Submission #1068851

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
1068851	2024-08-21T12:36:41 Z	hashiryo	Safety (NOI18_safety)	C++17	100 / 100	375 ms	59816 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
#include <optional>
// 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 << (20 + 2 * persistent)> class PiecewiseLinearConvex {
 using D= make_long_t<T>;
 struct Node {
  int ch[2]= {0, 0};
  T z= 0, x= 0, d= 0, a= 0;
  D s= 0;
  size_t sz= 0;
  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]{Node{}};
 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++; }
 static inline bool lt(T a, T b) {
  if constexpr (std::is_floating_point_v<T>) return 1e-15 < b - a;
  else return a < b;
 }
 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 (lt(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 (lt(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 (lt(x, n[t].x)) return join<0>(insert(n[t].ch[0], x, d), t, n[t].ch[1]);
  if (lt(n[t].x, x)) return join<0>(n[t].ch[0], t, insert(n[t].ch[1], x, d));
  return n[t].d+= d, update(t), t;
 }
 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 g> static inline bool lgt(T a, T b) {
  if constexpr (g) return lt(b, a);
  else return lt(a, b);
 }
 template <bool r> static inline int cut(int t, T x) {
  if (!t) return t;
  if (push(t); lgt<r>(n[t].x, x)) return cut<r>(n[t].ch[!r], x);
  if (lgt<r>(x, n[t].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]);
  }
  return n[t].ch[!r];
 }
 template <bool r> static inline D calc_y(int t, T x, T ol, D ou) {
  for (; t;) {
   if (push(t); lgt<r>(n[t].x, x)) t= n[t].ch[!r];
   else {
    ol+= n[n[t].ch[!r]].a, ou+= n[n[t].ch[!r]].s;
    if (!lgt<r>(x, n[t].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 (lt(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 (lt(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 lt(a, b);
  else return !lt(b, a);
 }
 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 (lt(x, n[mn].x)) return -calc_y<0>(lr[0], x, o[0], D(n[mn].x) * o[0]);
  if (lt(n[mn].x, x)) return calc_y<1>(lr[1], x, o[1], D(n[mn].x) * o[1]);
  return 0;
 }
 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] && !lgt<r>(bx[r], x0)) return;
  if (assert(!bf[!r] || !lgt<r>(bx[!r], x0)), bf[r]= true, bx[r]= x0; !mn) return;
  if (lgt<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 (lt(d, 0)) y-= D(d) * x, rem+= d, d= -d;
   if (!lt(0, d)) continue;
   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 && !lt(w[t - 1].second, w[i].second) && !lt(w[i].second, w[t - 1].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(lt(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 (lt(n[mn].x, x0)) lr[1]= insert(lr[1], x0, c), y-= D(a) * x0, rem+= a;
   else if (lt(x0, n[mn].x)) lr[0]= insert(lr[0], x0, c), y-= D(b) * x0, rem+= b;
   else {
    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 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 (lt(0, a)) add_max(0, a, x0);
  else if (lt(a, 0)) add_max(a, 0, x0);
 }
 // f(x) += a|x-x0|, \/
 void add_abs(T a, T x0) {
  if (assert(!lt(a, 0)); lt(0, a)) 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] && !lt(bx[0], bx[1])) y+= D(rem) * bx[0], rem= 0;
  else if (bool r= lt(rem, 0); r || lt(0, rem)) {
   T u= (r ? -rem : rem) - o[r] - n[lr[r]].a;
   if (!lt(u, 0)) {
    if (r ^ rev) {
     if (lt(0, u) && 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]), lr[!rev]= 0, o[!rev]= 0;
     }
    } 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[0]= lr[1]= 0, o[0]= o[1]= 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 (!lt(0, o[rev])) {
    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] && !lt(bx[0], bx[1])) y+= D(rem) * bx[0], rem= 0;
  else {
   if (bool r= lt(rem, 0); r || lt(0, rem)) {
    T u= (r ? -rem : rem) - o[r] - n[lr[r]].a;
    if (lt(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 (!lt(0, o[0])) prop(ub);
    else if (!lt(0, o[1])) 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;
 }
 std::optional<D> operator()(T x) {
  if (bf[0] && x < bx[0]) return std::nullopt;
  if (bf[1] && bx[1] < x) return std::nullopt;
  return calc_y(x) + D(rem) * x + y;
 }
 std::optional<D> min() {
  bool r= lt(rem, 0);
  if (!r && !lt(0, rem)) return y;
  T u= (r ? -rem : rem) - o[r] - n[lr[r]].a;
  if (lt(0, u)) {
   if (!bf[r]) return std::nullopt;
   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 (bool r= lt(rem, 0); r || lt(0, rem)) {
   if (lt(o[r] + n[lr[r]].a, (r ? -rem : rem))) {
    if (!bf[r]) return {1, 0};  // no solution
    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= lt(0, o[0]);
  if (r && lt(0, o[1])) 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 if (!bf[r]) return {1, 0};  // no solution
  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;
 }
};
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().value() << '\n';
 return 0;
}

