답안 #1060837

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
1060837	2024-08-16T02:06:18 Z	hashiryo	Safety (NOI18_safety)	C++17	100 / 100	344 ms	23508 KB

safety

// #define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
// clang-format off
std::ostream&operator<<(std::ostream&os,std::int8_t x){return os<<(int)x;}
std::ostream&operator<<(std::ostream&os,std::uint8_t x){return os<<(int)x;}
std::ostream&operator<<(std::ostream&os,const __int128_t &u){if(!u)os<<"0";__int128_t tmp=u<0?(os<<"-",-u):u;std::string s;while(tmp)s+='0'+(tmp%10),tmp/=10;return std::reverse(s.begin(),s.end()),os<<s;}
std::ostream&operator<<(std::ostream&os,const __uint128_t &u){if(!u)os<<"0";__uint128_t tmp=u;std::string s;while(tmp)s+='0'+(tmp%10),tmp/=10;return std::reverse(s.begin(),s.end()),os<<s;}
#define checkpoint() (void(0))
#define debug(...) (void(0))
#define debugArray(x,n) (void(0))
#define debugMatrix(x,h,w) (void(0))
// clang-format on
// clang-format off
template<class T>struct make_long{using type= T;};
template<>struct make_long<int8_t>{using type= int16_t;};
template<>struct make_long<uint8_t>{using type= uint16_t;};
template<>struct make_long<int16_t>{using type= int32_t;};
template<>struct make_long<uint16_t>{using type= uint32_t;};
template<>struct make_long<int32_t>{using type= int64_t;};
template<>struct make_long<uint32_t>{using type= uint64_t;};
template<>struct make_long<int64_t>{using type= __int128_t;};
template<>struct make_long<uint64_t>{using type= __uint128_t;};
template<>struct make_long<float>{using type= double;};
template<>struct make_long<double>{using type= long double;};
template<class T> using make_long_t= typename make_long<T>::type;
// clang-format on
template <class T, bool persistent= false, size_t NODE_SIZE= 1 << 22> class PiecewiseLinearConvex {
 using D= make_long_t<T>;
 struct Node {
  int ch[2];
  T z, x, d, a;
  D s;
  size_t sz;
  friend std::ostream &operator<<(std::ostream &os, const Node &t) { return os << "{z:" << t.z << ",x:" << t.x << ",d:" << t.d << ",a:" << t.a << ",s:" << t.s << ",sz:" << t.sz << ",ch:(" << t.ch[0] << "," << t.ch[1] << ")}"; }
 };
 static inline size_t ni= 1;
 static inline Node *n= new Node[NODE_SIZE];
 static inline void info(int t, int d, std::stringstream &ss) {
  if (!t) return;
  info(n[t].ch[0], d + 1, ss);
  for (int i= 0; i < d; ++i) ss << "   ";
  ss << " ■ " << n[t] << '\n', info(n[t].ch[1], d + 1, ss);
 }
 static inline void dump_xs(int t, std::vector<T> &xs) {
  if (t) push(t), dump_xs(n[t].ch[0], xs), xs.push_back(n[t].x), dump_xs(n[t].ch[1], xs);
 }
 static inline void dump_slopes_l(int t, T ofs, std::vector<T> &as) {
  if (t) push(t), dump_slopes_l(n[t].ch[1], ofs, as), ofs+= n[n[t].ch[1]].a + n[t].d, as.push_back(-ofs), dump_slopes_l(n[t].ch[0], ofs, as);
 }
 static inline void dump_slopes_r(int t, T ofs, std::vector<T> &as) {
  if (t) push(t), dump_slopes_r(n[t].ch[0], ofs, as), ofs+= n[n[t].ch[0]].a + n[t].d, as.push_back(ofs), dump_slopes_r(n[t].ch[1], ofs, as);
 }
 static inline int create(T d, T x) { return n[ni].d= d, n[ni].x= x, n[ni].z= 0, ni++; }
 template <class Iter> static inline int build(Iter bg, Iter ed) {
  if (bg == ed) return 0;
  auto md= bg + (ed - bg) / 2;
  int t= create(md->first, md->second);
  return n[t].ch[0]= build(bg, md), n[t].ch[1]= build(md + 1, ed), update(t), t;
 }
 template <class Iter> static inline void dump(Iter itr, int t) {
  if (!t) return;
  push(t);
  size_t sz= n[n[t].ch[0]].sz;
  dump(itr, n[t].ch[0]), *(itr + sz)= {n[t].d, n[t].x}, dump(itr + sz + 1, n[t].ch[1]);
