#include #define FOR(v, a, b) for(int v = (a); v < (b); ++v) #define FORE(v, a, b) for(int v = (a); v <= (b); ++v) #define REP(v, n) FOR(v, 0, n) #define REPE(v, n) FORE(v, 0, n) #define REV(v, a, b) for(int v = (a); v >= (b); --v) #define ALL(x) (x).begin(), (x).end() #define ITR(it, c) for(auto it = (c).begin(); it != (c).end(); ++it) #define RITR(it, c) for(auto it = (c).rbegin(); it != (c).rend(); ++it) #define EXIST(c,x) ((c).find(x) != (c).end()) #define LLI long long int #define fst first #define snd second #ifndef M_PI #define M_PI 3.14159265358979323846 #endif #ifndef M_E #define M_E 2.71828182845904523536 #endif #ifdef DEBUG #include #define dump(x) cerr << "L" << __LINE__ << ": in " << __PRETTY_FUNCTION__ << " \e[32;1m" << boost::core::demangle(typeid(x).name()) << "\e[37m" << " " << (#x) << " = " << (x) << "\e[m" << endl; #else #define dump(x) #endif using namespace std; #define gcd __gcd template constexpr T lcm(T m, T n){return m*n/gcd(m,n);} template using V = vector; template using P = pair; template void join(ostream &ost, I s, I t, string d=" "){for(auto i=s; i!=t; ++i){if(i!=s)ost< istream& operator>>(istream &is, vector &v){for(auto &a : v) is >> a; return is;} template istream& operator>>(istream &is, pair &p){is >> p.first >> p.second; return is;} template ostream& out_container(ostream &os, Iter first, Iter last){ os << "{"; auto itr = first; while(itr != last){if(itr != first) os << ","; os << *itr; ++itr;} os << "}"; return os; } template ostream& operator<<(ostream &os, const vector &c){return out_container(os,ALL(c));} template ostream& operator<<(ostream &os, const deque &c){return out_container(os,ALL(c));} template ostream& operator<<(ostream &os, const set &c){return out_container(os,ALL(c));} template ostream& operator<<(ostream &os, const unordered_set &c){return out_container(os,ALL(c));} template ostream& operator<<(ostream &os, const map &c){return out_container(os,ALL(c));} template ostream& operator<<(ostream &os, const unordered_map &c){return out_container(os,ALL(c));} template ostream& operator<<(ostream& os, const pair &p){os << "(" << p.first << "," << p.second << ")"; return os;} template T& chmin(T &a, const T &b){return a = min(a,b);} template T& chmax(T &a, const T &b){return a = max(a,b);} // 追加直線の傾きが単調減少、minクエリの値が単調増加 template class ConvexHullTrick{ public: deque> lines; bool is_needless(pair a, pair b, pair c){ return (a.snd-b.snd)*(a.fst-c.fst) >= (a.snd-c.snd)*(a.fst-b.fst); } void add(T a, T b){ if(!lines.empty()){ auto l = lines.back(); if(l.fst == a){ if(l.snd < b) return; else lines.pop_back(); } } while(lines.size()>=2 && is_needless(make_pair(a,b), lines.back(), *(lines.end()-2))){ lines.pop_back(); } lines.push_back(make_pair(a,b)); } T apply(pair f, T x){ return f.fst*x + f.snd; } T query(T x){ while(lines.size()>=2 && apply(lines[0],x)>apply(lines[1],x)){ lines.pop_front(); } return apply(lines[0],x); } }; class Rational{ public: int64_t nume, deno; Rational(): nume(0), deno(1){} Rational(int64_t num): nume(num), deno(1){} Rational(int64_t num, int64_t den){ int64_t g = gcd(num,den); nume = num/g; deno = den/g; } Rational& operator+=(const Rational &a); Rational& operator-=(const Rational &a); Rational& operator*=(const Rational &a); Rational& operator/=(const Rational &a); }; ostream& operator<<(ostream &os, const Rational &r){os << r.nume << "/" << r.deno; return os;} istream& operator>>(istream &is, Rational &r){is >> r.nume; r.deno = 1; return is;} Rational operator-(const Rational &a){return Rational(-a.nume, a.deno);} Rational operator+(const Rational &a, const Rational &b){int64_t l = lcm(a.deno,b.deno); return Rational(a.nume*l/a.deno + b.nume*l/b.deno, l);} Rational operator-(const Rational &a, const Rational &b){int64_t l = lcm(a.deno,b.deno); return Rational(a.nume*l/a.deno - b.nume*l/b.deno, l);} Rational operator*(const Rational &a, const Rational &b){return Rational(a.nume*b.nume, a.deno*b.deno);} Rational operator/(const Rational &a, const Rational &b){return Rational(a.nume*b.deno, a.deno*b.nume);} bool operator==(const Rational &a, const Rational &b){return a.nume == b.nume && a.deno == b.deno;} bool operator!=(const Rational &a, const Rational &b){return !(a==b);} bool operator<(const Rational &a, const Rational &b){return a.nume*b.deno < b.nume*a.deno;} bool operator<=(const Rational &a, const Rational &b){return a.nume*b.deno <= b.nume*a.deno;} bool operator>(const Rational &a, const Rational &b){return !(a<=b);} bool operator>=(const Rational &a, const Rational &b){return !(a> N >> A >> B >> W){ vector D(N); cin >> D; vector dp(N); ConvexHullTrick cht; dp[0] = W+D[0]; cht.add(-B/2,dp[0]+A*0+B*0*(0+1)/2); FOR(i,1,N){ Rational t = cht.query(Rational(i)); //dump(t); dp[i] = D[i]-A*(i-1)+B*i*i/2+t; chmin(dp[i], D[i]+W-A*i+B*i*(i+1)/2); cht.add(-B*(2*i+1)/2,dp[i]+A*i+B*i*(i+1)/2); } //dump(dp); Rational ans = -A*(N-1)+B*N*N/2+cht.query(N); chmin(ans, W-A*N+B*N*(N+1)/2); cout << ans.nume << endl; } return 0; }