#line 1 "/home/maspy/compro/library/my_template.hpp" #pragma GCC optimize("Ofast") #pragma GCC optimize("unroll-loops") #include using namespace std; using ll = long long; using pi = pair; using vi = vector; using u32 = unsigned int; using u64 = unsigned long long; using i128 = __int128; template using vc = vector; template using vvc = vector>; template using vvvc = vector>; template using vvvvc = vector>; template using vvvvvc = vector>; template using pq = priority_queue; template using pqg = priority_queue, greater>; #define vec(type, name, ...) vector name(__VA_ARGS__) #define vv(type, name, h, ...) \ vector> name(h, vector(__VA_ARGS__)) #define vvv(type, name, h, w, ...) \ vector>> name( \ h, vector>(w, vector(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector>>> name( \ a, vector>>( \ b, vector>(c, vector(__VA_ARGS__)))) // https://trap.jp/post/1224/ #define FOR1(a) for (ll _ = 0; _ < ll(a); ++_) #define FOR2(i, a) for (ll i = 0; i < ll(a); ++i) #define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i) #define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c)) #define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i) #define FOR4_R(i, a, b, c) for (ll i = (b)-1; i >= ll(a); i -= (c)) #define overload4(a, b, c, d, e, ...) e #define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__) #define FOR_R(...) \ overload4(__VA_ARGS__, FOR4_R, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__) #define FOR_subset(t, s) for (ll t = s; t >= 0; t = (t == 0 ? -1 : (t - 1) & s)) #define all(x) x.begin(), x.end() #define len(x) ll(x.size()) #define elif else if #define eb emplace_back #define mp make_pair #define mt make_tuple #define fi first #define se second #define stoi stoll template T SUM(const vector &A) { T sum = 0; for (auto &&a: A) sum += a; return sum; } #define MIN(v) *min_element(all(v)) #define MAX(v) *max_element(all(v)) #define LB(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define UB(c, x) distance((c).begin(), upper_bound(all(c), (x))) #define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()) int popcnt(int x) { return __builtin_popcount(x); } int popcnt(u32 x) { return __builtin_popcount(x); } int popcnt(ll x) { return __builtin_popcountll(x); } int popcnt(u64 x) { return __builtin_popcountll(x); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2) int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2) int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } template T pick(deque &que) { T a = que.front(); que.pop_front(); return a; } template T pick(pq &que) { T a = que.top(); que.pop(); return a; } template T pick(pqg &que) { assert(que.size()); T a = que.top(); que.pop(); return a; } template T pick(vc &que) { assert(que.size()); T a = que.back(); que.pop_back(); return a; } template T ceil(T x, U y) { return (x > 0 ? (x + y - 1) / y : x / y); } template T floor(T x, U y) { return (x > 0 ? x / y : (x - y + 1) / y); } template pair divmod(T x, U y) { T q = floor(x, y); return {q, x - q * y}; } template ll binary_search(F check, ll ok, ll ng) { assert(check(ok)); while (abs(ok - ng) > 1) { auto x = (ng + ok) / 2; tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x)); } return ok; } template double binary_search_real(F check, double ok, double ng, int iter = 100) { FOR(iter) { double x = (ok + ng) / 2; tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x)); } return (ok + ng) / 2; } template inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); } template inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); } vc s_to_vi(const string &S, char first_char) { vc