 }
 static inline void update(int t) {
  int l= n[t].ch[0], r= n[t].ch[1];
  n[t].sz= 1 + n[l].sz + n[r].sz, n[t].a= n[t].d + n[l].a + n[r].a, n[t].s= D(n[t].x) * n[t].d + n[l].s + n[r].s;
 }
 template <bool b= 1> static inline void prop(int &t, T v) {
  if constexpr (persistent && b) {
   if (!t) return;
   n[ni]= n[t], t= ni++;
  }
  n[t].z+= v, n[t].s+= D(v) * n[t].a, n[t].x+= v;
 }
 static inline void push(int t) {
  if (n[t].z != 0) prop(n[t].ch[0], n[t].z), prop(n[t].ch[1], n[t].z), n[t].z= 0;
 }
 template <bool r> static inline int join_(int t, int a, int b) {
  push(a);
  if constexpr (r) b= join<0>(b, t, n[a].ch[0]);
  else b= join<0>(n[a].ch[1], t, b);
  if constexpr (persistent) n[ni]= n[a], a= ni++;
  if (n[n[a].ch[r]].sz * 4 >= n[b].sz) return n[a].ch[!r]= b, update(a), a;
  return n[a].ch[!r]= n[b].ch[r], update(a), n[b].ch[r]= a, update(b), b;
 }
 template <bool b= 1> static inline int join(int l, int t, int r) {
  if constexpr (persistent && b) n[ni]= n[t], t= ni++;
  if (n[l].sz > n[r].sz * 4) return join_<0>(t, l, r);
  if (n[r].sz > n[l].sz * 4) return join_<1>(t, r, l);
  return n[t].ch[0]= l, n[t].ch[1]= r, update(t), t;
 }
 static inline std::array<int, 3> split(int t, T x) {
  if (!t) return {0, 0, 0};
  push(t);
  if (n[t].x < x) {
   auto [a, b, c]= split(n[t].ch[1], x);
   return {join(n[t].ch[0], t, a), b, c};
  } else if (x < n[t].x) {
   auto [a, b, c]= split(n[t].ch[0], x);
   return {a, b, join(c, t, n[t].ch[1])};
  }
  return {n[t].ch[0], t, n[t].ch[1]};
 }
 static inline int unite(int l, int r) {
  if (!l) return r;
  if (!r) return l;
  push(l);
  if constexpr (persistent) n[ni]= n[l], l= ni++;
  auto [a, b, c]= split(r, n[l].x);
  return n[l].d+= n[b].d, join<0>(unite(a, n[l].ch[0]), l, unite(n[l].ch[1], c));
 }
 static inline int insert(int t, T x, T d) {
  if (!t) return n[ni]= Node{{0, 0}, 0, x, d, d, D(x) * d, 1}, ni++;
  push(t);
  if constexpr (persistent) n[ni]= n[t], t= ni++;
  if (n[t].x == x) return n[t].d+= d, update(t), t;
  return x < n[t].x ? join<0>(insert(n[t].ch[0], x, d), t, n[t].ch[1]) : join<0>(n[t].ch[0], t, insert(n[t].ch[1], x, d));
 }
 template <bool r> static inline std::pair<int, int> pop(int t) {
  if (push(t); !n[t].ch[r]) return {n[t].ch[!r], t};
  auto [a, s]= pop<r>(n[t].ch[r]);
  if constexpr (r) return {join(n[t].ch[!r], t, a), s};
  else return {join(a, t, n[t].ch[!r]), s};
 }
 template <bool r> static inline bool lt(T a, T b) {
  if constexpr (r) return b < a;
  else return a < b;
 }
 template <bool r> static inline int cut(int t, T x) {
  if (!t) return t;
  if (push(t); n[t].x == x) return n[t].ch[!r];
  if (lt<r>(n[t].x, x)) return cut<r>(n[t].ch[!r], x);
  if constexpr (r) return join(n[t].ch[0], t, cut<1>(n[t].ch[1], x));
  else return join(cut<0>(n[t].ch[0], x), t, n[t].ch[1]);
 }
 template <bool r> static inline D calc_y(int t, T x, T ol, D ou) {
  for (; t;) {
   if (push(t); lt<r>(n[t].x, x)) t= n[t].ch[!r];
   else {
    if (ol+= n[n[t].ch[!r]].a, ou+= n[n[t].ch[!r]].s; n[t].x == x) break;
    ol+= n[t].d, ou+= D(n[t].x) * n[t].d, t= n[t].ch[r];
   }
  }
  return D(x) * ol - ou;
 }
 template <bool r> static inline std::array<int, 3> split(int t, T p, T &ol, D &ou) {
  push(t);
  T s= ol + n[n[t].ch[!r]].a;
  if (p < s) {
   auto [a, b, c]= split<r>(n[t].ch[!r], p, ol, ou);
   if constexpr (r) return {a, b, join(c, t, n[t].ch[r])};
   else return {join(n[t].ch[r], t, a), b, c};
  }
  ol= s + n[t].d;
  if (ol < p) {
   ou+= n[n[t].ch[!r]].s + D(n[t].x) * n[t].d;
