Problem p02644 (C++) — buggy submission, verdict: Time Limit Exceeded


// #pragma GCC optimize ("-O3")
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <complex>
#include <cstdio>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <regex>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <time.h>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <vector>
#ifdef _MSC_VER
#include <intrin.h>
#define popcnt __popcnt64
// #  define __builtin_popcount __popcnt
#else
#define popcnt __builtin_popcountll
#endif
// #include "boost/variant.hpp"

using namespace std;

typedef long long ll;
constexpr ll MOD = 1000000007LL;
constexpr ll INF = 1LL << 60;

#define rep(i, N, M) for (ll i = N, i##_len = (M); i < i##_len; ++i)
#define rep_skip(i, N, M, ...)                                                 \\
  for (ll i = N, i##_len = (M); i < i##_len; i += (skip))
#define rrep(i, N, M) for (ll i = (M)-1, i##_len = (N - 1); i > i##_len; --i)
#define repbit(bit, N, DIG) rep(bit, (N), (1LL << (DIG)))
#define pb push_back
#define fir first
#define sec second
#define all(a) (a).begin(), (a).end()
#define rall(a) (a).rbegin(), (a).rend()
#define perm(c)                                                                \\
  sort(all(c));                                                                \\
  for (bool c##perm = 1; c##perm;                                              \\
       c##perm = next_permutation(                                             \\
           all(c))) // perm(c){write(c)} writes all permutation of c
constexpr ll dceil(ll x, ll y) {
  if (y < 0) {
    x *= -1;
    y *= -1;
  };
  return x > 0 ? (x + y - 1) / y : x / y;
} // ceil for x/y
constexpr ll dfloor(ll x, ll y) {
  if (y < 0) {
    x *= -1;
    y *= -1;
  };
  return x > 0 ? x / y : -dceil((-x), y);
} // floor for x/y

typedef pair<double, double> pd;
typedef pair<ll, ll> pll;
typedef vector<ll> vll;
typedef vector<vll> vvll;
typedef vector<pll> vpll;
typedef vector<bool> vb;
typedef vector<vb> vvb;
typedef vector<string> vs;
template <typename T>
using pq_greater = priority_queue<T, vector<T>, greater<T>>;
template <typename T> using vpt = vector<complex<T>>;

template <int n> struct tll_impl {
  using type = decltype(tuple_cat(tuple<ll>(),
                                  declval<typename tll_impl<n - 1>::type>()));
};
template <> struct tll_impl<1> {
  using type = tuple<ll>;
};
template <int n> using tll = typename tll_impl<n>::type;

template <class T> constexpr ll SZ(T &v) { return static_cast<ll>(v.size()); };

template <int n, typename T> struct vec_t_impl {
  using type = vector<typename vec_t_impl<n - 1, T>::type>;
};
template <typename T> struct vec_t_impl<1, T> {
  using type = vector<T>;
};
template <int n, typename T> using vec_t = typename vec_t_impl<n, T>::type;
// check
static_assert(is_same<vec_t<3, ll>, vector<vector<vector<ll>>>>::value, "");

// decompose vector into basetype and dimension.
template <typename T> struct vec_dec {
  static constexpr int dim = 0;
  using type = T;
};
template <typename T> struct vec_dec<vector<T>> {
  static constexpr int dim = vec_dec<T>::dim + 1;
  using type = typename vec_dec<T>::type;
};
static_assert(is_same<typename vec_dec<vec_t<3, ll>>::type, ll>::value, "");
static_assert(vec_dec<vec_t<3, ll>>::dim == 3, "");

template <typename T = ll> vector<T> makev(size_t a) { return vector<T>(a); }

template <typename T = ll, typename... Ts> auto makev(size_t a, Ts... ts) {
  return vector<decltype(makev<T>(ts...))>(a, makev<T>(ts...));
} // ex:  auto dp =  makev<ll>(4,5) => vector<vector<ll>> dp(4,vector<ll>(5));

template <typename T>
struct is_vector : std::false_type {}; // check if T is vector

template <typename T> struct is_vector<vector<T>> : std::true_type {};
static_assert(is_vector<vector<ll>>::value == true &&
                  is_vector<ll>::value == false,
              "");

// check if T is vector
template <typename T> struct is_pair : std::false_type {};

template <typename T, typename S>
struct is_pair<pair<T, S>> : std::true_type {};
static_assert(is_pair<pll>::value == true && is_pair<ll>::value == false, "");

template <typename T, typename V,
          typename enable_if<!is_vector<T>::value, nullptr_t>::type = nullptr>
void fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V,
          typename enable_if<is_vector<T>::value, nullptr_t>::type = nullptr>
void fill_v(T &t, const V &v) {
  for (auto &&x : t)
    fill_v(x, v);
} // ex:  fill_v(dp, INF);

namespace std {
template <class T> bool operator<(const complex<T> &a, const complex<T> &b) {
  return a.real() == b.real() ? a.imag() < b.imag() : a.real() < b.real();
}
}; // namespace std

template <typename T, typename S>
istream &operator>>(istream &istr, pair<T, S> &x) {
  return istr >> x.first >> x.second;
}
template <typename T> istream &operator>>(istream &istr, vector<T> &x) {
  rep(i, 0, x.size()) istr >> x[i];
  return istr;
}
template <typename T> istream &operator>>(istream &istr, complex<T> &x) {
  T r, i;
  istr >> r >> i;
  x.real(r);
  x.imag(i);
  return istr;
}