A(S.size()); FOR(i, S.size()) { A[i] = S[i] - first_char; } return A; } template vector cumsum(vector &A, int off = 1) { int N = A.size(); vector B(N + 1); FOR(i, N) { B[i + 1] = B[i] + A[i]; } if (off == 0) B.erase(B.begin()); return B; } template vc bincount(const vc &A, int size) { vc C(size); for (auto &&x: A) { ++C[x]; } return C; } // stable template vector argsort(const vector &A) { vector ids(A.size()); iota(all(ids), 0); sort(all(ids), [&](int i, int j) { return A[i] < A[j] || (A[i] == A[j] && i < j); }); return ids; } // A[I[0]], A[I[1]], ... template vc rearrange(const vc &A, const vc &I) { int n = len(I); vc B(n); FOR(i, n) B[i] = A[I[i]]; return B; } #line 1 "/home/maspy/compro/library/other/io.hpp" // based on yosupo's fastio #include namespace detail { template std::true_type check_value(int); template std::false_type check_value(long); } // namespace detail template struct is_modint : decltype(detail::check_value(0)) {}; template using is_modint_t = enable_if_t::value>; template using is_not_modint_t = enable_if_t::value>; struct Scanner { FILE *fp; char line[(1 << 15) + 1]; size_t st = 0, ed = 0; void reread() { memmove(line, line + st, ed - st); ed -= st; st = 0; ed += fread(line + ed, 1, (1 << 15) - ed, fp); line[ed] = '\0'; } bool succ() { while (true) { if (st == ed) { reread(); if (st == ed) return false; } while (st != ed && isspace(line[st])) st++; if (st != ed) break; } if (ed - st <= 50) { bool sep = false; for (size_t i = st; i < ed; i++) { if (isspace(line[i])) { sep = true; break; } } if (!sep) reread(); } return true; } template ::value, int> = 0> bool read_single(T &ref) { if (!succ()) return false; while (true) { size_t sz = 0; while (st + sz < ed && !isspace(line[st + sz])) sz++; ref.append(line + st, sz); st += sz; if (!sz || st != ed) break; reread(); } return true; } template ::value, int> = 0> bool read_single(T &ref) { if (!succ()) return false; bool neg = false; if (line[st] == '-') { neg = true; st++; } ref = T(0); while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); } if (neg) ref = -ref; return true; } template * = nullptr> bool read_single(T &ref) { long long val = 0; bool f = read_single(val); ref = T(val); return f; } bool read_single(double &ref) { string s; if (!read_single(s)) return false; ref = std::stod(s); return true; } bool read_single(char &ref) { string s; if (!read_single(s) || s.size() != 1) return false; ref = s[0]; return true; } template bool read_single(vector &ref) { for (auto &d: ref) { if (!read_single(d)) return false; } return true; } template bool read_single(pair &p) { return (read_single(p.first) && read_single(p.second)); } template bool read_single(tuple &p) { return (read_single(get<0>(p)) && read_single(get<1>(p)) && read_single(get<2>(p))); } template bool read_single(tuple &p) { return (read_single(get<0>(p)) && read_single(get<1>(p)) && read_single(get<2>(p)) && read_single(get<3>(p))); } void read() {} template void read(H &h, T &... t) { bool f = read_single(h); assert(f); read(t...); } Scanner(FILE *fp) : fp(fp) {} }; struct Printer { Printer(FILE *_fp) : fp(_fp) {} ~Printer() { flush(); } static constexpr size_t SIZE = 1 << 15; FILE *fp; char line[SIZE], small[50]; size_t pos = 0; void flush() { fwrite(line, 1, pos, fp); pos = 0; } void write(const char &val) { if (pos == SIZE) flush(); line[pos++] = val; } template ::value, int> = 0> void write(T val) { if (pos > (1 << 15) - 50) flush(); if (val == 0) { write('0'); return; } if (val < 0) { write('-'); val = -val; // todo min } size_t len = 0; while (val) { small[len++] = char(0x30 | (val % 10)); val /= 10; } for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; } pos += len; } void write(const string &s) { for (char c: s) write(c); } void write(const char *s) { size_t len = strlen(s); for (size_t i = 0; i < len; i++) write(s[i]); } void write(const double &x) { ostringstream oss; oss << fixed << setprecision(15) << x; string s = oss.str(); write(s); } void write(const long double &x) { ostringstream oss; oss << fixed << setprecision(15) << x; string s = oss.str(); write(s); } template * = nullptr> void write(T &ref) { write(ref.val); } template void write(const vector &val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) write(' '); write(val[i]); } } template void write(const pair &val) { write(val.first); write(' '); write(val.second); } template void write(const tuple &val) { auto &[a, b, c] = val; write(a), write(' '), write(b), write(' '), write(c); } template void write(const tuple &val) { auto &[a, b, c, d] = val; write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d); } template void write(const tuple &val) { auto &[a, b, c, d, e] = val; write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e); } template void write(const tuple &val) { auto &[a, b, c, d, e, f] = val; write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e), write(' '), write(f); } template void write(const array &val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) write(' '); write(val[i]); } } void write(i128 val) { string s; bool negative = 0; if(val < 0){ negative = 1; val = -val; } while (val) { s += '0' + int(val % 10); val /= 10; } if(negative) s += "-"; reverse(all(s)); if (len(s) == 0) s = "0"; write(s); } }; Scanner scanner = Scanner(stdin); Printer printer = Printer(stdout); void flush() { printer.flush(); } void print() { printer.write('\n'); } template void print(Head &&head, Tail &&... tail) { printer.write(head); if (sizeof...(Tail)) printer.write(' '); print(forward(tail)...); } void read() {} template void read(Head &head, Tail &... tail) { scanner.read(head); read(tail...); } #define INT(...) \ int __VA_ARGS__; \ read(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ read(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ read(__VA_ARGS__) #define CHAR(...) \ char __VA_ARGS__; \ read(__VA_ARGS__) #define DBL(...) \ double __VA_ARGS__; \ read(__VA_ARGS__) #define VEC(type, name, size) \ vector name(size); \ read(name) #define VV(type, name, h, w) \ vector> name(h, vector(w)); \ read(name) void YES(bool t = 1) { print(t ? "YES" : "NO"); } void NO(bool t = 1) { YES(!t); } void Yes(bool t = 1) { print(t ? "Yes" : "No"); } void No(bool t = 1) { Yes(!t); } void yes(bool t = 1) { print(t ? "yes" : "no"); } void no(bool t = 1) { yes(!t); } #line 1 "/home/maspy/compro/library/ds/cht/cht_monotone.hpp" template struct CHT_monotone { #define F first #define S second using P = pair; deque

H; CHT_monotone() = default; bool empty() const { return H.empty(); } void clear() { H.clear(); } inline int sgn(T x) { return x == 0 ? 0 : (x < 0 ? -1 : 1); } using D = long double; inline bool check(const P &a, const P &b, const P &c) { if (b.S == a.S || c.S == b.S) return sgn(b.F - a.F) * sgn(c.S - b.S) >= sgn(c.F - b.F) * sgn(b.S - a.S); // return (b.F-a.F)*(c.S-b.S) >= (b.S-a.S)*(c.F-b.F); return D(b.F - a.F) * sgn(c.S - b.S) / D(abs(b.S - a.S)) >= D(c.F - b.F) * sgn(b.S - a.S) / D(abs(c.S - b.S)); } void add(T a, T b) { if (!isMin) a *= -1, b *= -1; P line(a, b); if (empty()) { H.emplace_front(line); return; } if (H.front().F <= a) { if (H.front().F == a) { if (H.front().S <= b) return; H.pop_front(); } while (H.size() >= 2 && check(line, H.front(), H[1])) H.pop_front(); H.emplace_front(line); } else { assert(a <= H.back().F); if (H.back().F == a) { if (H.back().S <= b) return; H.pop_back(); } while (H.size() >= 2 && check(H[H.size() - 2], H.back(), line)) H.pop_back(); H.emplace_back(line); } } inline T get_y(const P &a, const T &x) { return a.F * x + a.S; } T query(T x) { assert(!empty()); int l = -1, r = H.size() - 1; while (l + 1 < r) { int m = (l + r) >> 1; if (get_y(H[m], x) >= get_y(H[m + 1], x)) l = m; else r = m; } if (isMin) return get_y(H[r], x); return -get_y(H[r], x); } T query_monotone_inc(T x) { assert(!empty()); while (H.size() >= 2 && get_y(H.front(), x) >= get_y(H[1], x)) H.pop_front(); if (isMin) return get_y(H.front(), x); return -get_y(H.front(), x); } T query_monotone_dec(T x) { assert(!empty()); while (H.size() >= 2 && get_y(H.back(), x) >= get_y(H[H.size() - 2], x)) H.pop_back(); if (isMin) return get_y(H.back(), x); return -get_y(H.back(), x); } #undef F #undef S }; #line 1 "/home/maspy/compro/library/ds/cht/cht.hpp" template struct Line { mutable T k, m, p; bool operator<(const Line& o) const { return k < o.k; } bool operator<(T x) const { return p < x; } }; template T lc_inf() { return numeric_limits::max(); } template <> long double lc_inf() { return 1 / .0; } template T lc_div(T a, T b) { return a / b - ((a ^ b) < 0 and a % b); } template <> long double lc_div(long double a, long double b) { return a / b; }; template <> double lc_div(double a, double b) { return a / b; }; template struct LineContainer : multiset, less<>> { using super = multiset, less<>>; using super::begin, super::end, super::insert, super::erase; using super::empty, super::lower_bound; const T inf = lc_inf(); bool insect(typename super::iterator x, typename super::iterator y) { if (y == end()) return x->p = inf, false; if (x->k == y->k) x->p = (x->m > y->m ? inf : -inf); else x->p = lc_div(y->m - x->m, x->k - y->k); return x->p >= y->p; } void add(T k, T m) { if (MINIMIZE) { k = -k, m = -m; } auto z = insert({k, m, 0}), y = z++, x = y; while (insect(y, z)) z = erase(z); if (x != begin() and insect(--x, y)) insect(x, y = erase(y)); while ((y = x) != begin() and (--x)->p >= y->p) insect(x, erase(y)); } T query(T x) { assert(!empty()); auto l = *lower_bound(x); T v = (l.k * x + l.m); return (MINIMIZE ? -v : v); } }; template using CHT_min = LineContainer; template using CHT_max = LineContainer; /* long long / double で動くと思う。クエリあたり O(log N) ・add(a, b):ax + by の追加 ・get_max(x,y):max_{a,b} (ax + by) ・get_min(x,y):max_{a,b} (ax + by) */ template struct CHT_xy { using ld = long double; CHT_min cht_min; CHT_max cht_max; T amax = -1e18, amin = 1e18, bmax = -1e18, bmin = 1e18; void add(T a, T b) { cht_min.add(b, a); cht_max.add(b, a); chmax(amax, a), chmin(amin, a), chmax(bmax, b), chmin(bmin, b); } T get_max(T x, T y) { if (x == 0) { return max(bmax * y, bmin * y); } ld z = ld(y) / x; if (x > 0) { auto l = cht_max.lower_bound(z); ll a = l->m, b = l->k; return a * x + b * y; } auto l = cht_min.lower_bound(z); ll a = -(l->m), b = -(l->k); return a * x + b * y; } T get_min(T x, T y) { return -get_max(-x, -y); } }; #line 5 "main.cpp" void solve() { LL(N, C); const ll INF = 1LL << 60; vi dp(N + 1, INF); dp[0] = 0; CHT_monotone X2; CHT_min X1; FOR(i, N + 1) { if (i) dp[i] = X1.query(i) + (i * i - i) * C; if (i == N) break; { ll a = i; ll b = dp[i] + (i * i - i) * C; X2.add(a, b); } LL(A, B); A *= 2, B *= 2; ll x = -2 * C * i - A; ll y = X2.query(x); y += 2 * (i * i + i) * C + B; { ll a = A - 2 * C * i; ll b = y; X1.add(a, b); } } ll ANS = dp[N] / 2; print(ANS); } signed main() { cout << fixed << setprecision(15); ll T = 1; // LL(T); FOR(T) solve(); return 0; }