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: Accepted)

import math
#import sys
#input = sys.stdin.readline

def make_divisors(n):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n//i)

    # divisors.sort()
    return divisors

def ValueToBits(x,digit):
    res = [0 for i in range(digit)]
    now = x
    for i in range(digit):
        res[i]=now%2
        now = now >> 1
    return res

def BitsToValue(arr):
    n = len(arr)
    ans = 0
    for i in range(n):
        ans+= arr[i] * 2**i
    return ans

def ZipArray(a):
    aa = [[a[i],i]for i in range(n)]

    aa.sort(key = lambda x : x[0])
    for i in range(n):
        aa[i][0]=i+1
    aa.sort(key = lambda x : x[1])
    b=[aa[i][0] for i in range(len(a))]
    return b

def ValueToArray10(x, digit):
    ans = [0 for i in range(digit)]
    now = x
    for i in range(digit):
        ans[digit-i-1] = now%10
        now = now //10
    return ans

def Zeros(a,b):
    if(b<=-1):
        return [0 for i in range(a)]
    else:
        return [[0 for i in range(b)] for i in range(a)]

def AddV2(v,w):
    return [v[0]+w[0],v[1]+w[1]]

dir4 = [[1,0],[0,1],[-1,0],[0,-1]]


def clamp(x,y,z):
    return max(y,min(z,x))

class Bit:
    def __init__(self, n):
        self.size = n
        self.tree = [0] * (n + 1)
 
    def sum(self, i):
        s = 0
        while i > 0:
            s += self.tree[i]
            i -= i & -i
        return s
 
    def add(self, i, x):
        while i <= self.size:
            self.tree[i] += x
            i += i & -i
            
#
def Zaatsu(a):
    a.sort()
    now = a[0][0]
    od = 0
    for i in range(n):
        if(now==a[i][0]):
            a[i][0]=od
        else:
            now = a[i][0]
            od+=1
            a[i][0] = od
    
    a.sort(key = lambda x : x[1])
    return a

class UnionFind:
    def __init__(self, n):
        self.par = [i for i in range(n+1)]
        self.rank = [0] * (n+1)

    # 検索
    def find(self, x):
        if self.par[x] == x:
            return x
        else:
            self.par[x] = self.find(self.par[x])
            return self.par[x]

    # 併合
    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)
        if self.rank[x] < self.rank[y]:
            self.par[x] = y
        else:
            self.par[y] = x
            if self.rank[x] == self.rank[y]:
                self.rank[x] += 1

    # 同じ集合に属するか判定
    def same_check(self, x, y):
        return self.find(x) == self.find(y)


'''
def cmb(n, r, p):
    if (r < 0) or (n < r):
        return 0
    r = min(r, n - r)
    return fact[n] * factinv[r] * factinv[n-r] % p

p = 2
N = 10 ** 6 + 2
fact = [1, 1]  # fact[n] = (n! mod p)
factinv = [1, 1]  # factinv[n] = ((n!)^(-1) mod p)
inv = [0, 1]  # factinv 計算用

for i in range(2, N + 1):
    fact.append((fact[-1] * i) % p)
    inv.append((-inv[p % i] * (p // i)) % p)
    factinv.append((factinv[-1] * inv[-1]) % p)

'''

def rl(x):
    return range(len(x))

# a = list(map(int, input().split()))

#################################################
#################################################
#################################################
#################################################


#11-


h,w,k = list(map(int, input().split()))

y1,x1,y2,x2 = list(map(int, input().split()))
x1-=1
y1-=1
x2-=1
y2-=1

mapa = []
visited = [[[0,0] for j in range(w)] for i in range(h)]
visited[y1][x1] = [1,1]

for i in range(h):
    mapa.append( input() )

#
queue = [[y1,x1,0]]
done = 0

while(True):
    if(len(queue)==done):
        break
    now = queue[done]
    # move-y
    for i in range(1,min(k+1,h-now[0])):
        seey,seex = now[0]+i,now[1]
        if(seey == y2 and seex == x2):
            print(now[2]+1)
            exit()
        if(mapa[seey][seex]=='@'):
            break
        elif(visited[seey][seex][0]==0 and mapa[seey][seex]=='.'):
            queue.append([seey,seex,now[2]+1])
            visited[seey][seex][0]=now[2]+1
            if(visited[seey][seex][1]<=now[2] and visited[seey][seex][1]!=0):
                break
        else:
            break
    for i in range(1,min(k+1,now[0]+1)):
        seey,seex = now[0]-i,now[1]
        if(seey == y2 and seex == x2):
            print(now[2]+1)
            exit()
        if(mapa[seey][seex]=='@'):
            break
        elif(visited[seey][seex][0]==0 and mapa[seey][seex]=='.'):
            queue.append([seey,seex,now[2]+1])
            visited[seey][seex][0]=now[2]+1
            if(visited[seey][seex][1]<=now[2] and visited[seey][seex][1]!=0):
                break
        else:
            break
    # move-x
    for i in range(1,min(k+1,w-now[1])):
        seey,seex = now[0],now[1]+i
        if(seey == y2 and seex == x2):
            print(now[2]+1)
            exit()
        if(mapa[seey][seex]=='@'):
            break
        elif(visited[seey][seex][1]==0 and mapa[seey][seex]=='.'):
            queue.append([seey,seex,now[2]+1])
            visited[seey][seex][1]=now[2]+1
            if(visited[seey][seex][0]<=now[2] and visited[seey][seex][0]!=0):
                break
        else:
            break
    for i in range(1,min(k+1,now[1]+1)):
        seey,seex = now[0],now[1]-i
        if(seey == y2 and seex == x2):
            print(now[2]+1)
            exit()
        if(mapa[seey][seex]=='@'):
            break
        elif(visited[seey][seex][1]==0 and mapa[seey][seex]=='.'):
            queue.append([seey,seex,now[2]+1])
            visited[seey][seex][1]=now[2]+1
            if(visited[seey][seex][0]<=now[2] and visited[seey][seex][0]!=0):
                break
        else:
            break
    done+=1

print(-1)