template <typename T, typename Delim_t = string,
          typename enable_if<!is_vector<T>::value, nullptr_t>::type = nullptr>
void write(T &x, Delim_t delim = " ") {
  cout << x << delim;
}
template <typename T, typename Delim_t = string,
          typename enable_if<is_vector<T>::value, nullptr_t>::type = nullptr>
void write(T &x, Delim_t delim = " ") {
  rep(i, 0, x.size()) write(x[i], (i == (x.size() - 1) ? "" : delim));
  cout << '\\n';
}

template <typename T> void chmin(T &a, T b) {
  if (a > b)
    a = b;
}
template <typename T> void chmax(T &a, T b) {
  if (a < b)
    a = b;
}

vll seq(ll i, ll j) {
  vll res(j - i);
  rep(k, i, j) res[k] = i + k;
  return res;
}

constexpr ll POW_0(ll x, ll y) {
  if (y == 0)
    return 1;
  if (y == 1)
    return x;
  if (y == 2)
    return x * x;
  if (y % 2 == 0)
    return POW_0(POW_0(x, y / 2), 2LL);
  return ((POW_0(POW_0(x, y / 2), 2LL)) * (x));
}

constexpr ll POW(ll x, ll y, ll mod = 0) {
  if (mod == 0)
    return POW_0(x, y);
  if (y == 0)
    return 1;
  if (y == 1)
    return x % mod;
  if (y == 2)
    return x * x % mod;
  if (y % 2 == 0)
    return POW(POW(x, y / 2, mod), 2LL, mod) % mod;
  return ((POW(POW(x, y / 2, mod), 2LL, mod)) * (x % mod)) % mod;
}

template <typename Inputs, typename Functor,
          typename T = typename Inputs::value_type>
void sort_by(Inputs &inputs, Functor f) {
  std::sort(std::begin(inputs), std::end(inputs),
            [&f](const T &lhs, const T &rhs) { return f(lhs) < f(rhs); });
}

template <int pos, typename Inputs, typename T = typename Inputs::value_type>
void sort_by(Inputs &inputs) {
  std::sort(
      std::begin(inputs), std::end(inputs),
      [](const T &lhs, const T &rhs) { return get<pos>(lhs) < get<pos>(rhs); });
}

template <typename Inputs, typename Functor,
          typename T = typename Inputs::value_type>
void stable_sort_by(Inputs &inputs, Functor f) {
  std::stable_sort(
      std::begin(inputs), std::end(inputs),
      [&f](const T &lhs, const T &rhs) { return f(lhs) < f(rhs); });
}

template <typename Inputs> void sort_uniq(Inputs &inputs) {
  sort(all(inputs));
  inputs.erase(unique(all(inputs)), inputs.end());
}

vector<string> split(const string &s, char delim) {
  vector<string> elems;
  stringstream ss(s);
  string item;
  if (s.size() > 0 && s.front() == delim) {
    elems.push_back("");
  }
  while (getline(ss, item, delim)) {
    if (!item.empty()) {
      elems.push_back(item);
    }
  }
  if (s.size() > 0 && s.back() == delim) {
    elems.push_back("");
  }
  return elems;
}

template <class T> map<T, ll> inv_map(vector<T> &x) {
  map<T, ll> res;
  rep(i, 0, x.size()) { res[x[i]] = i; }
  return res;
}
template <class K, class V> map<V, K> inv_map(map<K, V> &m) {
  map<V, K> res;
  for (const auto &x : m) {
    res[x.second] = x.first;
  }
  return res;
}
template <class T, class val_t = typename T::value_type,
          enable_if_t<!is_same<T, set<val_t>>::value> * = nullptr>
constexpr bool exist(const T &container, val_t val) {
  return find(all(container), val) != container.end();
}
template <class T, class val_t = typename T::value_type,
          enable_if_t<is_same<T, set<val_t>>::value> * = nullptr>
constexpr bool exist(const T &container, val_t val) {
  return container.find(val) != container.end();
}

// inner prod: |a||b|cos(theta)
template <class T> T dot(complex<T> a, complex<T> b) {
  return a.real() * b.real() + a.imag() * b.imag();
}
// outer prod |a||b|sin(theta)
template <class T> T cross(complex<T> a, complex<T> b) {
  return a.real() * b.imag() - a.imag() * b.real();
}

template <typename T, typename S = nullptr_t>
struct has_unit : public false_type {};

template <typename T>
struct has_unit<
    T, typename conditional<false, decltype(T::unit()), nullptr_t>::type>
    : public true_type {};
template <typename T, typename S = nullptr_t>
struct has_append : public false_type {};

template <typename T>
struct has_append<
    T,
    typename conditional<
        false, decltype(T::append(T::underlying_type(), T::underlying_type())),
        nullptr_t>::type> : public true_type {};

template <typename Monoid> struct segment_tree {

  using underlying_type = typename Monoid::underlying_type;

  segment_tree(ll a_n, underlying_type unit = Monoid::unit())
      : size_original(a_n), unit(unit) {
    vector<underlying_type> initial_value = vector<underlying_type>(a_n, unit);
    segment_tree_impl(a_n, initial_value);
  }