   auto [a, b, c]= split<r>(n[t].ch[r], p, ol, ou);
   if constexpr (r) return {join(n[t].ch[!r], t, a), b, c};
   else return {a, b, join(c, t, n[t].ch[!r])};
  }
  ou+= n[n[t].ch[!r]].s;
  return {n[t].ch[0], t, n[t].ch[1]};
 }
 template <bool l> static inline bool lte(T a, T b) {
  if constexpr (l) return a < b;
  else return a <= b;
 }
 template <bool l, bool r> static inline std::pair<int, int> split_cum(int t, T p, T &ol, D &ou) {
  push(t);
  T s= ol + n[n[t].ch[!r]].a;
  if (lte<l>(p, s)) {
   auto [c, b]= split_cum<l, r>(n[t].ch[!r], p, ol, ou);
   if constexpr (l) {
    if constexpr (r) return {join(c, t, n[t].ch[r]), b};
    else return {join(n[t].ch[r], t, c), b};
   } else return {c, b};
  }
  ol= s + n[t].d;
  if (lte<!l>(ol, p)) {
   ou+= n[n[t].ch[!r]].s + D(n[t].x) * n[t].d;
   auto [a, b]= split_cum<l, r>(n[t].ch[r], p, ol, ou);
   if constexpr (l) return {a, b};
   else {
    if constexpr (r) return {join(n[t].ch[!r], t, a), b};
    else return {join(a, t, n[t].ch[!r]), b};
   }
  }
  ou+= n[n[t].ch[!r]].s;
  return {n[t].ch[!r ^ l], t};
 }
 int mn, lr[2];
 bool bf[2];
 T o[2], rem, bx[2];
 D y;
 inline D calc_y(T x) {
  if (!mn) return 0;
  if (n[mn].x == x) return 0;
  return x < n[mn].x ? -calc_y<0>(lr[0], x, o[0], D(n[mn].x) * o[0]) : calc_y<1>(lr[1], x, o[1], D(n[mn].x) * o[1]);
 }
 inline void slope_eval(bool neg) {
  T p= neg ? -rem : rem, ol= o[neg];
  if (p <= ol) o[neg]-= p, o[!neg]+= p, y+= D(n[mn].x) * rem;
  else {
   D ou= D(n[mn].x) * ol;
   auto [a, b, c]= neg ? split<1>(lr[neg], p, ol, ou) : split<0>(lr[neg], p, ol, ou);
   o[neg]= ol - p, ol-= n[b].d, ou+= D(n[b].x) * (o[!neg]= p - ol);
   if (neg) y-= ou, lr[!neg]= join(lr[!neg], mn, a), lr[neg]= c;
   else y+= ou, lr[!neg]= join(c, mn, lr[!neg]), lr[neg]= a;
   mn= b;
  }
  rem= 0;
 }
 template <bool l, bool neg> inline void slope_eval_cum() {
  T p= neg ? -rem : rem, ol= o[neg];
  if (lte<l>(p, ol)) o[neg]-= p, o[!neg]+= p, y+= D(n[mn].x) * rem;
  else {
   D ou= D(n[mn].x) * ol;
   auto [a, b]= split_cum<l, neg>(lr[neg], p, ol, ou);
   o[neg]= ol - p, ol-= n[b].d, ou+= D(n[b].x) * (o[!neg]= p - ol);
   if constexpr (l) lr[neg]= a;
   else {
    if constexpr (neg) lr[!neg]= join(lr[!neg], mn, a);
    else lr[!neg]= join(a, mn, lr[!neg]);
   }
   if constexpr (neg) y-= ou;
   else y+= ou;
   mn= b;
  }
  rem= 0;
 }
 template <bool r> void add_inf(T x0) {
  if (bf[r] && !lt<r>(bx[r], x0)) return;
  if (assert(!bf[!r] || !lt<r>(bx[!r], x0)), bf[r]= true, bx[r]= x0; !mn) return;
  if (lt<r>(x0, n[mn].x)) return lr[r]= cut<r>(lr[r], x0), void();
  D q= n[lr[!r]].s + D(n[mn].x) * o[!r];
  T v= o[!r] + n[lr[!r]].a;
  lr[!r]= cut<r>(lr[!r], x0);
  if (!r) y-= q, rem+= v;
  else y+= q, rem-= v;
  if (lr[!r]) std::tie(lr[r], mn)= pop<!r>(lr[!r]), lr[!r]= 0;
  else mn= lr[r]= 0;
  o[r]= n[mn].d, o[!r]= 0;
 }
 inline void prop(T x) {
  if constexpr (persistent) mn= create(n[mn].d, n[mn].x);
  n[mn].x+= x;
 }
public:
 // f(x) := 0
 PiecewiseLinearConvex(): mn(0), lr{0, 0}, bf{0, 0}, o{0, 0}, rem(0), bx{0, 0}, y(0) {}
 //  f(x) := sum max(0, a(x-x0))
 PiecewiseLinearConvex(const std::vector<std::pair<T, T>> &ramps): PiecewiseLinearConvex() {
  int m= ramps.size();
  if (!m) return;
  std::vector<std::pair<T, T>> w(m);
  int s= 0, t= 0;
  for (auto [d, x]: ramps) {
   if (d == 0) continue;
   if (d < 0) y-= D(d) * x, rem+= d, d= -d;
   w[s++]= {d, x};
  }
  std::sort(w.begin(), w.begin() + s, [](auto a, auto b) { return a.second < b.second; });
  for (int i= 0; i < s; ++i) {
