/** * author: tomo0608 * created: 01.05.2023 18:24:08 **/ #ifdef __LOCAL #define _GLIBCXX_DEBUG #endif #pragma GCC optimize("Ofast") #include #include namespace tomo0608 { typedef long long ll; typedef long double ld; template using V = std::vector; template using VV = V>; template using VVV = V>; typedef std::pair pii; typedef std::pair pll; templatevoid input(T&... a) { (std::cin >> ... >> a); }; #define INT(...) int __VA_ARGS__; input(__VA_ARGS__) #define LL(...) long long __VA_ARGS__; input(__VA_ARGS__) #define STR(...) string __VA_ARGS__; input(__VA_ARGS__) #define DBL(...) double __VA_ARGS__; input(__VA_ARGS__) std::istream& operator>>(std::istream& is, atcoder::modint998244353& a) { long long v; is >> v; a = v; return is; } std::ostream& operator<<(std::ostream& os, const atcoder::modint998244353& a) { return os << a.val(); } std::istream& operator>>(std::istream& is, atcoder::modint1000000007& a) { long long v; is >> v; a = v; return is; } std::ostream& operator<<(std::ostream& os, const atcoder::modint1000000007& a) { return os << a.val(); } template std::istream& operator>>(std::istream& is, atcoder::static_modint& a) { long long v; is >> v; a = v; return is; } template std::ostream& operator<<(std::ostream& os, const atcoder::static_modint& a) { return os << a.val(); } template std::istream& operator>>(std::istream& is, atcoder::dynamic_modint& a) { long long v; is >> v; a = v; return is; } template std::ostream& operator<<(std::ostream& os, const atcoder::dynamic_modint& a) { return os << a.val(); } template std::istream& operator>>(std::istream& is, std::pair& p) { is >> p.first >> p.second; return is; } template std::ostream& operator<<(std::ostream& os, const std::pair& p) { os << '(' << p.first << ", " << p.second << ')'; return os; } template std::istream& operator>>(std::istream& is, std::vector& v) { for (auto& e : v) is >> e; return is; } template std::ostream& operator<<(std::ostream& os, const std::vector& v) { for (auto& e : v) os << e << ' '; return os; } template std::ostream& operator << (std::ostream& os, std::set& set_var) { os << "{"; for (auto itr = set_var.begin(); itr != set_var.end(); itr++) { os << *itr;++itr;if (itr != set_var.end()) os << ", ";itr--; }os << "}";return os; } template std::ostream& operator<<(std::ostream& os, std::map& map_var) { os << "{";for (auto itr = map_var.begin(); itr != map_var.end(); itr++) { os << *itr;itr++;if (itr != map_var.end()) os << ", ";itr--; }os << "}";return os; } void print() { std::cout << '\n'; } templatevoid print(const T& a, const Ts&... b) { std::cout << a; (std::cout << ... << (std::cout << ' ', b)); std::cout << '\n'; } void drop() { std::cout << '\n';exit(0); } templatevoid drop(const T& a, const Ts&... b) { std::cout << a; (std::cout << ... << (std::cout << ' ', b)); std::cout << '\n';exit(0); } #ifdef __LOCAL void debug_out() { std::cerr << std::endl; } template < class Head, class... Tail> void debug_out(Head H, Tail... T) { std::cerr << ' ' << H; debug_out(T...); } #define debug(...) std::cerr << 'L' << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__) #define dump(x) std::cerr << 'L' << __LINE__ << " " << #x << " = " << (x) << std::endl #else #define debug(...) (void(0)) #define dump(x) (void(0)) #endif #define rep1(a) for(long long i = 0; i < a; i++) #define rep2(i, a) for(long long i = 0; i < a; i++) #define rep3(i, a, b) for(long long i = a; i < b; i++) #define rep4(i, a, b, c) for(long long i = a; i < b; i += c) #define drep1(a) for(long long i = a-1; i >= 0; i--) #define drep2(i, a) for(long long i = a-1; i >= 0; i--) #define drep3(i, a, b) for(long long i = a-1; i >= b; i--) #define drep4(i, a, b, c) for(long long i = a-1; i >= b; i -= c) #define overload4(a, b, c, d, e, ...) e #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define drep(...) overload4(__VA_ARGS__, drep4, drep3, drep2, drep1)(__VA_ARGS__) } // namespace tomo0608 int dx[8] = { 1, 0, -1, 0, 1, 1, -1, -1 }; int dy[8] = { 0, 1, 0, -1, 1, -1, -1, 1 }; #define endl '\n' namespace tomo0608 { #define all(x) x.begin(),x.end() template T SUM(const S& v) { return accumulate(all(v), T(0)); } #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()) template