#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } const std::vector> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}}; int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); } template std::pair operator+(const std::pair &l, const std::pair &r) { return std::make_pair(l.first + r.first, l.second + r.second); } template std::pair operator-(const std::pair &l, const std::pair &r) { return std::make_pair(l.first - r.first, l.second - r.second); } template std::vector sort_unique(std::vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template IStream &operator>>(IStream &is, std::vector &vec) { for (auto &v : vec) is >> v; return is; } template OStream &operator<<(OStream &os, const std::vector &vec); template OStream &operator<<(OStream &os, const std::array &arr); template OStream &operator<<(OStream &os, const std::unordered_set &vec); template OStream &operator<<(OStream &os, const pair &pa); template OStream &operator<<(OStream &os, const std::deque &vec); template OStream &operator<<(OStream &os, const std::set &vec); template OStream &operator<<(OStream &os, const std::multiset &vec); template OStream &operator<<(OStream &os, const std::unordered_multiset &vec); template OStream &operator<<(OStream &os, const std::pair &pa); template OStream &operator<<(OStream &os, const std::map &mp); template OStream &operator<<(OStream &os, const std::unordered_map &mp); template OStream &operator<<(OStream &os, const std::tuple &tpl); template OStream &operator<<(OStream &os, const std::vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } #if __cplusplus >= 201703L template std::istream &operator>>(std::istream &is, std::tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template OStream &operator<<(OStream &os, const std::tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } #endif template OStream &operator<<(OStream &os, const std::unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::pair &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; } template OStream &operator<<(OStream &os, const std::map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl #define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr) #else #define dbg(x) ((void)0) #define dbgif(cond, x) ((void)0) #endif // Slope trick: fast operations for convex piecewise-linear functions // Implementation idea: // - https://maspypy.com/slope-trick-1-%E8%A7%A3%E8%AA%AC%E7%B7%A8 // - https://ei1333.github.io/library/structure/others/slope-trick.cpp template ::max() / 2> class slope_trick { T min_f; T displacement_l, displacement_r; std::priority_queue, std::less> L; std::priority_queue, std::greater> R; void pushR(const T &a) { R.push(a - displacement_r); } T topR() const { return R.empty() ? INF : R.top() + displacement_r; } T popR() { auto ret = topR(); if (R.size()) R.pop(); return ret; } void pushL(const T &a) { L.push(a + displacement_l); } T topL() const { return L.empty() ? -INF : L.top() - displacement_l; } T popL() { auto ret = topL(); if (L.size()) L.pop(); return ret; } public: // Initialize, f(x) = 0 everywhere // Complexity: O(1) slope_trick() : min_f(0), displacement_l(0), displacement_r(0) { static_assert(INF > 0, "INF must be greater than 0"); } inline int sizeL() const noexcept { return L.size(); } inline int sizeR() const noexcept { return R.size(); } // argmin f(x), min f(x) // Complexity: O(1) using Q = struct { T min, lo, hi; }; Q get_min() const { return {min_f, topL(), topR()}; } // f(x) += b // Complexity: O(1) slope_trick &add_const(const T &b) { min_f += b; return *this; } // f(x) += max(x - a, 0) _/ // Complexity: O(log n) slope_trick &add_relu(const T &a) { min_f += std::max(T(0), topL() - a), pushL(a), pushR(popL()); return *this; } // f(x) += max(a - x, 0) \_ // Complexity: O(log n) slope_trick &add_irelu(const T &a) { min_f += std::max(T(0), a - topR()), pushR(a), pushL(popR()); return *this; } // f(x) += |x - a| \/ // Complexity: O(log n) slope_trick &add_abs(const T &a) { return add_relu(a).add_irelu(a); } // f(x) <- min_{0 <= y <= w} f(x + y) .