  segment_tree(ll a_n, vector<underlying_type> &initial_value,
               underlying_type unit = Monoid::unit())
      : size_original(a_n), unit(unit) {
    segment_tree_impl(a_n, initial_value);
  }

  void update(int i, underlying_type z) { // 0-based
    assert(0 <= i && i < 2 * n - 1);
    a[i + n - 1] = z;
    for (i = (i + n) / 2; i > 0; i /= 2) { // 1-based
      a[i - 1] = Monoid::append(a[2 * i - 1], a[2 * i]);
    }
  }

  underlying_type query(ll l, ll r) { // 0-based, [l, r)
    underlying_type lacc = unit, racc = unit;
    assert(l <= r && r <= n);
    l += n;
    r += n;
    for (; l < r; l /= 2, r /= 2) { // 1-based loop, 2x faster than recursion
      if (l % 2 == 1)
        lacc = Monoid::append(lacc, a[(l++) - 1]);
      if (r % 2 == 1)
        racc = Monoid::append(a[(--r) - 1], racc);
    }
    return Monoid::append(lacc, racc);
  }

  underlying_type query(ll i) { // return value at i
    assert(0 <= i && i < size_original);
    return a[i + n - 1];
  }

  ll size() { return size_original; }

private:
  ll size_original;
  ll n;
  vector<underlying_type> a;
  underlying_type unit;
  void segment_tree_impl(ll a_n, vector<underlying_type> &initial_value) {
    assert(a_n == initial_value.size());
    n = 1;
    while (n < a_n)
      n *= 2;
    a.resize(2 * n - 1, unit);
    rep(i, 0, initial_value.size()) { a[i + (n - 1)] = initial_value[i]; }
    rrep(i, 0, n - 1) a[i] =
        Monoid::append(a[2 * i + 1], a[2 * i + 2]); // propagate initial values
  }
};

namespace M {

template <typename T = ll> struct sum_t {
  typedef T underlying_type;
  static underlying_type unit() { return 0; }
  static underlying_type append(underlying_type a, underlying_type b) {
    return a + b;
  }
  static underlying_type iterate(underlying_type a, int n) { return a * n; }
};

template <typename S, typename T> struct pair_t {
  typedef pair<typename S::underlying_type, typename T::underlying_type>
      underlying_type;
  static underlying_type unit() { return make_pair(S::unit(), T::unit()); }
  static underlying_type append(underlying_type a, underlying_type b) {
    return make_pair(S::append(a.first, b.first),
                     T::append(a.second, b.second));
  }
  static underlying_type iterate(underlying_type a, int n) {
    return make_pair(S::iterate(a.first, n), T::iterate(a.second, n));
  }
};

template <typename T = ll> struct min_t {
  typedef T underlying_type;
  static underlying_type unit() { return numeric_limits<T>::max(); }
  static underlying_type append(underlying_type a, underlying_type b) {
    return min(a, b);
  }
  static underlying_type iterate(underlying_type a, size_t n) { return a; }
};

template <typename T = ll> struct max_t {
  typedef T underlying_type;
  static underlying_type unit() { return numeric_limits<T>::min(); }
  static underlying_type append(underlying_type a, underlying_type b) {
    return max(a, b);
  }
  static underlying_type iterate(underlying_type a, size_t n) { return a; }
};

template <typename T = ll, typename IndexType = ll> struct min_indexed_t {
  typedef pair<typename min_t<T>::underlying_type, IndexType> underlying_type;
  static underlying_type unit() {
    return make_pair(numeric_limits<T>::max(), IndexType{});
  }
  static underlying_type append(underlying_type a, underlying_type b) {
    return min(a, b);
  }
  static underlying_type iterate(underlying_type a, int n) { return a; }
};
template <typename T = ll, typename IndexType = ll> struct max_indexed_t {
  typedef pair<typename min_t<T>::underlying_type, IndexType> underlying_type;
  static underlying_type unit() {
    return make_pair(numeric_limits<T>::min(), IndexType{});
  }
  static underlying_type append(underlying_type a, underlying_type b) {
    return max(a, b);
  }
  static underlying_type iterate(underlying_type a, int n) { return a; }
};

struct linear_t {
  typedef pd underlying_type;
  static underlying_type unit() { return underlying_type{1., 0.}; }
  static underlying_type append(underlying_type a, underlying_type b) {
    return underlying_type{a.first * b.first, b.first * a.second + b.second};
  }
};

template <typename under = ll, under uni = 0, typename F = decltype(plus<ll>())>
struct monoid_t {
  using underlying_type = under;
  static underlying_type unit() { return uni; }
  static underlying_type append(underlying_type a, underlying_type b) {
    return F(a, b);
  }
  static underlying_type act(underlying_type a, underlying_type b) {
    return F(a, b);
  }
};

} // namespace M

template <typename T> struct AddAct : T {
  static typename T::underlying_type act(typename T::underlying_type a,
                                         typename T::underlying_type b) {
    return T::append(a, b);
  }
};

