=b; }
friend fraction operator+(ll a,const fraction &b){ return b+a; }
friend fraction operator-(ll a,const fraction &b){ return -b+a; }
friend fraction operator*(ll a,const fraction &b){ return b*a; }
friend fraction operator/(ll a,const fraction &b){ return b.inv()*a; }
bool operator==(const fraction &b)const{
return bunsi==b.bunsi && bunbo==b.bunbo;
}
bool operator!=(const fraction &b)const{ return !(*this==b); }
bool operator<(const fraction &b)const{
return (b-*this).bunsi>0;
}
bool operator>(const fraction &b)const{ return b<*this; }
bool operator>=(const fraction &b)const{ return !(*this<b); }
bool operator<=(const fraction &b)const{ return b>=*this; }
friend ostream &operator << (ostream &os,const fraction &a){
return os<<a.bunsi<<'/'<<a.bunbo;
}
string to_string()const{ return std::to_string(bunsi)+'/'+std::to_string(bunbo); }
fraction inv()const{
if(bunsi<0) return {-bunbo,-bunsi,0};
else return {bunbo, bunsi,0};
}
};
/*
- 定義 ↓b分のa (a/b)
fraction x(a,b);
. ↓整数a
fraction x(a);
. ↓正規化無(約分と分母正化なしで良い時)
fraction x(a,b,true);
fraction y=x.inv(); 逆数
x+y,x-y,x*y,x/y,-x, x+=y,x-=y,x*=y,x/=y, x==y,x!=y,x<y,x>y,x<=y,x>=y
cout << x; //"a/b"と表示
*/
#if 0
#define MODLL (1000000007LL)
#else
#define MODLL (998244353LL)
#endif
using mll = mll_<MODLL>;
//using mll = fraction;
// １
//０┼２
// ３ 左 上 右 下
vector<pll> dxys={{0,-1},{-1,0},{0,1},{1,0},};
namespace SolvingSpace{
template<class T> using vector = Vector<T>;
using vll=vector< ll>; using vmll=vector< mll>; using vdd=vector< dd>;
using vvll=vector< vll>; using vvmll=vector< vmll>; using vvdd=vector< vdd>;
using vvvll=vector< vvll>; using vvvmll=vector< vvmll>; using vvvdd=vector< vvdd>;
using vvvvll=vector<vvvll>; using vvvvmll=vector<vvvmll>; using vvvvdd=vector<vvvdd>;
using vpll=vector< pll>; using vtll=vector< tll>; using vqll=vector< qll>;
using vvpll=vector< vpll>; using vvtll=vector< vtll>; using vvqll=vector< vqll>;
using vll2=vector< ll2>; using vll3=vector< ll3>; using vll4=vector< ll4>;
using vvll2=vector< vll2>; using vvll3=vector< vll3>; using vvll4=vector< vll4>;
using vvvll2=vector<vvll2>; using vvvll3=vector< vvll3>; using vvvll4=vector<vvll4>;
using vss=vector<string>;
template<class T> vector<T> cinv(ll nm){ return vector<T>(nm,[](ll i){ (void)i; return cin1<T>(); }); }
template<class T> vector<vector<T>> cinvv(ll H,ll W){ return vector<vector<T>>(H,[&](ll i){ (void)i; return cinv<T>(W); }); }
template<class T,class CALC,class INID,class SETD,class GETD> struct scanlineAlgorithm{
using Int=long long;
using ll=long long;
using pll=pair<ll,ll>;
using vpll=vector<pll>;
CALC calc;
INID inid;
SETD setd;
GETD getd;
vpll P,Q;
vpll Pz,Qz;//座圧後P,Q
vector<tuple<ll,ll,ll,ll>> events; //<X,Y,ki,i/j> ki:eventの種類
vector<T> Pcum;//Pcum[i]:Pi左上総積
vector<T> Pval,Qval;//Pval[i]:Piで計算した値、Qval[j]:Qjで取得した値
scanlineAlgorithm(T,const vector<pair<Int,Int>> &P_,const vector<pair<Int,Int>> &Q_,
Int dir,Int xyBoundType,bool isCalcP,CALC calc,INID inid,SETD setd,GETD getd)
:calc(calc),inid(inid),setd(setd),getd(getd),P(P_.begin(),P_.end()),
Q(Q_.begin(),Q_.end()),Pcum(P.size()),Pval(P.size()),Qval(Q.size())