   if (t && w[t - 1].second == w[i].second) w[t - 1].first+= w[i].first;
   else w[t++]= w[i];
  }
  mn= create(w[0].first, w[0].second), o[1]= n[mn].d, lr[1]= build(w.begin() + 1, w.begin() + t);
 }
 std::string info() {
  std::stringstream ss;
  if (ss << "\n rem:" << rem << ", y:" << y << ", mn:" << mn << ", lr:{" << lr[0] << ", " << lr[1] << "}\n bf[0]:" << bf[0] << ", bf[1]:" << bf[1] << ", bx[0]:" << bx[0] << ", bx[1]:" << bx[1] << "\n " << "o[0]:" << o[0] << ", o[1]:" << o[1] << "\n"; mn) {
   if (lr[0]) info(lr[0], 1, ss);
   ss << " ■ " << n[mn] << '\n';
   if (lr[1]) info(lr[1], 1, ss);
  }
  return ss.str();
 }
 template <class... Args> static inline void rebuild(Args &...plc) {
  static_assert(std::conjunction_v<std::is_same<PiecewiseLinearConvex, Args>...>);
  constexpr size_t m= sizeof...(Args);
  std::array<std::vector<std::pair<T, T>>, m> ls, rs;
  std::array<std::pair<T, T>, m> mns;
  int i= 0;
  (void)(int[]){(mns[i]= {n[plc.mn].d, n[plc.mn].x}, ls[i].resize(n[plc.lr[0]].sz), rs[i].resize(n[plc.lr[1]].sz), dump(ls[i].begin(), plc.lr[0]), dump(rs[i].begin(), plc.lr[1]), ++i)...};
  ni= 1, i= 0;
  (void)(int[]){((plc.mn ? (plc.mn= create(mns[i].first, mns[i].second)) : 0), plc.lr[0]= build(ls[i].begin(), ls[i].end()), plc.lr[1]= build(rs[i].begin(), rs[i].end()), ++i)...};
 }
 static inline void rebuild(std::vector<PiecewiseLinearConvex> &plcs) {
  size_t m= plcs.size();
  std::vector<std::vector<std::pair<T, T>>> ls(m), rs(m);
  std::vector<std::pair<T, T>> mns(m);
  for (int i= m; i--;) mns[i]= {n[plcs[i].mn].d, n[plcs[i].mn].x}, ls[i].resize(n[plcs[i].lr[0]].sz), rs[i].resize(n[plcs[i].lr[1]].sz), dump(ls[i].begin(), plcs[i].lr[0]), dump(rs[i].begin(), plcs[i].lr[1]);
  ni= 1;
  for (int i= m; i--;) (plcs[i].mn ? (plcs[i].mn= create(mns[i].first, mns[i].second)) : 0), plcs[i].lr[0]= build(ls[i].begin(), ls[i].end()), plcs[i].lr[1]= build(rs[i].begin(), rs[i].end());
 }
 static void reset() { ni= 1; }
 static bool pool_empty() {
  if constexpr (persistent) return ni >= NODE_SIZE * 0.8;
  else return ni + 1000 >= NODE_SIZE;
 }
 // f(x) += c
 void add_const(D c) { y+= c; }
 // f(x) += ax, /
 void add_linear(T a) { rem+= a; }
 //  f(x) += max(a(x-x0),b(x-x0)), (a < b)
 void add_max(T a, T b, T x0) {
  assert(a < b);
  if (bf[0] && x0 <= bx[0]) y-= D(b) * x0, rem+= b;
  else if (bf[1] && bx[1] <= x0) y-= D(a) * x0, rem+= a;
  else if (T c= b - a; mn) {
   if (n[mn].x == x0) {
    if constexpr (persistent) mn= create(n[mn].d, n[mn].x);
    n[mn].d+= c, o[1]+= c, y-= D(a) * x0, rem+= a;
   } else {
    if (n[mn].x < x0) lr[1]= insert(lr[1], x0, c), y-= D(a) * x0, rem+= a;
    else lr[0]= insert(lr[0], x0, c), y-= D(b) * x0, rem+= b;
   }
  } else mn= create(c, x0), y-= D(a) * x0, rem+= a, o[0]= 0, o[1]= c;
 }
 // f(x) +=  max(0, a(x-x0))
 void add_ramp(T a, T x0) {
  if (a != 0) a > 0 ? add_max(0, a, x0) : add_max(a, 0, x0);
 }
 // f(x) += a|x-x0|, \/
 void add_abs(T a, T x0) {
  if (assert(a >= 0); a != 0) add_max(-a, a, x0);
 }
 // right=false : f(x) +=  inf  (x < x_0), right=true: f(x) += inf  (x_0 < x)
 void add_inf(bool right= false, T x0= 0) { return right ? add_inf<1>(x0) : add_inf<0>(x0); }
 // f(x) <- f(x-x0)
 void shift(T x0) {
  if (bx[0]+= x0, bx[1]+= x0, y-= D(rem) * x0; mn) prop(x0), prop(lr[0], x0), prop(lr[1], x0);
 }
 // rev=false: f(x) <- min_{y<=x} f(y), rev=true : f(x) <- min_{x<=y} f(y)
 void chmin_cum(bool rev= false) {
  if (bf[0] && bf[1] && bx[0] == bx[1]) y+= D(rem) * bx[0], rem= 0;
  else if (rem != 0) {
   bool r= rem < 0;