// 1) E is acting on T and 2) both should be monoid and 3) the action preserving
// monoid structure. requires
template <typename Monoid, typename ActionMonoid = AddAct<Monoid>>
struct LazySegmentTree {
  int n;
  using M = typename Monoid::underlying_type;
  using E = typename ActionMonoid::underlying_type;
  function<M(M, M)> f = Monoid::append;
  function<M(M, E)> act = ActionMonoid::act;

  function<E(E, E)> h = ActionMonoid::append;
  function<E(E, int)> iterate = ActionMonoid::iterate;
  M m0 = Monoid::unit();
  E e0 = ActionMonoid::unit();
  vector<M> dat;
  vector<E> laz;

  // Monoid has append, unit, iterate functions.
  // template<typename Monoid>
  LazySegmentTree(int n_, vector<M> v = vector<M>()) {
    init(n_);
    if (n_ == (int)v.size())
      build(n_, v);
  }

  LazySegmentTree(
      int n_, function<M(M, M)> f, function<M(M, E)> act, function<E(E, E)> h,
      M m0, E e0, vector<M> v = vector<M>(),
      function<E(E, int)> iterate = [](E a, int) { return a; })
      : f(f), act(act), h(h), m0(m0), e0(e0), iterate(iterate) {
    init(n_);
    if (n_ == (int)v.size())
      build(n_, v);
  }
  void init(int n_) {
    n = 1;
    while (n < n_)
      n *= 2;
    dat.clear();
    dat.resize(2 * n - 1, m0);
    laz.clear();
    laz.resize(2 * n - 1, e0);
  }
  void build(int n_, vector<M> v) {
    for (int i = 0; i < n_; i++)
      dat[i + n - 1] = v[i];
    for (int i = n - 2; i >= 0; i--)
      dat[i] = f(dat[i * 2 + 1], dat[i * 2 + 2]);
  }
  inline void eval(int len, int k) {
    if (laz[k] == e0)
      return;
    if (k * 2 + 1 < n * 2 - 1) {
      laz[k * 2 + 1] = h(laz[k * 2 + 1], laz[k]);
      laz[k * 2 + 2] = h(laz[k * 2 + 2], laz[k]);
    }
    dat[k] = act(dat[k], iterate(laz[k], len));
    laz[k] = e0;
  }
  M update(int a, int b, E x, int k, int l, int r) {
    eval(r - l, k);
    if (r <= a || b <= l)
      return dat[k];
    if (a <= l && r <= b) {
      laz[k] = h(laz[k], x);
      return act(dat[k], iterate(laz[k], r - l));
    }
    return dat[k] = f(update(a, b, x, k * 2 + 1, l, (l + r) / 2),
                      update(a, b, x, k * 2 + 2, (l + r) / 2, r));
  }
  M update(int a, int b, E x) { return update(a, b, x, 0, 0, n); }
  M update(int a, E x) { return update(a, a + 1, x); }
  M query(int a, int b, int k, int l, int r) {
    eval(r - l, k);
    if (r <= a || b <= l)
      return m0;
    if (a <= l && r <= b)
      return dat[k];
    M vl = query(a, b, k * 2 + 1, l, (l + r) / 2);
    M vr = query(a, b, k * 2 + 2, (l + r) / 2, r);
    return f(vl, vr);
  }
  M query(int a, int b) { return query(a, b, 0, 0, n); }
};

struct D2 {
  D2(ll h, ll w) : h(h), w(w), Dir{1, -1, w, -w} {};
  bool in(ll n, ll d, ll k = 1) {
    if ((n % w <= k - 1) && d == -1)
      return false;
    if ((n % w >= w - 1 - (k - 1)) && d == 1)
      return false;
    if ((n / w <= k - 1) && d == -w)
      return false;
    if ((n / w >= h - 1 - (k - 1)) && d == w)
      return false;
    return true;
  };
  ll h, w;
  vll Dir;
};

int main() {

  cin.tie(0);
  cout.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(12);

  ll H, W, K;
  cin >> H >> W >> K;
  ll N = H * W;
  ll x1, y1, x2, y2;
  cin >> x1 >> y1 >> x2 >> y2;
  x1--;
  y1--;
  x2--;
  y2--;
  ll st = x1 * W + y1;
  ll gl = x2 * W + y2;
  vs c(H);
  cin >> c;
  using cost_t = ll;
  vector<ll> from_list;
  ll node_size = N;
  vector<cost_t> dist(node_size, INF);
  auto d2 = D2(H, W);

  from_list.resize(node_size);
  fill_v(from_list, -1);
  dist[st] = 0;
  ll cur = 0;
  vector<pll> pq;
  pq.push_back({0, st});
  while (cur < pq.size()) {
    auto node = pq[cur];
    cur++;
    // if not shortest path fixed, fix
    ll to = node.second;
    if (from_list[to] != -1)
      continue;
    from_list[to] = 1;
    for (auto d : d2.Dir) {
      rep(k, 1, K + 1) {
        ll adj = to + d * k;
        if (!d2.in(to, d, k) || c[adj / W][adj % W] == '@' ||
            from_list[adj] != -1) {
          break;
        }
        cost_t cost = dist[to] + 1;
        if (dist[adj] > cost) {
          dist[adj] = min(dist[adj], cost);
          pq.push_back({cost, adj});
        } else if (dist[adj] < cost) {
          break;
        }
      }
    }
    if (dist[gl] != INF) {
      cout << dist[gl] << endl;
      return 0;
    }
  }

  cout << (dist[gl] == INF ? -1 : dist[gl]) << endl;
  return 0;
}


Error: TLE

Fixed submission:


