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 PyPy3 (7.3.0) (judge verdict: Runtime Error)

#!/usr/bin/env python3
from collections import defaultdict,deque
from heapq import heappush, heappop
from bisect import bisect_left, bisect_right
import sys, random, itertools, math
sys.setrecursionlimit(10**5)
input = sys.stdin.buffer.readlin
sqrt = math.sqrt
def LI(): return map(int, input().split())
def LF(): return list(map(float, input().split()))
def LI_(): return list(map(lambda x: int(x)-1, input().split()))
def II(): return int(input())
def IF(): return float(input())
def S(): return input().rstrip()
def LS(): return S().split()
def IR(n): return [II() for _ in range(n)]
def LIR(n): return [LI() for _ in range(n)]
def FR(n): return [IF() for _ in range(n)]
def LFR(n): return [LI() for _ in range(n)]
def LIR_(n): return [LI_() for _ in range(n)]
def SR(n): return [S() for _ in range(n)]
def LSR(n): return [LS() for _ in range(n)]
mod = 1000000007
inf = float("INF")

#solve
def solve():
    mxy = [(0, 1), (1, 0), (-1, 0), (0, -1)]
    h, w, K = LI()
    y1, x1, y2, x2 = LI()
    q = deque()
    field = [[False] * (w + 2)] + [None] * h + [[False] * (w + 2)]
    for i in range(1, h + 1):
        field[i] = [False] + [True] * w + [False]
    for i in range(1, h + 1):
        s = input()
        for j in range(1, w + 1):
            if s[j-1] == "@":
                field[i][j] = False
    q.append((x1, y1))
    ans = 0
    c = defaultdict(int)
    while q:
        next_q = deque()

        while q:
            x, y = q.popleft()
            if (x, y) == (x2, y2):
                print(ans)
                return
            if field[y][x]:
                for i in range(1, K + 1):
                    if field[y + i][x]:
                        if not c[(y + i, x)]:
                            next_q.append((x, y + i))
                            c[(y + i, x)] = 1
                    else:
                        break
                for i in range(1, K + 1):
                    if field[y][x + i]:
                        if not c[(y, x + i)]:
                            next_q.append((x + i, y))
                            c[(y, x + i)] = 1
                    else:
                        break
                for i in range(1, K + 1):
                    if field[y - i][x]:
                        if not c[(y - i, x)]:
                            next_q.append((x, y - i))
                            c[(y - i, x)] = 1
                    else:
                        break
                for i in range(1, K + 1):
                    if field[y][x - i]:
                        if not c[(y, x - i)]:
                            next_q.append((x - i, y))
                            c[(y, x - i)] = 1
                    else:
                        break
                field[y][x] = False
        ans += 1
        q = next_q
    print(-1)
    return


#main
if __name__ == '__main__':
    solve()