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: Wrong Answer)


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

public class Main
{
    public static void print(String str,int val){
        System.out.println(str+"  "+val);
    }



    public static void debug(long[][] arr){
        int len = arr.length;
        for(int i=0;i<len;i++){
            System.out.println(Arrays.toString(arr[i]));
        }
    }
    public static void debug(int[][] arr){
        int len = arr.length;
        for(int i=0;i<len;i++){
            System.out.println(Arrays.toString(arr[i]));
        }
    }
    public static void debug(String[] arr){
        int len = arr.length;
        for(int i=0;i<len;i++){
            System.out.println(arr[i]);
        }
    }

    public static void print(int[] arr){
        int len = arr.length;
        for(int i=0;i<len;i++){
            System.out.print(arr[i]+" ");
        }
        System.out.print('\n');
    }
    public static void print(String[] arr){
        int len = arr.length;
        for(int i=0;i<len;i++){
            System.out.print(arr[i]+" ");
        }
        System.out.print('\n');
    }
    public static void print(long[] arr){
        int len = arr.length;
        for(int i=0;i<len;i++){
            System.out.print(arr[i]+" ");
        }
        System.out.print('\n');
    }

    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;


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

        public FastReader(String path) throws FileNotFoundException {
            br = new BufferedReader(new FileReader(path));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }


    public static void main(String[] args) throws FileNotFoundException {
//        FastReader s=new FastReader();
        FastReader s = new FastReader();
        int n = s.nextInt();
        int m = s.nextInt();
        int k = s.nextInt();
        int start_x = s.nextInt() - 1;
        int start_y = s.nextInt() - 1;
        int end_x = s.nextInt() - 1;
        int end_y = s.nextInt() - 1;
        char[][] grid = new char[n][m];
        for (int i = 0; i < n; i++) {
            String str = s.nextLine();
            for (int j = 0; j < m; j++) {
                grid[i][j] = str.charAt(j);
            }
        }
        boolean[][] visited = new boolean[n][m];
        int[][] dist = new int[n][m];
        for(int[] a:dist){
            Arrays.fill(a,Integer.MAX_VALUE);
        }
        Queue<Pair> queue = new LinkedList<>();
        queue.add(new Pair(start_x,start_y));
        dist[start_x][start_y] =0;
        visited[start_x][start_y] = true;
        while (!queue.isEmpty()){
            Pair p = queue.poll();
            //now right
            for(int i=1;i<=k;i++){
                int x = p.x;
                int y = p.y+i;
                if(y<m && grid[x][y]!='@' && !(dist[x][y]<(1+dist[p.x][p.y]))){
                    dist[x][y] = Math.min(dist[p.x][p.y]+1,dist[x][y]);
                    if(!visited[x][y]){
                        visited[x][y] = true;
                        queue.add(new Pair(x,y));
                    }
                }
                else {
                    break;
                }
            }
            //now left
            for(int i=1;i<=k;i++){
                int x = p.x;
                int y = p.y-i;
                if(y>=0 && grid[x][y]!='@' && dist[x][y]>(1+dist[p.x][p.y])){
                    dist[x][y] = Math.min(dist[p.x][p.y]+1,dist[x][y]);
                    if(!visited[x][y]){
                        visited[x][y] = true;
                        queue.add(new Pair(x,y));
                    }
                }
                else {
                    break;
                }
            }
            for(int i=1;i<=k;i++){
                int x = p.x+i;
                int y = p.y;
                if(x<n && grid[x][y]!='@' && dist[x][y]>(1+dist[p.x][p.y])){
                    dist[x][y] = Math.min(dist[p.x][p.y]+1,dist[x][y]);
                    if(!visited[x][y]){
                        visited[x][y] = true;
                        queue.add(new Pair(x,y));
                    }
                }
                else {
                    break;
                }
            }
            for(int i=1;i<=k;i++){
                int x = p.x-i;
                int y = p.y;
                if(x>=0 && grid[x][y]!='@' && dist[x][y]>(1+dist[p.x][p.y])){
                    dist[x][y] = Math.min(dist[p.x][p.y]+1,dist[x][y]);
                    if(!visited[x][y]){
                        visited[x][y] = true;
                        queue.add(new Pair(x,y));
                    }
                }
                else {
                    break;
                }
            }
        }
        if(visited[end_x][end_y]){
            System.out.println(dist[end_x][end_y]);
        }
        else {
            System.out.println(-1);
        }



    }
    static boolean isequal(Pair a,Pair b){
        return (a.x==b.x) && (a.y==b.y);
    }
     static class Pair{
        int x ;
        int y;
        Pair(int x,int y){
            this.x = x;
            this.y = y;
        }
    }




//    OutputStream out = new BufferedOutputStream( System.out );
//        for(int i=1;i<n;i++){
//    out.write((arr[i]+" ").getBytes());
//}
//        out.flush();

    //  long start = System.currentTimeMillis();
//  long end = System.currentTimeMillis();
//  System.out.println((end - start) + "ms");



}