// #pragma GCC optimize ("-O3")
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <complex>
#include <cstdio>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <regex>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <time.h>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <vector>
#ifdef _MSC_VER
#include <intrin.h>
#define popcnt __popcnt64
// #  define __builtin_popcount __popcnt
#else
#define popcnt __builtin_popcountll
#endif
// #include "boost/variant.hpp"

using namespace std;

typedef long long ll;
constexpr ll MOD = 1000000007LL;
constexpr ll INF = 1LL << 60;

#define rep(i, N, M) for (ll i = N, i##_len = (M); i < i##_len; ++i)
#define rep_skip(i, N, M, ...)                                                 \\
  for (ll i = N, i##_len = (M); i < i##_len; i += (skip))
#define rrep(i, N, M) for (ll i = (M)-1, i##_len = (N - 1); i > i##_len; --i)
#define repbit(bit, N, DIG) rep(bit, (N), (1LL << (DIG)))
#define pb push_back
#define fir first
#define sec second
#define all(a) (a).begin(), (a).end()
#define rall(a) (a).rbegin(), (a).rend()
#define perm(c)                                                                \\
  sort(all(c));                                                                \\
  for (bool c##perm = 1; c##perm;                                              \\
       c##perm = next_permutation(                                             \\
           all(c))) // perm(c){write(c)} writes all permutation of c
constexpr ll dceil(ll x, ll y) {
  if (y < 0) {
    x *= -1;
    y *= -1;
  };
  return x > 0 ? (x + y - 1) / y : x / y;
} // ceil for x/y
constexpr ll dfloor(ll x, ll y) {
  if (y < 0) {
    x *= -1;
    y *= -1;
  };
  return x > 0 ? x / y : -dceil((-x), y);
} // floor for x/y

typedef pair<double, double> pd;
typedef pair<ll, ll> pll;
typedef vector<ll> vll;
typedef vector<vll> vvll;
typedef vector<pll> vpll;
typedef vector<bool> vb;
typedef vector<vb> vvb;
typedef vector<string> vs;
template <typename T>
using pq_greater = priority_queue<T, vector<T>, greater<T>>;
template <typename T> using vpt = vector<complex<T>>;

template <int n> struct tll_impl {
  using type = decltype(tuple_cat(tuple<ll>(),
                                  declval<typename tll_impl<n - 1>::type>()));
};
template <> struct tll_impl<1> {
  using type = tuple<ll>;
};
template <int n> using tll = typename tll_impl<n>::type;

template <class T> constexpr ll SZ(T &v) { return static_cast<ll>(v.size()); };

template <int n, typename T> struct vec_t_impl {
  using type = vector<typename vec_t_impl<n - 1, T>::type>;
};
template <typename T> struct vec_t_impl<1, T> {
  using type = vector<T>;
};
template <int n, typename T> using vec_t = typename vec_t_impl<n, T>::type;
// check
static_assert(is_same<vec_t<3, ll>, vector<vector<vector<ll>>>>::value, "");

// decompose vector into basetype and dimension.
template <typename T> struct vec_dec {
  static constexpr int dim = 0;
  using type = T;
};
template <typename T> struct vec_dec<vector<T>> {
  static constexpr int dim = vec_dec<T>::dim + 1;
  using type = typename vec_dec<T>::type;
};
static_assert(is_same<typename vec_dec<vec_t<3, ll>>::type, ll>::value, "");
static_assert(vec_dec<vec_t<3, ll>>::dim == 3, "");

template <typename T = ll> vector<T> makev(size_t a) { return vector<T>(a); }

template <typename T = ll, typename... Ts> auto makev(size_t a, Ts... ts) {
  return vector<decltype(makev<T>(ts...))>(a, makev<T>(ts...));
} // ex:  auto dp =  makev<ll>(4,5) => vector<vector<ll>> dp(4,vector<ll>(5));

template <typename T>
struct is_vector : std::false_type {}; // check if T is vector

template <typename T> struct is_vector<vector<T>> : std::true_type {};
static_assert(is_vector<vector<ll>>::value == true &&
                  is_vector<ll>::value == false,
              "");

// check if T is vector
template <typename T> struct is_pair : std::false_type {};

template <typename T, typename S>
struct is_pair<pair<T, S>> : std::true_type {};
static_assert(is_pair<pll>::value == true && is_pair<ll>::value == false, "");

template <typename T, typename V,
          typename enable_if<!is_vector<T>::value, nullptr_t>::type = nullptr>
void fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V,
          typename enable_if<is_vector<T>::value, nullptr_t>::type = nullptr>
void fill_v(T &t, const V &v) {
  for (auto &&x : t)
    fill_v(x, v);
} // ex:  fill_v(dp, INF);

namespace std {
template <class T> bool operator<(const complex<T> &a, const complex<T> &b) {
  return a.real() == b.real() ? a.imag() < b.imag() : a.real() < b.real();
}
}; // namespace std

template <typename T, typename S>
istream &operator>>(istream &istr, pair<T, S> &x) {
  return istr >> x.first >> x.second;
}
template <typename T> istream &operator>>(istream &istr, vector<T> &x) {
  rep(i, 0, x.size()) istr >> x[i];
  return istr;
}
template <typename T> istream &operator>>(istream &istr, complex<T> &x) {
  T r, i;
  istr >> r >> i;
  x.real(r);
  x.imag(i);
  return istr;
}