Subtask #1

3.0 / 3.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	14 ms	57692 KB	Output is correct
2	Correct	20 ms	57688 KB	Output is correct
3	Correct	8 ms	57692 KB	Output is correct
4	Correct	8 ms	57764 KB	Output is correct
5	Correct	12 ms	57692 KB	Output is correct
6	Correct	22 ms	57824 KB	Output is correct
7	Correct	20 ms	57692 KB	Output is correct

Subtask #2

4.0 / 4.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	9 ms	57692 KB	Output is correct
2	Correct	21 ms	57692 KB	Output is correct
3	Correct	21 ms	57692 KB	Output is correct
4	Correct	9 ms	57692 KB	Output is correct
5	Correct	9 ms	57928 KB	Output is correct

Subtask #3

9.0 / 9.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	8 ms	57692 KB	Output is correct
2	Correct	10 ms	57924 KB	Output is correct
3	Correct	7 ms	57688 KB	Output is correct
4	Correct	7 ms	57692 KB	Output is correct
5	Correct	7 ms	57744 KB	Output is correct
6	Correct	8 ms	57692 KB	Output is correct

Subtask #4

5.0 / 5.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	91 ms	58960 KB	Output is correct
2	Correct	144 ms	59556 KB	Output is correct
3	Correct	144 ms	59568 KB	Output is correct

Subtask #5

6.0 / 6.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	14 ms	57692 KB	Output is correct
2	Correct	20 ms	57688 KB	Output is correct
3	Correct	8 ms	57692 KB	Output is correct
4	Correct	8 ms	57764 KB	Output is correct
5	Correct	12 ms	57692 KB	Output is correct
6	Correct	22 ms	57824 KB	Output is correct
7	Correct	20 ms	57692 KB	Output is correct
8	Correct	9 ms	57692 KB	Output is correct
9	Correct	21 ms	57692 KB	Output is correct
10	Correct	21 ms	57692 KB	Output is correct
11	Correct	9 ms	57692 KB	Output is correct
12	Correct	9 ms	57928 KB	Output is correct
13	Correct	8 ms	57688 KB	Output is correct
14	Correct	9 ms	57692 KB	Output is correct
15	Correct	9 ms	57872 KB	Output is correct
16	Correct	9 ms	57692 KB	Output is correct
17	Correct	8 ms	57792 KB	Output is correct
18	Correct	13 ms	57780 KB	Output is correct
19	Correct	12 ms	57692 KB	Output is correct

Subtask #6

11.0 / 11.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	14 ms	57692 KB	Output is correct
2	Correct	20 ms	57688 KB	Output is correct
3	Correct	8 ms	57692 KB	Output is correct
4	Correct	8 ms	57764 KB	Output is correct
5	Correct	12 ms	57692 KB	Output is correct
6	Correct	22 ms	57824 KB	Output is correct
7	Correct	20 ms	57692 KB	Output is correct
8	Correct	9 ms	57692 KB	Output is correct
9	Correct	21 ms	57692 KB	Output is correct
10	Correct	21 ms	57692 KB	Output is correct
11	Correct	9 ms	57692 KB	Output is correct
12	Correct	9 ms	57928 KB	Output is correct
13	Correct	8 ms	57688 KB	Output is correct
14	Correct	9 ms	57692 KB	Output is correct
15	Correct	9 ms	57872 KB	Output is correct
16	Correct	9 ms	57692 KB	Output is correct
17	Correct	8 ms	57792 KB	Output is correct
18	Correct	13 ms	57780 KB	Output is correct
19	Correct	12 ms	57692 KB	Output is correct
20	Correct	8 ms	57692 KB	Output is correct
21	Correct	10 ms	57692 KB	Output is correct
22	Correct	8 ms	57912 KB	Output is correct
23	Correct	10 ms	57692 KB	Output is correct
24	Correct	9 ms	57692 KB	Output is correct
25	Correct	9 ms	57832 KB	Output is correct
26	Correct	9 ms	57692 KB	Output is correct
27	Correct	10 ms	57932 KB	Output is correct

