// #define _GLIBCXX_DEBUG #include // 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 &v){if(!v)os<<"0";__int128_t tmp=v<0?(os<<"-",-v):v;std::string s;while(tmp)s+='0'+(tmp%10),tmp/=10;return std::reverse(s.begin(),s.end()),os< class PiecewiseLinearConvexfunction { using i64= long long; using i128= __int128_t; using node_id= int; static constexpr i64 INF= 1ll << 41; template static inline std::string str(Int x) { if (x >= INF) return "inf"; if (x <= -INF) return "-inf"; std::stringstream ss; ss << x; return ss.str(); } struct Node { node_id ch[2], par; int sz; i64 dx, slope, laz, x; i128 y; }; friend std::ostream &operator<<(std::ostream &os, Node *t) { if (!t) return os << "nullptr"; return os << "{dx:" << str(t->dx) << ",slope:" << str(t->slope) << ",x:" << str(t->x) << ",y:" << str(t->y) << ",laz:" << str(t->laz) << "}"; } static inline Node ns[NODE_SIZE]; static inline node_id ni= 1; static inline node_id new_node() { return ni++; } static inline node_id new_node(i64 dx, i64 slope) { return ns[ni].ch[0]= ns[ni].ch[1]= ns[ni].par= ns[ni].laz= 0, ns[ni].y= i128(ns[ni].x= ns[ni].dx= dx) * (ns[ni].slope= slope), ns[ni].sz= 1, ni++; } static inline void propagate(node_id i, i64 a) { if (i) ns[i].slope+= a, ns[i].laz+= a, ns[i].y+= i128(a) * ns[i].x; } static inline void push(node_id i) { if (ns[i].laz) propagate(ns[i].ch[0], ns[i].laz), propagate(ns[i].ch[1], ns[i].laz), ns[i].laz= 0; } static inline void update(node_id i) { ns[i].sz= 1, ns[i].x= ns[i].dx, ns[i].y= i128(ns[i].slope) * ns[i].dx; if (int j= ns[i].ch[0]; j) ns[i].sz+= ns[j].sz, ns[i].x+= ns[j].x, ns[i].y+= ns[j].y; if (int j= ns[i].ch[1]; j) ns[i].sz+= ns[j].sz, ns[i].x+= ns[j].x, ns[i].y+= ns[j].y; } static inline int dir(node_id i) { return ns[ns[i].par].ch[1] == i; } static inline void rot(node_id i) { node_id p= ns[i].par; int d= dir(i); if ((ns[p].ch[d]= ns[i].ch[!d])) ns[ns[p].ch[d]].par= p; ns[i].ch[!d]= p; if ((ns[i].par= ns[p].par)) ns[ns[p].par].ch[dir(p)]= i; ns[p].par= i, update(p); } static inline void splay(node_id i) { for (node_id p= ns[i].par; p; rot(i), p= ns[i].par) if (node_id pp= ns[p].par; pp) rot(dir(i) == dir(p) ? p : i); update(i); } static inline void slope_search(node_id &i, i64 k) { for (node_id s;; i= s) { push(i); i64 tmp= ns[i].slope; if (tmp == k) break; if (s= ns[i].ch[tmp < k]; !s) break; } splay(i); } static inline void x_search(node_id &i, i64 x) { for (bool c;; i= ns[i].ch[c]) { push(i); i64 l= ns[i].ch[0] ? ns[ns[i].ch[0]].x : 0, r= l + ns[i].dx; if (l <= x && x <= r) return splay(i); if ((c= (r < x))) x-= r; } } static inline void add(node_id i, i64 &x, i64 &p, PiecewiseLinearConvexfunction &f) { if (!i) return; push(i); add(ns[i].ch[0], x, p, f); f.add_ax_bx_c(0, ns[i].slope - p, x); x+= ns[i].dx, p= ns[i].slope; add(ns[i].ch[1], x, p, f); } static inline void debugoutput(node_id i, int d) { if (!i) return; push(i); debugoutput(ns[i].ch[0], d + 1); for (int i= 0; i < d; ++i) std::cerr << " "; std::cerr << "■ " << (i ? ns + i : nullptr) << '\n'; debugoutput(ns[i].ch[1], d + 1); } node_id root; i64 lx, lslope; i128 ly; void chmin_sliding_window(i64 a) { if (!a) return; assert(a > 0); if (root) { slope_search(root, 