template <typename T, typename Delim_t = string,
          typename enable_if<!is_vector<T>::value, nullptr_t>::type = nullptr>
void write(T &x, Delim_t delim = " ") {
  cout << x << delim;
}
template <typename T, typename Delim_t = string,
          typename enable_if<is_vector<T>::value, nullptr_t>::type = nullptr>
void write(T &x, Delim_t delim = " ") {
  rep(i, 0, x.size()) write(x[i], (i == (x.size() - 1) ? "" : delim));
  cout << '\\n';
}

template <typename T> void chmin(T &a, T b) {
  if (a > b)
    a = b;
}
template <typename T> void chmax(T &a, T b) {
  if (a < b)
    a = b;
}

vll seq(ll i, ll j) {
  vll res(j - i);
  rep(k, i, j) res[k] = i + k;
  return res;
}

constexpr ll POW_0(ll x, ll y) {
  if (y == 0)
    return 1;
  if (y == 1)
    return x;
  if (y == 2)
    return x * x;
  if (y % 2 == 0)
    return POW_0(POW_0(x, y / 2), 2LL);
  return ((POW_0(POW_0(x, y / 2), 2LL)) * (x));
}

constexpr ll POW(ll x, ll y, ll mod = 0) {
  if (mod == 0)
    return POW_0(x, y);
  if (y == 0)
    return 1;
  if (y == 1)
    return x % mod;
  if (y == 2)
    return x * x % mod;
  if (y % 2 == 0)
    return POW(POW(x, y / 2, mod), 2LL, mod) % mod;
  return ((POW(POW(x, y / 2, mod), 2LL, mod)) * (x % mod)) % mod;
}

template <typename Inputs, typename Functor,
          typename T = typename Inputs::value_type>
void sort_by(Inputs &inputs, Functor f) {
  std::sort(std::begin(inputs), std::end(inputs),
            [&f](const T &lhs, const T &rhs) { return f(lhs) < f(rhs); });
}

template <int pos, typename Inputs, typename T = typename Inputs::value_type>
void sort_by(Inputs &inputs) {
  std::sort(
      std::begin(inputs), std::end(inputs),
      [](const T &lhs, const T &rhs) { return get<pos>(lhs) < get<pos>(rhs); });
}

template <typename Inputs, typename Functor,
          typename T = typename Inputs::value_type>
void stable_sort_by(Inputs &inputs, Functor f) {
  std::stable_sort(
      std::begin(inputs), std::end(inputs),
      [&f](const T &lhs, const T &rhs) { return f(lhs) < f(rhs); });
}

template <typename Inputs> void sort_uniq(Inputs &inputs) {
  sort(all(inputs));
  inputs.erase(unique(all(inputs)), inputs.end());
}

vector<string> split(const string &s, char delim) {
  vector<string> elems;
  stringstream ss(s);
  string item;
  if (s.size() > 0 && s.front() == delim) {
    elems.push_back("");
  }
  while (getline(ss, item, delim)) {
    if (!item.empty()) {
      elems.push_back(item);
    }
  }
  if (s.size() > 0 && s.back() == delim) {
    elems.push_back("");
  }
  return elems;
}

template <class T> map<T, ll> inv_map(vector<T> &x) {
  map<T, ll> res;
  rep(i, 0, x.size()) { res[x[i]] = i; }
  return res;
}
template <class K, class V> map<V, K> inv_map(map<K, V> &m) {
  map<V, K> res;
  for (const auto &x : m) {
    res[x.second] = x.first;
  }
  return res;
}
template <class T, class val_t = typename T::value_type,
          enable_if_t<!is_same<T, set<val_t>>::value> * = nullptr>
constexpr bool exist(const T &container, val_t val) {
  return find(all(container), val) != container.end();
}
template <class T, class val_t = typename T::value_type,
          enable_if_t<is_same<T, set<val_t>>::value> * = nullptr>
constexpr bool exist(const T &container, val_t val) {
  return container.find(val) != container.end();
}

// inner prod: |a||b|cos(theta)
template <class T> T dot(complex<T> a, complex<T> b) {
  return a.real() * b.real() + a.imag() * b.imag();
}
// outer prod |a||b|sin(theta)
template <class T> T cross(complex<T> a, complex<T> b) {
  return a.real() * b.imag() - a.imag() * b.real();
}

template <typename T, typename S = nullptr_t>
struct has_unit : public false_type {};

template <typename T>
struct has_unit<
    T, typename conditional<false, decltype(T::unit()), nullptr_t>::type>
    : public true_type {};
template <typename T, typename S = nullptr_t>
struct has_append : public false_type {};

template <typename T>
struct has_append<
    T,
    typename conditional<
        false, decltype(T::append(T::underlying_type(), T::underlying_type())),
        nullptr_t>::type> : public true_type {};

template <typename Monoid> struct segment_tree {

  using underlying_type = typename Monoid::underlying_type;

  segment_tree(ll a_n, underlying_type unit = Monoid::unit())
      : size_original(a_n), unit(unit) {
    vector<underlying_type> initial_value = vector<underlying_type>(a_n, unit);
    segment_tree_impl(a_n, initial_value);
  }