   T u= (r ? -rem : rem) - o[r] - n[lr[r]].a;
   if (0 <= u) {
    if (r ^ rev) {
     if (u > 0 && bf[r]) {
      D q= n[lr[r]].s + D(n[mn].x) * o[r] + D(u) * bx[r];
      if (r ? y-= q : y+= q; mn) lr[!r]= join(lr[0], mn, lr[1]);
      o[!r]= u, rem= 0, mn= create(u, bx[r]);
     }
    } else {
     assert(bf[r]);
     D q= n[lr[r]].s + D(n[mn].x) * o[r] + D(u) * bx[r];
     (r ? y-= q : y+= q), rem= 0, mn= lr[r]= 0, o[r]= 0;
    }
    bf[!rev]= false;
    return;
   }
   if ((r ^ rev)) r ? slope_eval_cum<0, 1>() : slope_eval_cum<0, 0>();
   else r ? slope_eval_cum<1, 1>() : slope_eval_cum<1, 0>();
   if constexpr (persistent) mn= create(o[rev], n[mn].x);
   else n[mn].d= o[rev];
  } else if (mn) {
   if (o[rev] == 0) {
    if (lr[rev]) std::tie(lr[rev], mn)= rev ? pop<0>(lr[rev]) : pop<1>(lr[rev]), o[rev]= n[mn].d;
    else mn= 0;
   } else {
    if constexpr (persistent) mn= create(o[rev], n[mn].x);
    else n[mn].d= o[rev];
   }
  }
  bf[!rev]= false, lr[!rev]= 0, o[!rev]= 0;
 }
 //  f(x) <- min_{lb<=y<=ub} f(x-y). (lb <= ub), \_/ -> \__/
 void chmin_slide_win(T lb, T ub) {
  assert(lb <= ub);
  if (bf[0] && bf[1] && bx[0] == bx[1]) y+= D(rem) * bx[0], rem= 0;
  else {
   if (rem != 0) {
    bool r= rem < 0;
    T u= (r ? -rem : rem) - o[r] - n[lr[r]].a;
    if (0 < u) {
     T b[2]= {lb, ub};
     if (bf[r]) {
      D q= n[lr[r]].s + D(n[mn].x) * o[r] + D(u) * bx[r];
      if (r ? y-= q : y+= q; mn) lr[!r]= join(lr[0], mn, lr[1]), prop<0>(lr[!r], b[!r]);
      lr[r]= 0, rem= 0, o[!r]= u, o[r]= 0, mn= create(u, bx[r] + b[!r]);
     } else {
      y-= D(rem) * b[!r];
      if (mn) prop(b[!r]), prop(lr[0], b[!r]), prop(lr[1], b[!r]);
     }
     bx[0]+= lb, bx[1]+= ub;
     return;
    }
    slope_eval(r);
   }
   if (mn) {
    if (o[0] == 0) prop(ub);
    else if (o[1] == 0) prop(lb);
    else lr[1]= join<0>(0, create(o[1], n[mn].x), lr[1]), prop(lb), n[mn].d= o[0], o[1]= 0;
    prop(lr[0], lb), prop(lr[1], ub);
   }
  }
  bx[0]+= lb, bx[1]+= ub;
 }
 D operator()(T x) { return assert(!bf[0] || bx[0] <= x), assert(!bf[1] || x <= bx[1]), calc_y(x) + D(rem) * x + y; }
 D min() {
  if (rem == 0) return y;
  bool r= rem < 0;
  T u= (r ? -rem : rem) - o[r] - n[lr[r]].a;
  if (0 < u) {
   assert(bf[r]);
   D q= n[lr[r]].s + D(n[mn].x) * o[r] + D(u) * bx[r];
   return r ? y - q : y + q;
  }
  return slope_eval(r), y;
 }
 std::array<T, 2> argmin() {
  if (rem != 0) {
   bool r= rem < 0;
   if (o[r] + n[lr[r]].a < (r ? -rem : rem)) {
    assert(bf[r]);
    return {bx[r], bx[r]};
   }
   slope_eval(r);
  }
  std::array<T, 2> ret= {bx[0], bx[1]};
  int t= mn;
  if (!t) return ret;
  bool r= o[0] == 0;
  if (!r && o[1] != 0) ret[0]= ret[1]= n[t].x;
  else if (ret[r]= n[t].x, t= lr[!r]; t) {
   for (; push(t), n[t].ch[r];) t= n[t].ch[r];
   ret[!r]= n[t].x;
  } else assert(bf[!r]);
  return ret;
 }
 size_t size() { return n[lr[0]].sz + n[lr[1]].sz + !!mn; }
 PiecewiseLinearConvex &operator+=(const PiecewiseLinearConvex &g) { return *this= *this + g; }
 PiecewiseLinearConvex operator+(PiecewiseLinearConvex g) const {
  PiecewiseLinearConvex ret= *this;
  if (g.bf[0]) ret.add_inf(false, g.bx[0]);
  if (g.bf[1]) ret.add_inf(true, g.bx[1]);
  if (bf[0]) g.add_inf(false, bx[0]);
  if (bf[1]) g.add_inf(true, bx[1]);
  ret.y+= g.y, ret.rem+= g.rem;
  if (!g.mn) return ret;
  if (!ret.mn) return ret.mn= g.mn, ret.lr[0]= g.lr[0], ret.lr[1]= g.lr[1], ret.o[0]= g.o[0], ret.o[1]= g.o[1], ret;
  ret.y+= n[ret.lr[0]].s + D(n[ret.mn].x) * ret.o[0] + n[g.lr[0]].s + D(n[g.mn].x) * g.o[0], ret.rem-= ret.o[0] + n[ret.lr[0]].a + g.o[0] + n[g.lr[0]].a;