Subtask #7

11.0 / 11.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	14 ms	57692 KB	Output is correct
2	Correct	20 ms	57688 KB	Output is correct
3	Correct	8 ms	57692 KB	Output is correct
4	Correct	8 ms	57764 KB	Output is correct
5	Correct	12 ms	57692 KB	Output is correct
6	Correct	22 ms	57824 KB	Output is correct
7	Correct	20 ms	57692 KB	Output is correct
8	Correct	9 ms	57692 KB	Output is correct
9	Correct	21 ms	57692 KB	Output is correct
10	Correct	21 ms	57692 KB	Output is correct
11	Correct	9 ms	57692 KB	Output is correct
12	Correct	9 ms	57928 KB	Output is correct
13	Correct	8 ms	57688 KB	Output is correct
14	Correct	9 ms	57692 KB	Output is correct
15	Correct	9 ms	57872 KB	Output is correct
16	Correct	9 ms	57692 KB	Output is correct
17	Correct	8 ms	57792 KB	Output is correct
18	Correct	13 ms	57780 KB	Output is correct
19	Correct	12 ms	57692 KB	Output is correct
20	Correct	8 ms	57692 KB	Output is correct
21	Correct	10 ms	57692 KB	Output is correct
22	Correct	8 ms	57912 KB	Output is correct
23	Correct	10 ms	57692 KB	Output is correct
24	Correct	9 ms	57692 KB	Output is correct
25	Correct	9 ms	57832 KB	Output is correct
26	Correct	9 ms	57692 KB	Output is correct
27	Correct	10 ms	57932 KB	Output is correct
28	Correct	12 ms	57792 KB	Output is correct
29	Correct	13 ms	57948 KB	Output is correct
30	Correct	10 ms	57944 KB	Output is correct
31	Correct	13 ms	57944 KB	Output is correct
32	Correct	11 ms	57692 KB	Output is correct
33	Correct	12 ms	57816 KB	Output is correct
34	Correct	13 ms	57948 KB	Output is correct

Subtask #8

22.0 / 22.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	14 ms	57692 KB	Output is correct
2	Correct	20 ms	57688 KB	Output is correct
3	Correct	8 ms	57692 KB	Output is correct
4	Correct	8 ms	57764 KB	Output is correct
5	Correct	12 ms	57692 KB	Output is correct
6	Correct	22 ms	57824 KB	Output is correct
7	Correct	20 ms	57692 KB	Output is correct
8	Correct	9 ms	57692 KB	Output is correct
9	Correct	21 ms	57692 KB	Output is correct
10	Correct	21 ms	57692 KB	Output is correct
11	Correct	9 ms	57692 KB	Output is correct
12	Correct	9 ms	57928 KB	Output is correct
13	Correct	8 ms	57692 KB	Output is correct
14	Correct	10 ms	57924 KB	Output is correct
15	Correct	7 ms	57688 KB	Output is correct
16	Correct	7 ms	57692 KB	Output is correct
17	Correct	7 ms	57744 KB	Output is correct
18	Correct	8 ms	57692 KB	Output is correct
19	Correct	8 ms	57688 KB	Output is correct
20	Correct	9 ms	57692 KB	Output is correct
21	Correct	9 ms	57872 KB	Output is correct
22	Correct	9 ms	57692 KB	Output is correct
23	Correct	8 ms	57792 KB	Output is correct
24	Correct	13 ms	57780 KB	Output is correct
25	Correct	12 ms	57692 KB	Output is correct
26	Correct	8 ms	57692 KB	Output is correct
27	Correct	10 ms	57692 KB	Output is correct
28	Correct	8 ms	57912 KB	Output is correct
29	Correct	10 ms	57692 KB	Output is correct
30	Correct	9 ms	57692 KB	Output is correct
31	Correct	9 ms	57832 KB	Output is correct
32	Correct	9 ms	57692 KB	Output is correct
33	Correct	10 ms	57932 KB	Output is correct
34	Correct	12 ms	57792 KB	Output is correct
35	Correct	13 ms	57948 KB	Output is correct
36	Correct	10 ms	57944 KB	Output is correct
37	Correct	13 ms	57944 KB	Output is correct
38	Correct	11 ms	57692 KB	Output is correct
39	Correct	12 ms	57816 KB	Output is correct
40	Correct	13 ms	57948 KB	Output is correct
41	Correct	12 ms	57944 KB	Output is correct
42	Correct	9 ms	57748 KB	Output is correct
43	Correct	12 ms	57948 KB	Output is correct
44	Correct	10 ms	57928 KB	Output is correct
45	Correct	16 ms	57944 KB	Output is correct
46	Correct	11 ms	57948 KB	Output is correct