  segment_tree(ll a_n, vector<underlying_type> &initial_value,
               underlying_type unit = Monoid::unit())
      : size_original(a_n), unit(unit) {
    segment_tree_impl(a_n, initial_value);
  }

  void update(int i, underlying_type z) { // 0-based
    assert(0 <= i && i < 2 * n - 1);
    a[i + n - 1] = z;
    for (i = (i + n) / 2; i > 0; i /= 2) { // 1-based
      a[i - 1] = Monoid::append(a[2 * i - 1], a[2 * i]);
    }
  }

  underlying_type query(ll l, ll r) { // 0-based, [l, r)
    underlying_type lacc = unit, racc = unit;
    assert(l <= r && r <= n);
    l += n;
    r += n;
    for (; l < r; l /= 2, r /= 2) { // 1-based loop, 2x faster than recursion
      if (l % 2 == 1)
        lacc = Monoid::append(lacc, a[(l++) - 1]);
      if (r % 2 == 1)
        racc = Monoid::append(a[(--r) - 1], racc);
    }
    return Monoid::append(lacc, racc);
  }

  underlying_type query(ll i) { // return value at i
    assert(0 <= i && i < size_original);
    return a[i + n - 1];
  }

  ll size() { return size_original; }

private:
  ll size_original;
  ll n;
  vector<underlying_type> a;
  underlying_type unit;
  void segment_tree_impl(ll a_n, vector<underlying_type> &initial_value) {
    assert(a_n == initial_value.size());
    n = 1;
    while (n < a_n)
      n *= 2;
    a.resize(2 * n - 1, unit);
    rep(i, 0, initial_value.size()) { a[i + (n - 1)] = initial_value[i]; }
    rrep(i, 0, n - 1) a[i] =
        Monoid::append(a[2 * i + 1], a[2 * i + 2]); // propagate initial values
  }
};

namespace M {

template <typename T = ll> struct sum_t {
  typedef T underlying_type;
  static underlying_type unit() { return 0; }
  static underlying_type append(underlying_type a, underlying_type b) {
    return a + b;
  }
  static underlying_type iterate(underlying_type a, int n) { return a * n; }
};

template <typename S, typename T> struct pair_t {
  typedef pair<typename S::underlying_type, typename T::underlying_type>
      underlying_type;
  static underlying_type unit() { return make_pair(S::unit(), T::unit()); }
  static underlying_type append(underlying_type a, underlying_type b) {
    return make_pair(S::append(a.first, b.first),
                     T::append(a.second, b.second));
  }
  static underlying_type iterate(underlying_type a, int n) {
    return make_pair(S::iterate(a.first, n), T::iterate(a.second, n));
  }
};

template <typename T = ll> struct min_t {
  typedef T underlying_type;
  static underlying_type unit() { return numeric_limits<T>::max(); }
  static underlying_type append(underlying_type a, underlying_type b) {
    return min(a, b);
  }
  static underlying_type iterate(underlying_type a, size_t n) { return a; }
};

template <typename T = ll> struct max_t {
  typedef T underlying_type;
  static underlying_type unit() { return numeric_limits<T>::min(); }
  static underlying_type append(underlying_type a, underlying_type b) {
    return max(a, b);
  }
  static underlying_type iterate(underlying_type a, size_t n) { return a; }
};

template <typename T = ll, typename IndexType = ll> struct min_indexed_t {
  typedef pair<typename min_t<T>::underlying_type, IndexType> underlying_type;
  static underlying_type unit() {
    return make_pair(numeric_limits<T>::max(), IndexType{});
  }
  static underlying_type append(underlying_type a, underlying_type b) {
    return min(a, b);
  }
  static underlying_type iterate(underlying_type a, int n) { return a; }
};
template <typename T = ll, typename IndexType = ll> struct max_indexed_t {
  typedef pair<typename min_t<T>::underlying_type, IndexType> underlying_type;
  static underlying_type unit() {
    return make_pair(numeric_limits<T>::min(), IndexType{});
  }
  static underlying_type append(underlying_type a, underlying_type b) {
    return max(a, b);
  }
  static underlying_type iterate(underlying_type a, int n) { return a; }
};

struct linear_t {
  typedef pd underlying_type;
  static underlying_type unit() { return underlying_type{1., 0.}; }
  static underlying_type append(underlying_type a, underlying_type b) {
    return underlying_type{a.first * b.first, b.first * a.second + b.second};
  }
};

template <typename under = ll, under uni = 0, typename F = decltype(plus<ll>())>
struct monoid_t {
  using underlying_type = under;
  static underlying_type unit() { return uni; }
  static underlying_type append(underlying_type a, underlying_type b) {
    return F(a, b);
  }
  static underlying_type act(underlying_type a, underlying_type b) {
    return F(a, b);
  }
};

} // namespace M

template <typename T> struct AddAct : T {
  static typename T::underlying_type act(typename T::underlying_type a,
                                         typename T::underlying_type b) {
    return T::append(a, b);
  }
};

// 1) E is acting on T and 2) both should be monoid and 3) the action preserving
// monoid structure. requires
template <typename Monoid, typename ActionMonoid = AddAct<Monoid>>
struct LazySegmentTree {
  int n;
  using M = typename Monoid::underlying_type;
  using E = typename ActionMonoid::underlying_type;
  function<M(M, M)> f = Monoid::append;
  function<M(M, E)> act = ActionMonoid::act;

  function<E(E, E)> h = ActionMonoid::append;
  function<E(E, int)> iterate = ActionMonoid::iterate;
  M m0 = Monoid::unit();
  E e0 = ActionMonoid::unit();
  vector<M> dat;
  vector<E> laz;