{
ll nY=compress(dir,P,Q,Pz,Qz); //dirの違いを正規化して座圧
inid(nY); //データ構造初期化
MakeEvents(Pz,Qz,isCalcP,xyBoundType,events); //event作成
EventProc(); //event処理
}
vector<T> &getPval(){ return Pval; }
vector<T> &getQval(){ return Qval; }
private:
static ll normX(ll x,ll dir){ return (dir&2) ? -x : x; }
static ll normY(ll y,ll dir){ return (dir&1) ? -y : y; }
static ll x2X(ll x,const vll &xs){ //座圧前座標→座圧後座標
return lower_bound(xs.begin(),xs.end(),x)-xs.begin();
}
/*! @brief dirの違いを正規化して座圧 */
static ll compress(ll dir,vpll &P,vpll &Q,vpll &Pz,vpll &Qz){
vpll Pa,Qa;//方向正規化後P,Q
for(auto [x,y]:P) Pa.push_back({normX(x,dir),normY(y,dir)});
for(auto [x,y]:Q) Qa.push_back({normX(x,dir),normY(y,dir)});
vector<ll> xs,ys;
for(auto&&[x,y]:Pa) xs.push_back(x),ys.push_back(y);
for(auto&&[x,y]:Qa) xs.push_back(x),ys.push_back(y);
sort(xs.begin(),xs.end());
sort(ys.begin(),ys.end());
xs.erase(unique(xs.begin(),xs.end()),xs.end());
ys.erase(unique(ys.begin(),ys.end()),ys.end());
for(auto&&[x,y]:Pa) Pz.emplace_back(x2X(x,xs),x2X(y,ys));
for(auto&&[x,y]:Qa) Qz.emplace_back(x2X(x,xs),x2X(y,ys));
return (ll)ys.size();
}
/*! @brief event作成 */
static void MakeEvents(vpll &Pz,vpll &Qz,bool isCalcP,ll xyBoundType,
vector<tuple<ll,ll,ll,ll>> &events
){
auto adjX=[&](ll X){ return X-bool(~xyBoundType&1); };
auto adjY=[&](ll Y){ return Y-bool(~xyBoundType&2); };
for(ll i=0;i<(ll)Pz.size();++i){//セットevent追加
events.emplace_back(Pz[i].first,Pz[i].second,0,i);
}
if(isCalcP){//取得event追加 P
for(ll i=0;i<(ll)Pz.size();++i){
ll ki = xyBoundType==3 ? -1 : 1;
events.emplace_back(adjX(Pz[i].first),adjY(Pz[i].second),ki,i+1);
}
}
for(ll j=0;j<(ll)Qz.size();++j){//取得event追加 Q
events.emplace_back(adjX(Qz[j].first),adjY(Qz[j].second),1,-j-1);
}
sort(events.begin(),events.end());
}
/*! @brief event処理 */
void EventProc(){
for(auto&&[X,Y,ki,pos]:events){
if(ki==0){//値セットevent時
ll i=pos;
auto [x,y]=P[i];
Pval[i]=calc(x,y,i,Pcum[i]);
setd(X,Y,Pval[i]);
}
else{//取得event時
if(pos>0) Pcum[pos-1]=getd(X,Y);
else Qval[-pos-1]=getd(X,Y);
}
}
}
};
namespace FloorSum{
using ll=long long;
using pll=pair<ll,ll>;
ll floorsum(pll lr,ll m,ll a,ll b,bool ceil=false){ //Σfloor{(ax+b)/m}, x=l~r
if(ceil) return -floorsum(lr,m,-a,-b);
auto [l,r]=lr;
return atcoder::floor_sum(r-l+1,m,a,a*l+b);
}
ll floorsum(ll ax,ll ay,ll bx,ll by,bool on=true,ll l=INF,ll r=INF){
if(ax>bx) swap(ax,bx),swap(ay,by);//左がaxになるようswap
if(l==INF || r==INF) l=ax,r=bx;
ll n=r-l+1;
if(!on) return -n-floorsum(ax,-ay,bx,-by,true,l,r);//on=false時は上下反転を利用
ax-=l,bx-=l;//左端を原点に
ll m=bx-ax,a=by-ay,b=m*ay-a*ax;
return atcoder::floor_sum(n,m,a,b);
}
ll FloorModMum(pll lr,ll M,ll a,ll b){ return floorsum(lr,M,a,b)*M; }
ll LinearModSum(pll lr,ll M,ll a,ll b){ //Σ(ax+b)modM, x=l~r
auto [l,r]=lr;
/*
Σ(ax+b)modM = Σ(ax+b)-ΣFloorMod(ax+b,M)
Σ(ax+b) = 初項al+b,末項ar+b,項数N=r-l+1 = (al+b+ar+b)*N/2 = aN(l+r)/2 + bN
overflow時にmod2^64で正しいことを保証するため、overflow前に/2を処理
l+rとNのいずれかが偶数のため、偶数の方を/2する
*/
ll N=r-l+1;
ll L = N%2==0 ? N/2*(l+r)*a : (l+r)/2*N*a; //aN(l+r)/2
return L+b*N - FloorModMum(lr,M,a,b);
}