  int t= unite(join(ret.lr[0], ret.mn, ret.lr[1]), join(g.lr[0], g.mn, g.lr[1]));
  return std::tie(ret.lr[1], ret.mn)= pop<0>(t), ret.lr[0]= 0, ret.o[0]= 0, ret.o[1]= n[ret.mn].d, ret;
 }
 std::vector<T> dump_xs() {
  std::vector<T> xs;
  if (bf[0]) xs.push_back(bx[0]);
  dump_xs(lr[0], xs);
  if (mn) xs.push_back(n[mn].x);
  dump_xs(lr[1], xs);
  if (bf[1]) xs.push_back(bx[1]);
  return xs;
 }
 std::vector<std::pair<T, D>> dump_xys() {
  auto xs= dump_xs();
  std::vector<std::pair<T, D>> xys(xs.size());
  for (int i= xs.size(); i--;) xys[i]= {xs[i], operator()(xs[i])};
  return xys;
 }
 std::vector<T> dump_slopes() {
  std::vector<T> as;
  if (mn) as.push_back(-o[0]), dump_slopes_l(lr[0], o[0], as), std::reverse(as.begin(), as.end()), as.push_back(o[1]), dump_slopes_r(lr[1], o[1], as);
  else as.push_back(0);
  for (auto &a: as) a+= rem;
  return as;
 }
};
#include <type_traits>
#define _LR(name, IT, CT) \
 template <class T> struct name { \
  using Iterator= typename std::vector<T>::IT; \
  Iterator bg, ed; \
  Iterator begin() const { return bg; } \
  Iterator end() const { return ed; } \
  size_t size() const { return std::distance(bg, ed); } \
  CT &operator[](int i) const { return bg[i]; } \
 }
_LR(ListRange, iterator, T);
_LR(ConstListRange, const_iterator, const T);
#undef _LR
template <class T> struct CSRArray {
 std::vector<T> dat;
 std::vector<int> p;
 size_t size() const { return p.size() - 1; }
 ListRange<T> operator[](int i) { return {dat.begin() + p[i], dat.begin() + p[i + 1]}; }
 ConstListRange<T> operator[](int i) const { return {dat.cbegin() + p[i], dat.cbegin() + p[i + 1]}; }
};
template <template <class> class F, class T> std::enable_if_t<std::disjunction_v<std::is_same<F<T>, ListRange<T>>, std::is_same<F<T>, ConstListRange<T>>, std::is_same<F<T>, CSRArray<T>>>, std::ostream &> operator<<(std::ostream &os, const F<T> &r) {
 os << '[';
 for (int _= 0, __= r.size(); _ < __; ++_) os << (_ ? ", " : "") << r[_];
 return os << ']';
}
struct Edge: std::pair<int, int> {
 using std::pair<int, int>::pair;
 Edge &operator--() { return --first, --second, *this; }
 int to(int v) const { return first ^ second ^ v; }
 friend std::istream &operator>>(std::istream &is, Edge &e) { return is >> e.first >> e.second, is; }
};
struct Graph: std::vector<Edge> {
 size_t n;
 Graph(size_t n= 0, size_t m= 0): vector(m), n(n) {}
 size_t vertex_size() const { return n; }
 size_t edge_size() const { return size(); }
 size_t add_vertex() { return n++; }
 size_t add_edge(int s, int d) { return emplace_back(s, d), size() - 1; }
 size_t add_edge(Edge e) { return emplace_back(e), size() - 1; }
#define _ADJ_FOR(a, b) \
 for (auto [u, v]: *this) a; \
 for (size_t i= 0; i < n; ++i) p[i + 1]+= p[i]; \
 for (int i= size(); i--;) { \
  auto [u, v]= (*this)[i]; \
  b; \
 }
#define _ADJ(a, b) \
 vector<int> p(n + 1), c(size() << !dir); \
 if (!dir) { \
  _ADJ_FOR((++p[u], ++p[v]), (c[--p[u]]= a, c[--p[v]]= b)) \
 } else if (dir > 0) { \
  _ADJ_FOR(++p[u], c[--p[u]]= a) \
 } else { \
  _ADJ_FOR(++p[v], c[--p[v]]= b) \
 } \
 return {c, p}
 CSRArray<int> adjacency_vertex(int dir) const { _ADJ(v, u); }
 CSRArray<int> adjacency_edge(int dir) const { _ADJ(i, i); }
#undef _ADJ
#undef _ADJ_FOR
};
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 int N, H;
 cin >> N >> H;
 PiecewiseLinearConvex<long long> f;
 for (int i= 0; i < N; ++i) {
  int S;
  cin >> S;
  f.chmin_slide_win(-H, H);
  f.add_abs(1, S);
 }
 cout << f.min() << '\n';
 return 0;
}

