#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/slope.hpp" struct Slope_Trick { static constexpr ll LMIN = numeric_limits::lowest() / 2; static constexpr ll RMAX = numeric_limits::max() / 2; pq que_l; pqg que_r; ll add_l, add_r; i128 min_f; // INF を足し引きしても壊れないようにする Slope_Trick() : add_l(0), add_r(0), min_f(0) {} Slope_Trick(vc left, vc right) : que_l(all(left)), que_r(all(right)), add_l(0), add_r(0), min_f(0) {} int size() { return len(que_l) + len(que_r); } tuple get_min() { return {top_L(), top_R(), min_f}; } void add_const(ll a) { min_f += a; } // O(|a| log N) void add_linear(ll a, ll b) { min_f += b; FOR(max(a, 0)) { ll x = pop_L(); min_f += x; push_R(x); } FOR(max(-a, 0)) { ll x = pop_R(); min_f -= x; push_L(x); } } // (a-x)+ void add_a_minus_x(ll a) { min_f += max(0, a - top_R()); push_R(a), push_L(pop_R()); } // (x-a)+ void add_x_minus_a(ll a) { min_f += max(0, top_L() - a); push_L(a), push_R(pop_L()); } // |x-a| void add_abs(ll a) { add_a_minus_x(a); add_x_minus_a(a); } // 増加側を消して、減少側のみにする void clear_inc() { que_r = pqg(); } // 減少側を消して、増加側のみにする void clear_dec() { que_l = pq(); } void shift(const ll &a) { add_l += a, add_r += a; } // g(x) = min_{x-b <= y <= x-a} f(y) void sliding_window_minimum(const ll &a, const ll &b) { add_l += a, add_r += b; } // O(size) i128 eval(ll x) { i128 y = min_f; pq que_l_copy = que_l; pqg que_r_copy = que_r; while (len(que_l_copy)) { y += max(0, (pick(que_l_copy) + add_l) - x); } while (len(que_r_copy)) { y += max(0, x - (pick(que_r_copy) + add_r)); } return y; } void push_R(const ll &x) { que_r.emplace(x - add_r); } void push_L(const ll &x) { que_l.emplace(x - add_l); } ll top_R() { if (que_r.empty()) que_r.emplace(RMAX); return que_r.top() + add_r; } ll top_L() { if (que_l.empty()) que_l.emplace(LMIN); return que_l.top() + add_l; } ll pop_R() { ll res = top_R(); que_r.pop(); return res; } ll pop_L() { ll res = top_L(); que_l.pop(); return res; } void debug() { vi left, right; pq que_l_copy = que_l; pqg que_r_copy = que_r; while (len(que_l_copy)) { left.eb(pick(que_l_copy) + add_l); } while (len(que_r_copy)) { right.eb(pick(que_r_copy) + add_r); } sort(all(left)); sort(all(right)); print("min_f", min_f, "left", left, "right", right); } }; #line 2 "/home/maspy/compro/library/ds/hashmap.hpp" template struct HashMapLL { int N; ll* keys; Val* vals; vc IDS; bitset<1 << LOG> used; const int shift; const uint64_t r = 11995408973635179863ULL; HashMapLL() : N(1 << LOG), keys(new ll[N]), vals(new Val[N]), shift(64 - __lg(N)) {} int hash(ll x) { static const uint64_t FIXED_RANDOM = std::chrono::steady_clock::now().time_since_epoch().count(); return (uint64_t(x + FIXED_RANDOM) * r) >> shift; } int index(const ll& key) { int i = 0; for (i = hash(key); used[i] && keys[i] != key; (i += 1) &= (N - 1)) {} return i; } Val& operator[](const ll& key) { int i = index(key); if (!used[i]) IDS.eb(i), used[i] = 1, keys[i] = key, vals[i] = Val{}; return vals[i]; } Val get(const ll& key, Val default_value) { int i = index(key); if (!used[i]) return default_value; return vals[i]; } bool contain(const ll& key) { int i = index(key); return used[i] && keys[i] == key; } bool count(const ll& key) { int i = index(key); return used[i] && keys[i] == key; } void reset() { for (auto&& i: IDS) used[i] = 0; IDS.clear(); } vc> items() { vc> res; res.reserve(len(IDS)); for (auto&& i: IDS) res.eb(keys[i], vals[i]); return res; } }; template struct HashMap { HashMapLL MP; function f; HashMap(function f) : MP(), f(f) {} int index(const KEY& key) { return MP.index(f(key)); } VAL& operator[](const KEY& key) { return MP[f(key)]; } bool contain(const KEY& key) { return MP.contain(f(key)); } bool count(const KEY& key) { return MP.count(f(key)); } void reset() { MP.reset(); } }; #line 5 "main.cpp" void solve() { LL(N, M, K); HashMapLL RED, BLUE; vi key; FOR(N) { LL(x); RED[x % K].eb(x / K); key.eb(x % K); } FOR(M) { LL(x); BLUE[x % K].eb(x / K); key.eb(x % K); } UNIQUE(key); ll ANS = 0; for (auto&& k: key) { vi &A = RED[k], &B = BLUE[k]; if (N > M) swap(A, B); if (len(A) > len(B)) return print(-1); vc dat; for (auto&& x: A) dat.eb(x, 0); for (auto&& x: B) dat.eb(x, 1); sort(all(dat), [&](auto& x, auto& y) -> bool { return x.fi < y.fi; }); Slope_Trick f; FOR(i, len(dat)) { auto [x, t] = dat[i]; if (t == 0) { // g(x) = f(x-1) // G(x) = F(x) + x f.add_linear(1, 0); } if (t == 1) { // g(x) = min_{x<=y<=x+1} f(y) f.add_a_minus_x(0); } if (i + 1 < len(dat)) { ll nxt = dat[i + 1].fi; ll d = nxt - x; f.sliding_window_minimum(-d, d); } } ANS -= f.min_f; } print(ANS); } signed main() { cout << fixed << setprecision(15); ll T = 1; // LL(T); FOR(T) solve(); return 0; }