ll LinearModCount(pll lr,ll M,ll a,ll b,ll m1,ll m2){ //m1≦(ax+b)modM≦m2, x=l~r
return floorsum(lr,M,a,b-m1)-floorsum(lr,M,a,b-(m2+1));
}
}//end of namespace FloorSum
using FloorSum::floorsum; using FloorSum::FloorModMum;
using FloorSum::LinearModSum; using FloorSum::LinearModCount;
/*
・制約は全て 1≦m,M<2^32 0≦r-l+1<2^32
- -------- オリジナルのwrap 加算範囲をl~rに拡張,ceil_sum対応 --------
・Σfloor{(ax+b)/m}, x=l~r (ACLはx=0~N-1)
ll sm=floorsum({l,r},m,a,b);
ll sm=floorsum({l,r},m,a,b,true);
. ↑ceil_sum
- -------- 格子点系 --------
・直線の下側＆x軸より上 の格子点を数える
. ↓ ↓ 直線上の2点(ax,ay),(bx,by) 0<|ax-bx|<2^32
ll nm=floorsum(ax,ay,bx,by,true,l,r);
. true:直線上も数える↑ ↑区間[l,r]
・線分の下側＆x軸より上 の格子点を数える
ll nm=floorsum(ax,ay,bx,by,true);
. ↑ ↑ 端点(ax,ay),(bx,by) 0<|ax-bx|<2^32
- -------- mod演算系 --------
・Σ(ax+b)modM, x=l~r
ll sm=LinearModSum({l,r},M,a,b);
・m1≦(ax+b)modM≦m2 の回数(x=l~r) 0≦m1≦m2<M
ll nm=LinearModCount({l,r},M,a,b,m1,m2);
・ax+bをMの倍数に切り捨てたものの和 ΣFloormod(ax+b,M), x=l~r
ll sm=FloorModMum({l,r},M,a,b);
*/
template <class T> struct BIT_{
vector<T> v; ll N;
BIT_(){}
BIT_(ll N) { init(N); }
void init(ll N) { v.resize(N+1); this->N = N; }
void add(ll i,T x) { for(i++; i<=N; i+=i&(-i)) v[i]+=x; }
T sum(ll i) { if(i>=N)i=N-1; T s=0; for(i++; i>0; i-=i&(-i)) s+=v[i]; return s; }
T sum(ll i,ll j) { return sum(j)-sum(i-1); }
T sum() { return sum(N-1); } //総和
T operator[](ll i) { return sum(i,i); }
ll lower_bound(T s){
ll i=0,l=1; while(l<N) l<<=1;
for(; l>0; l>>=1) if(i+l<=N && v[i+l]<s) s-=v[i+=l];
return i;
}
void Dump() { rep(i,0,N-1) cerr<<setw(3)<< i <<" "<<setw(5)<< sum(i,i) <<'\n'; }
/*---- 集合管理用I/F ----*/
ll size() { return sum(); } //要素数
void insert(ll x) { add(x,1); }//集合にx追加
void erase(ll x) { add(x,-1); }//集合からx1つ削除
bool contains(ll x) { return (0<=x&&x<N) ? (*this)[x]>=1 : false; }//x∈集合ならtrue
ll rank(ll x) { return sum(x-1)+1; }//xが小さい方から何番目か 1-origin
ll rrank(ll x) { return sum(x+1,N-1)+1; }//xが大きい方から何番目か 1-origin
ll leftnumof(ll x) { return sum(x); }//x以下の個数
ll rightnumof(ll x) { return sum(x,N-1); }//x以上の個数
ll nthsmall(ll r) { return lower_bound(r); } //r番目に小さい要素 1-origin
ll nthbig(ll r) { return (size()<r) ? -1 : nthsmall(size()+1-r); }
//r番目に大きい要素 1-origin
/*---- 動的imos用I/F ----*/
void rangeadd(ll l,ll r,T x){ add(l,x),add(r+1,-x); }//[l,r]にx加算
T imos(ll i){ return sum(i); }//加算後の第i要素
};
using BIT = BIT_<ll>;
/*
BIT bit(n); //準備 0~n-1
ll nm=bit.size(); //集合の要素数
bit.insert(x); //集合にxを挿入
bit.erase(x); //集合からxを1つ削除
bool b=bit.contains(x); //x∈集合ならtrue
ll r = bit.rank(x); //xが小さい方から何番目か 1-origin
ll r = bit.rrank(x); //xが大きい方から何番目か 1-origin
ll nm=bit.leftnumof(x); //x以下の個数
ll nm=bit.rightnumof(x); //x以上の個数
ll nm=bit[x]; //xの個数
ll x=bit.nthsmall(r); //r番目に小さい要素 1-origin ない時はN
ll x=bit.nthbig(r); //r番目に大きい要素 1-origin ない時は-1
--- 動的imos用I/F ---
bit.rangeadd(l,r,x); //区間[l,r]に+x
ll x=bit.imos(i); //第i要素の値
*/
void cin2solve()
{
auto [N,M]=cins<ll,ll>();
auto D=cinv<ll>(N);
combination<mll> cmb(M+10);
;/*
mll v=cmb(n,r); // nCr 負も可、n<rも可、n巨大も愚直計算
mll v=cmb.P(n,r); // nPr
mll v=cmb.H(n,r); // nHr x1+…+xn=rの個数 初期化時cmb(n+r-1)以上必要
mll v=cmb.inv(n); // nの逆数
mll v=cmb.finv(n); // n!の逆数
mll v=cmb.fact(n); // n!