Subtask #1

3.0 / 3.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	344 KB	Output is correct
2	Correct	1 ms	348 KB	Output is correct
3	Correct	0 ms	348 KB	Output is correct
4	Correct	0 ms	348 KB	Output is correct
5	Correct	1 ms	348 KB	Output is correct
6	Correct	0 ms	348 KB	Output is correct
7	Correct	0 ms	348 KB	Output is correct

Subtask #2

4.0 / 4.0

#	결과	실행 시간	메모리	Grader output
1	Correct	0 ms	348 KB	Output is correct
2	Correct	0 ms	348 KB	Output is correct
3	Correct	0 ms	344 KB	Output is correct
4	Correct	0 ms	2396 KB	Output is correct
5	Correct	0 ms	348 KB	Output is correct

Subtask #3

9.0 / 9.0

#	결과	실행 시간	메모리	Grader output
1	Correct	0 ms	348 KB	Output is correct
2	Correct	0 ms	348 KB	Output is correct
3	Correct	0 ms	348 KB	Output is correct
4	Correct	0 ms	348 KB	Output is correct
5	Correct	0 ms	348 KB	Output is correct
6	Correct	0 ms	348 KB	Output is correct

Subtask #4

5.0 / 5.0

#	결과	실행 시간	메모리	Grader output
1	Correct	75 ms	9556 KB	Output is correct
2	Correct	126 ms	12556 KB	Output is correct
3	Correct	117 ms	12368 KB	Output is correct

Subtask #5

6.0 / 6.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	344 KB	Output is correct
2	Correct	1 ms	348 KB	Output is correct
3	Correct	0 ms	348 KB	Output is correct
4	Correct	0 ms	348 KB	Output is correct
5	Correct	1 ms	348 KB	Output is correct
6	Correct	0 ms	348 KB	Output is correct
7	Correct	0 ms	348 KB	Output is correct
8	Correct	0 ms	348 KB	Output is correct
9	Correct	0 ms	348 KB	Output is correct
10	Correct	0 ms	344 KB	Output is correct
11	Correct	0 ms	2396 KB	Output is correct
12	Correct	0 ms	348 KB	Output is correct
13	Correct	1 ms	344 KB	Output is correct
14	Correct	1 ms	344 KB	Output is correct
15	Correct	1 ms	348 KB	Output is correct
16	Correct	0 ms	348 KB	Output is correct
17	Correct	1 ms	2396 KB	Output is correct
18	Correct	1 ms	348 KB	Output is correct
19	Correct	0 ms	348 KB	Output is correct

Subtask #6

11.0 / 11.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	344 KB	Output is correct
2	Correct	1 ms	348 KB	Output is correct
3	Correct	0 ms	348 KB	Output is correct
4	Correct	0 ms	348 KB	Output is correct
5	Correct	1 ms	348 KB	Output is correct
6	Correct	0 ms	348 KB	Output is correct
7	Correct	0 ms	348 KB	Output is correct
8	Correct	0 ms	348 KB	Output is correct
9	Correct	0 ms	348 KB	Output is correct
10	Correct	0 ms	344 KB	Output is correct
11	Correct	0 ms	2396 KB	Output is correct
12	Correct	0 ms	348 KB	Output is correct
13	Correct	1 ms	344 KB	Output is correct
14	Correct	1 ms	344 KB	Output is correct
15	Correct	1 ms	348 KB	Output is correct
16	Correct	0 ms	348 KB	Output is correct
17	Correct	1 ms	2396 KB	Output is correct
18	Correct	1 ms	348 KB	Output is correct
19	Correct	0 ms	348 KB	Output is correct
20	Correct	1 ms	348 KB	Output is correct
21	Correct	1 ms	348 KB	Output is correct
22	Correct	0 ms	348 KB	Output is correct
23	Correct	1 ms	348 KB	Output is correct
24	Correct	0 ms	348 KB	Output is correct
25	Correct	1 ms	348 KB	Output is correct
26	Correct	0 ms	348 KB	Output is correct
27	Correct	1 ms	348 KB	Output is correct

Subtask #7

11.0 / 11.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	344 KB	Output is correct
2	Correct	1 ms	348 KB	Output is correct
3	Correct	0 ms	348 KB	Output is correct
4	Correct	0 ms	348 KB	Output is correct
5	Correct	1 ms	348 KB	Output is correct
6	Correct	0 ms	348 KB	Output is correct
7	Correct	0 ms	348 KB	Output is correct
8	Correct	0 ms	348 KB	Output is correct
9	Correct	0 ms	348 KB	Output is correct
10	Correct	0 ms	344 KB	Output is correct
11	Correct	0 ms	2396 KB	Output is correct
12	Correct	0 ms	348 KB	Output is correct
13	Correct	1 ms	344 KB	Output is correct
14	Correct	1 ms	344 KB	Output is correct
15	Correct	1 ms	348 KB	Output is correct
16	Correct	0 ms	348 KB	Output is correct
17	Correct	1 ms	2396 KB	Output is correct
18	Correct	1 ms	348 KB	Output is correct
19	Correct	0 ms	348 KB	Output is correct
20	Correct	1 ms	348 KB	Output is correct
21	Correct	1 ms	348 KB	Output is correct
22	Correct	0 ms	348 KB	Output is correct
23	Correct	1 ms	348 KB	Output is correct
24	Correct	0 ms	348 KB	Output is correct
25	Correct	1 ms	348 KB	Output is correct
26	Correct	0 ms	348 KB	Output is correct
27	Correct	1 ms	348 KB	Output is correct
28	Correct	3 ms	624 KB	Output is correct
29	Correct	2 ms	604 KB	Output is correct
30	Correct	2 ms	2396 KB	Output is correct
31	Correct	4 ms	816 KB	Output is correct
32	Correct	3 ms	860 KB	Output is correct
33	Correct	2 ms	644 KB	Output is correct
34	Correct	4 ms	2556 KB	Output is correct