\ -> \_ // Complexity: O(1) slope_trick &move_left_curve(const T &w) { return assert(w >= 0), displacement_l += w, *this; } // f(x) <- min_{0 <= y <= w} f(x - y) /. -> _/ // Complexity: O(1) slope_trick &move_right_curve(const T &w) { return assert(w >= 0), displacement_r += w, *this; } // f(x) <- f(x - dx) \/. -> .\/ // Complexity: O(1) slope_trick &translate(const T &dx) { return displacement_l -= dx, displacement_r += dx, *this; } // return f(x), f destructive T get_destructive(const T &x) { T ret = get_min().min; while (L.size()) ret += std::max(T(0), popL() - x); while (R.size()) ret += std::max(T(0), x - popR()); return ret; } // f(x) += g(x), g destructive slope_trick &merge_destructive(slope_trick &g) { if (sizeL() + sizeR() > g.sizeL() + g.sizeR()) { std::swap(min_f, g.min_f); std::swap(displacement_l, g.displacement_l); std::swap(displacement_r, g.displacement_r); std::swap(L, g.L); std::swap(R, g.R); } min_f += g.get_min().min; while (g.L.size()) add_irelu(g.popL()); while (g.R.size()) add_relu(g.popR()); return *this; } }; // https://maspypy.com/slope-trick-3-slope-trick-%E3%81%AE%E5%87%B8%E5%85%B1%E5%BD%B9 template ::max() / 2> class dual_slope_trick : private slope_trick { public: using Base = slope_trick; // Initialize: f(x) = 0 (x == 0), inf (otherwise) // Complexity: O(1) dual_slope_trick() : Base() {} // Get f(0) // Complexity: O(1) T get_at_zero() const { return -Base::get_min().min; } // f(x) <- f(x - d) (Move graph to right by d) // Complexity: O(log n) dual_slope_trick &shift(int d) { while (d > 0) --d, Base::add_relu(-INF).add_const(-INF); while (d < 0) ++d, Base::add_irelu(INF).add_const(-INF); return *this; } // f(x) += ax + b // Complexity: O(1) dual_slope_trick &add_linear(T a, T b) { return Base::translate(a).add_const(b), *this; } // f(x) += max(c(x - a), 0) // Complexity: O(|a| log n + 1) dual_slope_trick &add_linear_or_zero(T c, int a) { shift(-a); if (c > T()) Base::move_right_curve(c); if (c < T()) Base::move_left_curve(-c); shift(a); return *this; } // f(x) <- min f(x - d), a <= d <= b // Complexity: O((|a| + |b|) log n) dual_slope_trick &slide_min(int a, int b) { assert(a <= b); shift(a); for (int t = 0; t < b - a; ++t) Base::add_relu(T()); return *this; } }; int main() { dual_slope_trick dst; dst.shift(2).shift(-1); dbg(dst.get_at_zero()); dst.shift(-1); dbg(dst.get_at_zero()); dst.slide_min(0, 3); dbg(dst.get_at_zero()); dst.shift(-1); dbg(dst.get_at_zero()); dst.shift(-1); dbg(dst.get_at_zero()); dst.shift(-1); dbg(dst.get_at_zero()); dst.shift(-1); dbg(dst.get_at_zero()); int N, M, K; cin >> N >> M >> K; vector A(N), B(M); cin >> A >> B; map> mp; REP(i, N) { mp[A.at(i) % K].emplace_back(A.at(i) / K, 0); } REP(j, M) { mp[B.at(j) % K].emplace_back(B.at(j) / K, 1); } lint ret = 0; int nmatch = 0; for (auto [key, vs] : mp) { int n0 = 0, n1 = 0; for (auto [x, t] : vs) { (t ? n1 : n0)++; } nmatch += min(n0, n1); if (n0 > n1) { swap(n0, n1); for (auto &[x, t] : vs) t ^= 1; } sort(ALL(vs)); dbg(vs); dual_slope_trick dst; int last_x = vs.front().first; for (auto [x, tp] : vs) { int dx = x - last_x; dst.add_linear_or_zero(dx, 0).add_linear_or_zero(-dx, 0); dbg(make_tuple(dx, tp)); if (tp == 0) { dst.shift(1); } else { dst.slide_min(-1, 0); } last_x = x; } ret += dst.get_at_zero(); dbg(dst.get_at_zero()); assert(n0 <= n1); } if (nmatch < min(N, M)) ret = -1; cout << ret << endl; }