  // Monoid has append, unit, iterate functions.
  // template<typename Monoid>
  LazySegmentTree(int n_, vector<M> v = vector<M>()) {
    init(n_);
    if (n_ == (int)v.size())
      build(n_, v);
  }

  LazySegmentTree(
      int n_, function<M(M, M)> f, function<M(M, E)> act, function<E(E, E)> h,
      M m0, E e0, vector<M> v = vector<M>(),
      function<E(E, int)> iterate = [](E a, int) { return a; })
      : f(f), act(act), h(h), m0(m0), e0(e0), iterate(iterate) {
    init(n_);
    if (n_ == (int)v.size())
      build(n_, v);
  }
  void init(int n_) {
    n = 1;
    while (n < n_)
      n *= 2;
    dat.clear();
    dat.resize(2 * n - 1, m0);
    laz.clear();
    laz.resize(2 * n - 1, e0);
  }
  void build(int n_, vector<M> v) {
    for (int i = 0; i < n_; i++)
      dat[i + n - 1] = v[i];
    for (int i = n - 2; i >= 0; i--)
      dat[i] = f(dat[i * 2 + 1], dat[i * 2 + 2]);
  }
  inline void eval(int len, int k) {
    if (laz[k] == e0)
      return;
    if (k * 2 + 1 < n * 2 - 1) {
      laz[k * 2 + 1] = h(laz[k * 2 + 1], laz[k]);
      laz[k * 2 + 2] = h(laz[k * 2 + 2], laz[k]);
    }
    dat[k] = act(dat[k], iterate(laz[k], len));
    laz[k] = e0;
  }
  M update(int a, int b, E x, int k, int l, int r) {
    eval(r - l, k);
    if (r <= a || b <= l)
      return dat[k];
    if (a <= l && r <= b) {
      laz[k] = h(laz[k], x);
      return act(dat[k], iterate(laz[k], r - l));
    }
    return dat[k] = f(update(a, b, x, k * 2 + 1, l, (l + r) / 2),
                      update(a, b, x, k * 2 + 2, (l + r) / 2, r));
  }
  M update(int a, int b, E x) { return update(a, b, x, 0, 0, n); }
  M update(int a, E x) { return update(a, a + 1, x); }
  M query(int a, int b, int k, int l, int r) {
    eval(r - l, k);
    if (r <= a || b <= l)
      return m0;
    if (a <= l && r <= b)
      return dat[k];
    M vl = query(a, b, k * 2 + 1, l, (l + r) / 2);
    M vr = query(a, b, k * 2 + 2, (l + r) / 2, r);
    return f(vl, vr);
  }
  M query(int a, int b) { return query(a, b, 0, 0, n); }
};

struct D2 {
  D2(ll h, ll w) : h(h), w(w), Dir{1, -1, w, -w} {};
  bool in(ll n, ll d, ll k = 1) {
    if ((n % w <= k - 1) && d == -1)
      return false;
    if ((n % w >= w - 1 - (k - 1)) && d == 1)
      return false;
    if ((n / w <= k - 1) && d == -w)
      return false;
    if ((n / w >= h - 1 - (k - 1)) && d == w)
      return false;
    return true;
  };
  ll h, w;
  vll Dir;
};

int main() {

  cin.tie(0);
  cout.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(12);

  ll H, W, K;
  cin >> H >> W >> K;
  ll N = H * W;
  ll x1, y1, x2, y2;
  cin >> x1 >> y1 >> x2 >> y2;
  x1--;
  y1--;
  x2--;
  y2--;
  ll st = x1 * W + y1;
  ll gl = x2 * W + y2;
  vs c(H);
  cin >> c;
  using cost_t = ll;
  vector<ll> from_list;
  ll node_size = N;
  vector<cost_t> dist(node_size, INF);
  auto d2 = D2(H, W);

  from_list.resize(node_size);
  fill_v(from_list, -1);
  dist[st] = 0;
  ll cur = 0;
  vector<pll> pq;
  pq.push_back({0, st});
  while (cur < pq.size()) {
    auto node = pq[cur];
    cur++;
    // if not shortest path fixed, fix
    ll to = node.second;
    if (from_list[to] != -1)
      continue;
    from_list[to] = 1;
    for (auto d : d2.Dir) {
      vpll ls;
      rep(k, 1, K + 1) {
        ll adj = to + d * k;
        if (!d2.in(to, d, k) || c[adj / W][adj % W] == '@' ||
            from_list[adj] != -1) {
          break;
        }
        cost_t cost = dist[to] + 1;
        ls.push_back({adj, cost});
      }
      rrep(k, 0, ls.size()) {
        auto [adj, cost] = ls[k];
        if (dist[adj] > cost) {
          dist[adj] = min(dist[adj], cost);
          pq.push_back({cost, adj});
        }
      }
    }
    if (dist[gl] != INF) {
      cout << dist[gl] << endl;
      return 0;
    }
  }

  cout << (dist[gl] == INF ? -1 : dist[gl]) << endl;
  return 0;
}