Subtask #8

22.0 / 22.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	344 KB	Output is correct
2	Correct	1 ms	348 KB	Output is correct
3	Correct	0 ms	348 KB	Output is correct
4	Correct	0 ms	348 KB	Output is correct
5	Correct	1 ms	348 KB	Output is correct
6	Correct	0 ms	348 KB	Output is correct
7	Correct	0 ms	348 KB	Output is correct
8	Correct	0 ms	348 KB	Output is correct
9	Correct	0 ms	348 KB	Output is correct
10	Correct	0 ms	344 KB	Output is correct
11	Correct	0 ms	2396 KB	Output is correct
12	Correct	0 ms	348 KB	Output is correct
13	Correct	0 ms	348 KB	Output is correct
14	Correct	0 ms	348 KB	Output is correct
15	Correct	0 ms	348 KB	Output is correct
16	Correct	0 ms	348 KB	Output is correct
17	Correct	0 ms	348 KB	Output is correct
18	Correct	0 ms	348 KB	Output is correct
19	Correct	1 ms	344 KB	Output is correct
20	Correct	1 ms	344 KB	Output is correct
21	Correct	1 ms	348 KB	Output is correct
22	Correct	0 ms	348 KB	Output is correct
23	Correct	1 ms	2396 KB	Output is correct
24	Correct	1 ms	348 KB	Output is correct
25	Correct	0 ms	348 KB	Output is correct
26	Correct	1 ms	348 KB	Output is correct
27	Correct	1 ms	348 KB	Output is correct
28	Correct	0 ms	348 KB	Output is correct
29	Correct	1 ms	348 KB	Output is correct
30	Correct	0 ms	348 KB	Output is correct
31	Correct	1 ms	348 KB	Output is correct
32	Correct	0 ms	348 KB	Output is correct
33	Correct	1 ms	348 KB	Output is correct
34	Correct	3 ms	624 KB	Output is correct
35	Correct	2 ms	604 KB	Output is correct
36	Correct	2 ms	2396 KB	Output is correct
37	Correct	4 ms	816 KB	Output is correct
38	Correct	3 ms	860 KB	Output is correct
39	Correct	2 ms	644 KB	Output is correct
40	Correct	4 ms	2556 KB	Output is correct
41	Correct	2 ms	604 KB	Output is correct
42	Correct	2 ms	604 KB	Output is correct
43	Correct	4 ms	2652 KB	Output is correct
44	Correct	2 ms	604 KB	Output is correct
45	Correct	4 ms	860 KB	Output is correct
46	Correct	4 ms	2652 KB	Output is correct

Subtask #9

29.0 / 29.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	344 KB	Output is correct
2	Correct	1 ms	348 KB	Output is correct
3	Correct	0 ms	348 KB	Output is correct
4	Correct	0 ms	348 KB	Output is correct
5	Correct	1 ms	348 KB	Output is correct
6	Correct	0 ms	348 KB	Output is correct
7	Correct	0 ms	348 KB	Output is correct
8	Correct	0 ms	348 KB	Output is correct
9	Correct	0 ms	348 KB	Output is correct
10	Correct	0 ms	344 KB	Output is correct
11	Correct	0 ms	2396 KB	Output is correct
12	Correct	0 ms	348 KB	Output is correct
13	Correct	0 ms	348 KB	Output is correct
14	Correct	0 ms	348 KB	Output is correct
15	Correct	0 ms	348 KB	Output is correct
16	Correct	0 ms	348 KB	Output is correct
17	Correct	0 ms	348 KB	Output is correct
18	Correct	0 ms	348 KB	Output is correct
19	Correct	75 ms	9556 KB	Output is correct
20	Correct	126 ms	12556 KB	Output is correct
21	Correct	117 ms	12368 KB	Output is correct
22	Correct	1 ms	344 KB	Output is correct
23	Correct	1 ms	344 KB	Output is correct
24	Correct	1 ms	348 KB	Output is correct
25	Correct	0 ms	348 KB	Output is correct
26	Correct	1 ms	2396 KB	Output is correct
27	Correct	1 ms	348 KB	Output is correct
28	Correct	0 ms	348 KB	Output is correct
29	Correct	1 ms	348 KB	Output is correct
30	Correct	1 ms	348 KB	Output is correct
31	Correct	0 ms	348 KB	Output is correct
32	Correct	1 ms	348 KB	Output is correct
33	Correct	0 ms	348 KB	Output is correct
34	Correct	1 ms	348 KB	Output is correct
35	Correct	0 ms	348 KB	Output is correct
36	Correct	1 ms	348 KB	Output is correct
37	Correct	3 ms	624 KB	Output is correct
38	Correct	2 ms	604 KB	Output is correct
39	Correct	2 ms	2396 KB	Output is correct
40	Correct	4 ms	816 KB	Output is correct
41	Correct	3 ms	860 KB	Output is correct
42	Correct	2 ms	644 KB	Output is correct
43	Correct	4 ms	2556 KB	Output is correct
44	Correct	2 ms	604 KB	Output is correct
45	Correct	2 ms	604 KB	Output is correct
46	Correct	4 ms	2652 KB	Output is correct
47	Correct	2 ms	604 KB	Output is correct
48	Correct	4 ms	860 KB	Output is correct
49	Correct	4 ms	2652 KB	Output is correct
50	Correct	132 ms	13652 KB	Output is correct
51	Correct	98 ms	12484 KB	Output is correct
52	Correct	210 ms	20820 KB	Output is correct
53	Correct	344 ms	23508 KB	Output is correct
54	Correct	110 ms	15680 KB	Output is correct
55	Correct	269 ms	21476 KB	Output is correct
56	Correct	330 ms	22372 KB	Output is correct
57	Correct	298 ms	21328 KB	Output is correct
58	Correct	67 ms	9932 KB	Output is correct
59	Correct	184 ms	20560 KB	Output is correct