void zip(std::vector& x) { std::vector y = x;UNIQUE(y);for (int i = 0; i < x.size(); ++i) { x[i] = lb(y, x[i]); } } template using priority_queue_rev = std::priority_queue, std::greater>; template inline bool chmax(T& a, const U& b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, const U& b) { if (a > b) { a = b; return 1; } return 0; } template inline int count_between(std::vector& a, T l, T r) { return lower_bound(all(a), r) - lower_bound(all(a), l); } // [l, r) #define bit(n, k) ((n >> k) & 1) /*nのk bit目*/ int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); } int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); } int lowbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); } int lowbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); } template T mypow(T x, long long n) { T ret = 1;while (n > 0) { if (n & 1)(ret *= x);(x *= x);n >>= 1; }return ret; } } //typedef atcoder::modint1000000007 mint; typedef atcoder::modint998244353 mint; using namespace atcoder; using namespace std; using namespace tomo0608; #include const ll inf = 1e12; // https://ei1333.github.io/library/structure/convex-hull-trick/dynamic-li-chao-tree.hpp.html /** * @brief Dynamic-Li-Chao-Tree * @docs docs/dynamic-li-chao-tree.md */ template< typename T, T x_low, T x_high, T id > struct DynamicLiChaoTree { struct Line { T a, b; Line(T a, T b) : a(a), b(b) {} inline T get(T x) const { return a * x + b; } }; struct Node { Line x; Node* l, * r; Node(const Line& x) : x{ x }, l{ nullptr }, r{ nullptr } {} }; Node* root; DynamicLiChaoTree() : root{ nullptr } {} Node* add_line(Node* t, Line& x, const T& l, const T& r, const T& x_l, const T& x_r) { if (!t) return new Node(x); T t_l = t->x.get(l), t_r = t->x.get(r); if (t_l <= x_l && t_r <= x_r) { return t; } else if (t_l >= x_l && t_r >= x_r) { t->x = x; return t; } else { T m = (l + r) / 2; if (m == r) --m; T t_m = t->x.get(m), x_m = x.get(m); if (t_m > x_m) { swap(t->x, x); if (x_l >= t_l) t->l = add_line(t->l, x, l, m, t_l, t_m); else t->r = add_line(t->r, x, m + 1, r, t_m + x.a, t_r); } else { if (t_l >= x_l) t->l = add_line(t->l, x, l, m, x_l, x_m); else t->r = add_line(t->r, x, m + 1, r, x_m + x.a, x_r); } return t; } } void add_line(const T& a, const T& b) { Line x(a, b); root = add_line(root, x, x_low, x_high, x.get(x_low), x.get(x_high)); } Node* add_segment(Node* t, Line& x, const T& a, const T& b, const T& l, const T& r, const T& x_l, const T& x_r) { if (r < a || b < l) return t; if (a <= l && r <= b) { Line y{ x }; return add_line(t, y, l, r, x_l, x_r); } if (t) { T t_l = t->x.get(l), t_r = t->x.get(r); if (t_l <= x_l && t_r <= x_r) return t; } else { t = new Node(Line(0, id)); } T m = (l + r) / 2; if (m == r) --m; T x_m = x.get(m); t->l = add_segment(t->l, x, a, b, l, m, x_l, x_m); t->r = add_segment(t->r, x, a, b, m + 1, r, x_m + x.a, x_r); return t; } void add_segment(const T& l, const T& r, const T& a, const T& b) { Line x(a, b); root = add_segment(root, x, l, r - 1, x_low, x_high, x.get(x_low), x.get(x_high)); } T query(const Node* t, const T& l, const T& r, const T& x) const { if (!t) return id; if (l == r) return t->x.get(x); T m = (l + r) / 2; if (m == r) --m; if (x <= m) return min(t->x.get(x), query(t->l, l, m, x)); else return min(t->x.get(x), query(t->r, m + 1, r, x)); } T query(const T& x) const { return query(root, x_low, x_high, x); } }; void solve() { LL(n, m); V a(n), b(m), c(m);cin >> a >> b >> c; V ab(n + m + 1); rep(i, n)ab[i] = a[i]; ab[n] = -1; rep(j, m)ab[j + n + 1] = b[j]; V z_al = z_algorithm(ab); Vl(m); rep(i, m)l[i] = z_al[i + n + 1]; /*V dp(m + 1, inf); dp[0] = 0; rep(i, m) { if (dp[i] == inf)continue; rep(j, l[i] + 1) { chmin(dp[i + j], dp[i] + c[i] * j); } } if (dp[m] >= inf)dp[m] = -1; debug(dp); print(dp[m]); */ DynamicLiChaoTree LCT; rep(i, m) { ll dp_i = LCT.query(i); if (i == 0)dp_i = 0; if (dp_i == inf)continue; LCT.add_segment(i, i + l[i] + 1, c[i], dp_i - c[i] * i); } ll ans = LCT.query(m); if (ans >= inf || ans < 0)ans = -1; print(ans); } int main() { std::cin.tie(0); std::ios_base::sync_with_stdio(false); std::cout << std::setprecision(20); int codeforces = 1; //cin >> codeforces; while (codeforces--) { solve(); } return 0; }