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 1.8.0) (judge verdict: Time Limit Exceeded)

import java.io.*;
import java.util.*;

public class Main{
	static Scanner sc;
	static PrintWriter pw;
	static final int INF = (int) 1e9; // don't increase, avoid overflow
	static ArrayList<Edge>[] adjList;
	static int V, n, m, k;
	static char c[][];
	static int[] dx = { 1, 0, -1, 0 };
	static int[] dy = { 0, 1, 0, -1 };

	/*
	 * 1. Dijkstra's Algorithm for SSSP on weighted graphs
	 */
	static int dijkstra(pair S, pair T) // O(E log E)
	{
		int[][] dist = new int[n][m];
		for (int i = 0; i < n; i++) {
			Arrays.fill(dist[i], INF);
		}
		PriorityQueue<Edge> pq = new PriorityQueue<Edge>();
		dist[S.x][S.y] = 0;
		pq.add(new Edge(S, 0, 0, -1)); // may add more in case of MSSP (Mult-Source)
		while (!pq.isEmpty()) {
			Edge cur = pq.remove();
			if (cur.node.x == T.x && cur.node.y == T.y) { // remove if all computations are needed
				return cur.cost;
			}
			if (cur.cost > dist[cur.node.x][cur.node.y]) // lazy deletion
				continue;
			PriorityQueue<Edge> temp = new PriorityQueue<>();
			boolean f = true;
			for (int i = 0; i < 4; i++) {
				int x = cur.node.x + dx[i];
				int y = cur.node.y + dy[i];
				if (valid(x, y)) {
					if (cur.w == i && cur.c < k) {
						if (cur.cost < dist[x][y]) {
							pq.add(new Edge(new pair(x, y), dist[x][y] = cur.cost, cur.c + 1, i));
							f = false;
						}
						if (cur.cost == dist[x][y])
							temp.add(new Edge(new pair(x, y), dist[x][y] = cur.cost, cur.c + 1, i));

					} else {
						if (cur.cost + 1 < dist[x][y]) {
							f = false;
							pq.add(new Edge(new pair(x, y), dist[x][y] = cur.cost + 1, 1, i));
						}
						if (cur.cost + 1 == dist[x][y])
							temp.add(new Edge(new pair(x, y), dist[x][y] = cur.cost + 1, 1, i));
					}
				}
			}
			while (!temp.isEmpty()) {
				Edge e = temp.poll();
				if (e.cost <= dist[e.node.x][e.node.y])
					pq.add(e);
			}

		}

		return -1;
	}

	static class Edge implements Comparable<Edge> {
		pair node;
		int cost, c, w;

		Edge(pair a, int b, int q, int e) {
			node = a;
			cost = b;
			c = q;
			w = e;
		}

		public int compareTo(Edge e) {
			return cost - e.cost;
		}
	}

	static boolean valid(int i, int j) {
		return (i < n && i >= 0 && j >= 0 && j < m && c[i][j] == '.');
	}

	public static void main(String[] args) throws IOException {
		sc = new Scanner(System.in);
		pw = new PrintWriter(System.out);
		n = sc.nextInt();
		m = sc.nextInt();
		V = n * m;
		k = sc.nextInt();

		int is = sc.nextInt() - 1;
		int js = sc.nextInt() - 1;
		int it = sc.nextInt() - 1;
		int jt = sc.nextInt() - 1;
		c = new char[n][m];
		for (int i = 0; i < c.length; i++) {
			c[i] = sc.next().toCharArray();
		}

		pw.print(dijkstra(new pair(is, js), new pair(it, jt)));
		pw.flush();
	}

	/////////////////////////////////////////////////////////////////////////////////////////////////////
	static long gcd(long a, long b) {
		if (a == 0)
			return b;
		return gcd(b % a, a);
	}

	static long lcm(long a, long b) {
		return (a * b) / gcd(a, b);
	}

	public static int log(int n, int base) {
		int ans = 0;
		while (n + 1 > base) {
			ans++;
			n /= base;
		}
		return ans;
	}

	static int pow(int b, long e) {
		int ans = 1;
		while (e > 0) {
			if ((e & 1) == 1)
				ans = (int) ((ans * 1l * b));
			e >>= 1;
			{

			}
			b = (int) ((b * 1l * b));
		}
		return ans;
	}

	static int powmod(int b, long e, int mod) {
		int ans = 1;
		b %= mod;
		while (e > 0) {
			if ((e & 1) == 1)
				ans = (int) ((ans * 1l * b) % mod);
			e >>= 1;
			b = (int) ((b * 1l * b) % mod);
		}
		return ans;
	}

	static class pair implements Comparable<pair> {
		int x, y;

		pair(int s, int d) {
			x = s;
			y = d;
		}

		@Override
		public int compareTo(pair p) {
			if (x == p.x)
				return y - p.y;
			return x - p.x;
		}

		@Override
		public String toString() {
			return x + " " + y;

		}
	}

	static int ceil(int a, int b) {
		int ans = a / b;
		return a % b == 0 ? ans : ans + 1;
	}

	static long ceil(long a, long b) {
		long ans = a / b;
		return a % b == 0 ? ans : ans + 1;
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public int[] intArr(int n) throws IOException {
			int a[] = new int[n];
			for (int i = 0; i < a.length; i++) {
				a[i] = nextInt();
			}
			return a;
		}

		public long[] longArr(int n) throws IOException {
			long a[] = new long[n];
			for (int i = 0; i < a.length; i++) {
				a[i] = nextLong();
			}
			return a;
		}

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

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

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

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

		public double nextDouble() throws IOException {
			String x = next();
			StringBuilder sb = new StringBuilder("0");
			double res = 0, f = 1;
			boolean dec = false, neg = false;
			int start = 0;
			if (x.charAt(0) == '-') {
				neg = true;
				start++;
			}
			for (int i = start; i < x.length(); i++)
				if (x.charAt(i) == '.') {
					res = Long.parseLong(sb.toString());
					sb = new StringBuilder("0");
					dec = true;
				} else {
					sb.append(x.charAt(i));
					if (dec)
						f *= 10;
				}
			res += Long.parseLong(sb.toString()) / f;
			return res * (neg ? -1 : 1);
		}

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

	}

	public static void shuffle(int[] a) {
		int n = a.length;
		for (int i = 0; i < n; i++) {
			int r = i + (int) (Math.random() * (n - i));
			int tmp = a[i];
			a[i] = a[r];
			a[r] = tmp;
		}
	}

}