Subtask #9

29.0 / 29.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	14 ms	57692 KB	Output is correct
2	Correct	20 ms	57688 KB	Output is correct
3	Correct	8 ms	57692 KB	Output is correct
4	Correct	8 ms	57764 KB	Output is correct
5	Correct	12 ms	57692 KB	Output is correct
6	Correct	22 ms	57824 KB	Output is correct
7	Correct	20 ms	57692 KB	Output is correct
8	Correct	9 ms	57692 KB	Output is correct
9	Correct	21 ms	57692 KB	Output is correct
10	Correct	21 ms	57692 KB	Output is correct
11	Correct	9 ms	57692 KB	Output is correct
12	Correct	9 ms	57928 KB	Output is correct
13	Correct	8 ms	57692 KB	Output is correct
14	Correct	10 ms	57924 KB	Output is correct
15	Correct	7 ms	57688 KB	Output is correct
16	Correct	7 ms	57692 KB	Output is correct
17	Correct	7 ms	57744 KB	Output is correct
18	Correct	8 ms	57692 KB	Output is correct
19	Correct	91 ms	58960 KB	Output is correct
20	Correct	144 ms	59556 KB	Output is correct
21	Correct	144 ms	59568 KB	Output is correct
22	Correct	8 ms	57688 KB	Output is correct
23	Correct	9 ms	57692 KB	Output is correct
24	Correct	9 ms	57872 KB	Output is correct
25	Correct	9 ms	57692 KB	Output is correct
26	Correct	8 ms	57792 KB	Output is correct
27	Correct	13 ms	57780 KB	Output is correct
28	Correct	12 ms	57692 KB	Output is correct
29	Correct	8 ms	57692 KB	Output is correct
30	Correct	10 ms	57692 KB	Output is correct
31	Correct	8 ms	57912 KB	Output is correct
32	Correct	10 ms	57692 KB	Output is correct
33	Correct	9 ms	57692 KB	Output is correct
34	Correct	9 ms	57832 KB	Output is correct
35	Correct	9 ms	57692 KB	Output is correct
36	Correct	10 ms	57932 KB	Output is correct
37	Correct	12 ms	57792 KB	Output is correct
38	Correct	13 ms	57948 KB	Output is correct
39	Correct	10 ms	57944 KB	Output is correct
40	Correct	13 ms	57944 KB	Output is correct
41	Correct	11 ms	57692 KB	Output is correct
42	Correct	12 ms	57816 KB	Output is correct
43	Correct	13 ms	57948 KB	Output is correct
44	Correct	12 ms	57944 KB	Output is correct
45	Correct	9 ms	57748 KB	Output is correct
46	Correct	12 ms	57948 KB	Output is correct
47	Correct	10 ms	57928 KB	Output is correct
48	Correct	16 ms	57944 KB	Output is correct
49	Correct	11 ms	57948 KB	Output is correct
50	Correct	150 ms	59816 KB	Output is correct
51	Correct	116 ms	59472 KB	Output is correct
52	Correct	236 ms	59428 KB	Output is correct
53	Correct	375 ms	59568 KB	Output is correct
54	Correct	128 ms	59424 KB	Output is correct
55	Correct	284 ms	59436 KB	Output is correct
56	Correct	358 ms	59476 KB	Output is correct
57	Correct	347 ms	59472 KB	Output is correct
58	Correct	82 ms	58784 KB	Output is correct
59	Correct	247 ms	59556 KB	Output is correct