Problem:
Score : 600 points

Problem Statement

Snuke, a water strider, lives in a rectangular pond that can be seen as a grid with H east-west rows and W north-south columns. Let (i,j) be the square at the i-th row from the north and j-th column from the west.

Some of the squares have a lotus leaf on it and cannot be entered.
The square (i,j) has a lotus leaf on it if c_{ij} is @, and it does not if c_{ij} is ..

In one stroke, Snuke can move between 1 and K squares (inclusive) toward one of the four directions: north, east, south, and west.
The move may not pass through a square with a lotus leaf. Moving to such a square or out of the pond is also forbidden.

Find the minimum number of strokes Snuke takes to travel from the square (x_1,y_1) to (x_2,y_2).
If the travel from (x_1,y_1) to (x_2,y_2) is impossible, point out that fact.

Constraints

1 \leq H,W,K \leq 10^6

H \times W \leq 10^6

1 \leq x_1,x_2 \leq H

1 \leq y_1,y_2 \leq W

x_1 \neq x_2 or y_1 \neq y_2.

c_{i,j} is . or @.

c_{x_1,y_1} = .

c_{x_2,y_2} = .

All numbers in input are integers.

Input

Input is given from Standard Input in the following format:

H W K
x_1 y_1 x_2 y_2
c_{1,1}c_{1,2} .. c_{1,W}
c_{2,1}c_{2,2} .. c_{2,W}
:
c_{H,1}c_{H,2} .. c_{H,W}

Output

Print the minimum number of strokes Snuke takes to travel from the square (x_1,y_1) to (x_2,y_2), or print -1 if the travel is impossible.

Sample Input 1

3 5 2
3 2 3 4
.....
.@..@
..@..

Sample Output 1

5

Initially, Snuke is at the square (3,2).
He can reach the square (3, 4) by making five strokes as follows:

From (3, 2), go west one square to (3, 1).

From (3, 1), go north two squares to (1, 1).

From (1, 1), go east two squares to (1, 3).

From (1, 3), go east one square to (1, 4).

From (1, 4), go south two squares to (3, 4).

Sample Input 2

1 6 4
1 1 1 6
......

Sample Output 2

2

Sample Input 3

3 3 1
2 1 2 3
.@.
.@.
.@.

Sample Output 3

-1

Solution in Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.util.Arrays;
import java.util.Comparator;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.TreeSet;

public class Main {

  private static void solve() {
    int h = ni();
    int w = ni();
    int k = ni();

    int sy = ni() - 1;
    int sx = ni() - 1;
    int gy = ni() - 1;
    int gx = ni() - 1;

    char[][] map = new char[h][];
    for (int i = 0; i < h; i++) {
      map[i] = ns();
    }

    int ret = dijk(map, sy, sx, gy, gx, h, w, k);
    System.out.println(ret >= Integer.MAX_VALUE ? -1 : ret);
  }

  public static int dijk(char[][] map, int sy, int sx, int gy, int gx, int h, int w, int k) {
    int n = h * w;
    int[] d = new int[n];
    Arrays.fill(d, Integer.MAX_VALUE);
    Queue<int[]> q = new PriorityQueue<int[]>(100000, new Comparator<int[]>() {
      public int compare(int[] a, int[] b) {
        if (a[1] - b[1] != 0)
          return a[1] - b[1];
        if (a[2] - b[2] != 0) {
          return b[2] - a[2];
        }
        return a[0] - b[0];
      }
    });

    int from = sy * w + sx;
    q.add(new int[] { from, 0, 0 });

    d[from] = 0;
    int[][] dir = { { -1, 0 }, { 1, 0 }, { 0, -1 }, { 0, 1 } };

    while (q.size() > 0) {
      int[] cur = q.poll();
      int y = cur[0] / w;
      int x = cur[0] % w;

      if (y == gy && x == gx) {
        return d[gy * w + gx];
      }

      for (int[] dd : dir) {
        int ny = y;
        int nx = x;
        for (int i = 0; i < k; i++) {
          ny += dd[0];
          nx += dd[1];

          if (ny < 0 || nx < 0 || ny >= h || nx >= w || map[ny][nx] == '@') {
            break;
          }

          int next = ny * w + nx;
          int nd = d[cur[0]] + 1;
          if (nd < d[next]) {
            d[next] = nd;
            q.add(new int[] { next, nd, i });
          }
        }
      }
    }

    return d[gy * w + gx];
  }

  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = args.length > 0 ? args[0] : null;
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

  public static String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }

  private static double nd() {
    return Double.parseDouble(next());
  }

  private static long nl() {
    return Long.parseLong(next());
  }

  private static int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static char[] ns() {
    return next().toCharArray();
  }

  private static long[] nal(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = nl();
    return a;
  }

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

  private static int ni() {
    return Integer.parseInt(next());
  }

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}