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: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;

public class Main {
    static In in = new In();
    static Out out = new Out();
    static final long mod = 1000000007;
    static final long inf = 0x1fffffffffffffffL;
    static final int iinf = 0x3fffffff;
    static final int[] da = {-1, 0, 1, 0, -1, 1, 1, -1, -1};

    void solve() {
        int h = in.nextInt();
        int w = in.nextInt();
        int k = in.nextInt();
        int y1 = in.nextInt() - 1;
        int x1 = in.nextInt() - 1;
        int y2 = in.nextInt() - 1;
        int x2 = in.nextInt() - 1;
        char[][] c = in.nextCharGrid(h, w);
        int[][] dist = new int[h][w];
        for (int i = 0; i < h; i++) {
            Arrays.fill(dist[i], iinf);
        }
        Point.h = h;
        Point.w = w;
        dist[y1][x1] = 0;
        Deque<Point> deque = new ArrayDeque<>();
        deque.addLast(new Point(x1, y1));
        while (!deque.isEmpty()) {
            Point p = deque.pollFirst();
            for (int i = 0; i < 4; i++) {
                Point q = p;
                for (int j = 0; j < k; j++) {
                    q = q.move(i);
                    if (q.isInner() && c[q.y][q.x] == '.') {
                        if (dist[q.y][q.x] <= dist[p.y][p.x]) {
                            break;
                        }
                        if (dist[q.y][q.x] <= dist[p.y][p.x] + 1) {
                            continue;
                        }
                        dist[q.y][q.x] = dist[p.y][p.x] + 1;
                        deque.addLast(q);
                    } else {
                        break;
                    }
                }
            }
        }
        out.println(dist[y2][x2] == iinf ? -1 : dist[y2][x2]);
    }

    public static void main(String[]$) {
        new Main().solve();
        out.flush();
    }
}

class Point implements Comparable<Point> {
    static int h = -1, w = -1;
    final int x, y, z;

    Point(int z) {
        this.x = z % w;
        this.y = z / w;
        this.z = z;
    }

    Point(int x, int y) {
        this.x = x;
        this.y = y;
        this.z = y * w + x;
    }

    Point move(int d) {
        return new Point(x + Main.da[d], y + Main.da[d + 1]);
    }

    boolean isInner() {
        if (h == -1 || w == -1) {
            throw new IllegalStateException("h/w is not initialized!");
        }
        return 0 <= x && x < w && 0 <= y && y < h;
    }

    List<Point> aroundPoints(int type) {
        List<Point> list = new ArrayList<>();
        for (int i = 0; i < type; i++) {
            int nx = x + Main.da[i];
            int ny = y + Main.da[i + 1];
            Point point = new Point(nx, ny);
            if (point.isInner()) {
                list.add(point);
            }
        }
        return list;
    }

    int direction(Point o) {
        for (int i = 0; i < 8; i++) {
            if (move(i).equals(o)) {
                return i;
            }
        }
        return -1;
    }

    @Override
    public int compareTo(Point o) {
        return x == o.x ? Integer.compare(y, o.y) : Integer.compare(x, o.x);
    }

    @Override
    public boolean equals(Object o) {
        if (!(o instanceof Point)) {
            return false;
        }
        Point point = (Point)o;
        return x == point.x && y == point.y;
    }

    @Override
    public int hashCode() {
        return z;
    }

    @Override
    public String toString() {
        return String.format("(%d, %d)", x, y);
    }
}

class In {
    private BufferedReader reader = new BufferedReader(new InputStreamReader(System.in), 0x10000);
    private StringTokenizer tokenizer;

    String next() {
        try {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(reader.readLine());
            }
        } catch (IOException ignored) {
        }
        return tokenizer.nextToken();
    }

    int nextInt() {
        return Integer.parseInt(next());
    }

    long nextLong() {
        return Long.parseLong(next());
    }

    char[] nextCharArray() {
        return next().toCharArray();
    }

    char[][] nextCharGrid(int n, int m) {
        char[][] a = new char[n][m];
        for (int i = 0; i < n; i++) {
            a[i] = next().toCharArray();
        }
        return a;
    }

    int[] nextIntArray(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
        }
        return a;
    }

    int[] nextIntArray(int n, IntUnaryOperator op) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = op.applyAsInt(nextInt());
        }
        return a;
    }

    long[] nextLongArray(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextLong();
        }
        return a;
    }

    long[] nextLongArray(int n, LongUnaryOperator op) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = op.applyAsLong(nextLong());
        }
        return a;
    }
}

class Out {
    private PrintWriter out = new PrintWriter(System.out);
    boolean autoFlush = false;

    void println(Object... a) {
        StringJoiner joiner = new StringJoiner(" ");
        for (Object obj : a) {
            joiner.add(String.valueOf(obj));
        }
        out.println(joiner);
        if (autoFlush) {
            out.flush();
        }
    }

    void println(char[] s) {
        out.println(String.valueOf(s));
        if (autoFlush) {
            out.flush();
        }
    }

    void println(int[] a) {
        StringJoiner joiner = new StringJoiner(" ");
        for (int i : a) {
            joiner.add(Integer.toString(i));
        }
        out.println(joiner);
        if (autoFlush) {
            out.flush();
        }
    }

    void println(long[] a) {
        StringJoiner joiner = new StringJoiner(" ");
        for (long i : a) {
            joiner.add(Long.toString(i));
        }
        out.println(joiner);
        if (autoFlush) {
            out.flush();
        }
    }

    void flush() {
        out.flush();
    }
}