0); if (ns[root].slope) { node_id i= new_node(a, 0); bool c= ns[root].slope < 0; if ((ns[i].ch[c]= ns[root].ch[c])) ns[ns[i].ch[c]].par= i; update(i), ns[root].ch[c]= i, ns[i].par= root; } else ns[root].dx+= a; update(root); } else if (lslope >= 0) lx+= a; else root= new_node(a, 0); } public: static inline void clear() { ni= 1; } void debugoutput() { debugoutput(root, 0); } i64 upper_bound() { return lx + (root ? ns[root].x : 0); } // f(x) := 0 PiecewiseLinearConvexfunction(): root(0), lx(INF * 2), lslope(0), ly(0) {} // f(x) + c void add_const(i128 c) { ly+= c; } // f(x) + ax+c void add_linear(i64 a, i128 c= 0) { lslope+= a, ly+= i128(a) * lx + c, propagate(root, a); } // f(x-a) void shift(i64 a) { lx+= a; } // f(x) + a * max{x-c, 0} void add_relu(i64 a, i64 c) { if (!a) return; assert(a > 0); if (c < lx) { if (lslope < -INF) return add_linear(a, -i128(a) * c); node_id i= new_node(lx - c, lslope); if (root) x_search(root, 0), ns[root].ch[0]= i, ns[i].par= root, update(root); else root= i; ly-= ns[i].y, lx= c, propagate(root, a); return; } if (upper_bound() <= c) return; c-= lx, x_search(root, c); i64 l= ns[root].ch[0] ? ns[ns[root].ch[0]].x : 0, r= l + ns[root].dx; if (l == c) { node_id i= ns[root].ch[0]; ns[root].ch[0]= 0, propagate(root, a), push(root), ns[root].ch[0]= i; } else if (r == c) { propagate(ns[root].ch[1], a); } else { node_id i= new_node(r - c, ns[root].slope); if ((ns[i].ch[1]= ns[root].ch[1])) ns[ns[i].ch[1]].par= i; update(i), propagate(i, a), ns[root].ch[1]= i, ns[i].par= root, ns[root].dx= c - l, update(root); } } // f(x) + a * min{x-c,0} + b * max{x-c,0} void add_ax_bx_c(i64 a, i64 b, i64 c) { assert(a <= b), add_linear(a, -i128(a) * c), add_relu(b - a, c); } // f(x) + a * |x-c| void add_abs(i64 a, i64 c) { add_ax_bx_c(-a, a, c); } // ∞ if x>a else f(x) void chinfty_right(i64 a= 0) { assert(lx <= a || lslope >= -INF); if (root) { if (a-= lx; ns[root].x <= a) return; x_search(root, a); i64 l= ns[root].ch[0] ? ns[ns[root].ch[0]].x : 0; if (l == a) root= ns[root].ch[0], ns[root].par= 0; else ns[root].dx= a - l, ns[root].ch[1]= 0, update(root); } else lx= a; } // ∞ if x 0) { assert(root); x_search(root, a); i64 r= ns[root].dx; if (int i= ns[root].ch[0]; i) ly+= ns[i].y + i128(a - ns[i].x) * ns[root].slope, r+= ns[i].x; else ly+= i128(a) * ns[root].slope; if (r == a) root= ns[root].ch[1], ns[root].par= 0; else ns[root].dx= r - a, ns[root].ch[0]= 0, update(root); } lx+= a, lslope= -INF * 2; } // min_{y<=x} f(y) void cumulative_chmin() { assert(lslope <= 0); if (root) { slope_search(root, 0); if (ns[root].slope < 0) { if (!ns[root].ch[1]) ns[root].ch[1]= new_node(); node_id i= ns[root].ch[1]; ns[i].sz= 1, ns[i].x= ns[i].dx= INF * 2, ns[i].slope= ns[i].ch[0]= ns[i].ch[1]= ns[i].laz= ns[i].y= 0, ns[i].par= root; } else ns[root].ch[1]= 0, ns[root].dx= INF * 2, ns[root].slope= 0; update(root); } else if (lslope) root= new_node(INF * 2, 0); else lx= INF * 2; } // min_{y<=x ∧ y<=a} f(y) void cumulative_chmin_with_condition(i64 a) { chinfty_right(a), cumulative_chmin(); } // min_{y>=x} f(y) void cumulative_chmin_rev() { if (root) { slope_search(root, 0); i64 l= ns[root].ch[0] ? ns[ns[root].ch[0]].x : 0, r= l + ns[root].dx, x= ns[root].slope > 0 ? l : r; if (int i= ns[root].ch[0]; i) ly+= ns[i].y + i128(x - ns[i].x) * ns[root].slope; else ly+= i128(x) * ns[root].slope; if (ns[root].slope > 0) ns[root].ch[0]= 0, update(root); else root= ns[root].ch[1], ns[root].par= 0; lx+= x; } lslope= 0; } // min_{y>=x ∧ y>=a} f(y) void cumulative_chmin_rev_with_condition(i64 a) { chinfty_left(a), cumulative_chmin_rev(); } // min_{x-b<=y<=x-a} f(y) void chmin_sliding_window(i64 a, i64 b) { assert(a <= b), shift(a), chmin_sliding_window(b - a); } // inf_y { f(x-y) + ( a * min{y-c,0} + b * max{y-c,0} ) } void convex_convolution_with_ax_bx_c(i64 a, i64 b, i64 c) { assert(a <= b), shift(c), add_linear(-a), cumulative_chmin_rev(), add_linear(a), add_linear(-b), cumulative_chmin(), add_linear(b); } // inf_y { f(x-y) + a |y-c| } void convex_convolution_with_abs(i64 a, i64 c) { convex_convolution_with_ax_bx_c(-a, a, c); } std::array argmin() { assert(lslope <= 0); if (!lslope) return std::array{-INF, lx}; if (!root) return std::array{lx, lx}; slope_search(root, 0); i64 l= lx + (ns[root].ch[0] ? ns[ns[root].ch[0]].x : 0), r= l + ns[root].dx; if (ns[root].slope == 0) return {l, r}; return ns[root].slope < 0 ? std::array{r, r} : std::array{l, l}; } i64 min() { return eval(argmin()[1]); } i64 eval(i64 x) { if (x < lx && lslope < -INF) return INF; if (x <= lx) return ly + i128(x - lx) * lslope; if (!root) return INF; if (x-= lx; ns[root].x < x) return INF; x_search(root, x); if (int i= ns[root].ch[0]; i) return ly + ns[i].y + i128(x - ns[i].x) * ns[root].slope; return ly + i128(x) * ns[root].slope; } i64 operator()(i64 x) { return eval(x); } int size() { return root ? ns[root].sz : 0; } // destructive PiecewiseLinearConvexfunction operator+(PiecewiseLinearConvexfunction &r) { if (size() > r.size()) std::swap(*this, r); if (lslope < -INF) r.chinfty_left(lx); else r.add_ax_bx_c(lslope, 0, lx); r.chinfty_right(upper_bound()); long long x= lx, p= 0; add(root, x, p, r), r.add_const(ly); return r; } // destructive PiecewiseLinearConvexfunction &operator+=(PiecewiseLinearConvexfunction &r) { return *this= *this + r; } }; template auto compress(std::vector &v) { return std::sort(v.begin(), v.end()), v.erase(std::unique(v.begin(), v.end()), v.end()), [&v](T x) { return std::lower_bound(v.begin(), v.end(), x) - v.begin(); }; } using namespace std; signed main() { cin.tie(0); ios::sync_with_stdio(0); using PLCF= PiecewiseLinearConvexfunction<>; int N, M, K; cin >> N >> M >> K; unordered_map, 2>> mp; for (int i= 0; i < N; ++i) { int B; cin >> B; mp[B % K][N >= M].push_back(B / K); } for (int i= 0; i < M; ++i) { int R; cin >> R; mp[R % K][N < M].push_back(R / K); } long long ans= 0; for (auto &&[_, arr]: mp) { auto &&[A, B]= arr; if (A.size() > B.size()) return cout << -1 << '\n', 0; vector vec(A); for (int i: B) vec.push_back(i); auto id= compress(vec); int n= vec.size(); vector a(n), b(n); for (int i: A) ++a[id(i)]; for (int i: B) ++b[id(i)]; PLCF f; f.chinfty_left(), f.chinfty_right(); for (int i= 0; i < n; ++i) { f.cumulative_chmin(); f.shift(a[i] - b[i]); if (i < n - 1) f.add_abs(vec[i + 1] - vec[i], 0); } ans+= f.eval(0); PLCF::clear(); } cout << ans << '\n'; return 0; }