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.*;
import java.util.*;

public class Main {

	static TreeSet<Integer> rows[], cols[];

	static int n, m, K;

	static int INF = (int) 1e9;

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner();
		PrintWriter out = new PrintWriter(System.out);
		n = sc.nextInt();
		m = sc.nextInt();
		K = sc.nextInt();
		rows = new TreeSet[n];
		cols = new TreeSet[m];

		for (int i = 0; i < n; i++) {
			rows[i] = new TreeSet();

		}
		for (int i = 0; i < m; i++) {
			cols[i] = new TreeSet();

		}
		int sI = sc.nextInt() - 1, sJ = sc.nextInt() - 1;
		int [][]q=new int [n*m][2];
		int qh=0,qt=-1;
		q[++qt]=new int[] { sI, sJ };
		int endI = sc.nextInt() - 1, endJ = sc.nextInt() - 1;
		int[][] dist = new int[n][m];
		char[][] grid = new char[n][m];
		for (int i = 0; i < n; i++) {
			grid[i] = sc.next().toCharArray();
			for (int j = 0; j < m; j++)

				if (i == sI && j == sJ)
					dist[i][j] = 0;
				else {
					dist[i][j] = -1;
					rows[i].add(j);
					cols[j].add(i);

				}

		}

		while (qt>=qh) {
			Integer nxt;
			int[] curr = q[qh++];
			int i = curr[0], j = curr[1], d = dist[i][j];
			if(i==endI && j==endJ)
				break;
			// right;
			while (true) {

				nxt = rows[i].higher(j);
				if (nxt != null && nxt - j <= K && grid[i][nxt] == '.') {
					dist[i][nxt] = d + 1;
					cols[nxt].remove(i);
					rows[i].remove(nxt);
					q[++qt]=new int[] { i, nxt };
				} else
					break;
			}
			// left
			while (true) {

				nxt = rows[i].lower(j);
				if (nxt != null && Math.abs(nxt - j) <= K && grid[i][nxt] == '.') {
					dist[i][nxt] = d + 1;
					cols[nxt].remove(i);
					rows[i].remove(nxt);
					q[++qt]=new int[] { i, nxt };
				} else
					break;
			}

			// down
			while (true) {

				nxt = cols[j].higher(i);
				if (nxt != null && Math.abs(nxt - i) <= K && grid[nxt][j] == '.') {
					dist[nxt][j] = d + 1;
					cols[j].remove(nxt);
					rows[nxt].remove(j);
					q[++qt]=new int[] { nxt, j };
				} else
					break;
			}
			// left
			while (true) {

				nxt = cols[j].lower(i);
				if (nxt != null && Math.abs(nxt - i) <= K && grid[nxt][j] == '.') {
					dist[nxt][j] = d + 1;
					cols[j].remove(nxt);
					rows[nxt].remove(j);
					q[++qt]=new int[] { nxt, j };
				} else
					break;

			}
		}
		System.out.println(dist[endI][endJ]);
		out.close();

	}

	static class Scanner {
		BufferedReader br;
		StringTokenizer st;

		Scanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		Scanner(String fileName) throws FileNotFoundException {
			br = new BufferedReader(new FileReader(fileName));
		}

		String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		String nextLine() throws IOException {
			return br.readLine();
		}

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

		long nextLong() throws NumberFormatException, IOException {
			return Long.parseLong(next());
		}

		double nextDouble() throws NumberFormatException, IOException {
			return Double.parseDouble(next());
		}

		boolean ready() throws IOException {
			return br.ready();
		}

	}

	static void sort(int[] a) {
		shuffle(a);
		Arrays.sort(a);
	}

	static void shuffle(int[] a) {
		int n = a.length;
		Random rand = new Random();
		for (int i = 0; i < n; i++) {
			int tmpIdx = rand.nextInt(n);
			int tmp = a[i];
			a[i] = a[tmpIdx];
			a[tmpIdx] = tmp;
		}
	}

}