*/
ll Dx=maxe(D);
ll Q=min(200ll,Dx);
mll ans=0;
//大vs大
{
using VAL=mll;
vpll Pxys; //値をセットする点P {(x0,y0),(x1,y1),…}
rep(i,0,N-1){
ll d=D[i];
if(d<=Q)continue;
rep(y,d,M,d) Pxys.emplace_back(i,y);
}
vpll Qxys=Pxys; //左上総積が欲しい点Q Pと同じ点のときもセットする
ll dir=1; //0:左上,1:右上,2:左下,3:右下
ll xyBoundType=0; //左上総積境界条件 0:含まない,1:x含む,2:y含む,3:xy含む
bool isCalcP=false; //true:Pでの値セット時左上総積の計算値必要
auto calc=[&](ll x,ll y,ll i,VAL va){
return cmb.inv(M/D[x]);
};
BIT_<VAL> bit;
auto inid=[&](ll nY){ bit.init(nY); };
auto setd=[&](ll X,ll Y,VAL va){ bit.add(Y,va); };
auto getd=[&](ll X,ll Y){ return bit.sum(0,Y); };
scanlineAlgorithm sca(VAL(),Pxys,Qxys,dir,xyBoundType,isCalcP,calc,inid,setd,getd);
vector<VAL> qval=sca.getQval(); //qval[j]: Qjの左上総積
rep(I,0,sz(Pxys)-1){
auto [x,y]=Pxys[I];
ans+=cmb.inv(M/D[x])*qval[I];
}
}
cerr << timeget() <<"ms"<< '\n';
vvmll dw(Q+1,vll(Dx+1));
vvmll up(Q+1,vll(Dx+1));
rep(b,1,Q) rep(a,1,Dx){
ll total=(M/b)*(M/a);
//mll invtotal=mll(1)/total;
mll invtotal=cmb.inv(M/b)*cmb.inv(M/a);
ll nm=floorsum(0,0,a,b,false,1,M/b);
dw[b][a]=nm*invtotal;
ll g=lcm(a,b);
up[b][a]=(total-nm-M/g)*invtotal;
}
cerr << timeget() <<"ms"<< '\n';
//大vs小、小vs小
{
vll cnt(Q+1);
dep(i,N-1,0){
ll d=D[i];
rep(d2,1,Q) ans+=cnt[d2]*up[d2][d];
if(d<=Q) cnt[d]++;
}
}
cerr << timeget() <<"ms"<< '\n';
//小vs大
{
vll cnt(Q+1);
D.reverse();
dep(i,N-1,0){
ll d=D[i];
if(d>Q){
rep(d2,1,Q) ans+=cnt[d2]*dw[d2][d];
}
if(d<=Q) cnt[d]++;
}
}
for(auto&& d: D) ans*=M/d;
cout << ans << '\n';
return;
}
};//SolvingSpace
//////////////////////////////////////////
int main(){
#if 1
//SolvingSpace::labo();
SolvingSpace::cin2solve();
//SolvingSpace::generand();
#else
ll t; cin >> t;
rep(i,0,t-1){
SolvingSpace::cin2solve();
//SolvingSpace::generand();
}
#endif
cerr << timeget() <<"ms"<< '\n';
return 0;
}