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 C++ (GCC 9.2.1) (judge verdict: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;

#define FAST ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL)
#define pf printf
#define sc scanf

#define sf(n) scanf("%d",&n)
#define sff(n1,n2) scanf("%d %d",&n1,&n2)
#define sfff(n1,n2,n3) scanf("%d %d %d",&n1,&n2,&n3)
#define sl(n) scanf("%lld",&n)
#define sll(n1,n2) scanf("%lld %lld",&n1,&n2)
#define slll(n1,n2,n3) scanf("%lld %lld %lld",&n1,&n2,&n3)

#define rep0(i,n) for(i=0;i<n;i++)
#define rep(i,n) for(i=1;i<=n;i++)
#define reps(i,a,n) for(i=a;i<=n;i++)

#define fi first
#define se second
#define pb push_back
#define all(x) (x).begin(),(x).end()
#define sq(x) ((x)*(x))
#define sz(x) x.size()

#define mem(ara,n) memset(ara,n,sizeof(ara))
#define memb(ara) memset(ara,false,sizeof(ara))

#define pi pair<int,int>
#define pii pair<pair<int,int>,pair<int,int> >

#define endl "\n";
#define line puts("-------");
#define dbb(x) cout<<#x<<" : "<<x<<"\n";

void __print(int x) {cerr << x;} void __print(long x) {cerr << x;}
void __print(long long x) {cerr << x;} void __print(unsigned x) {cerr << x;}
void __print(unsigned long x) {cerr << x;} void __print(unsigned long long x) {cerr << x;}
void __print(float x) {cerr << x;} void __print(double x) {cerr << x;}
void __print(long double x) {cerr << x;} void __print(char x) {cerr << '\'' << x << '\'';}
void __print(const char *x) {cerr << '\"' << x << '\"';} void __print(const string &x) {cerr << '\"' << x << '\"';}
void __print(bool x) {cerr << (x ? "true" : "false");}

template<typename T, typename V> void __print(const pair<T, V> &x)
{cerr << '{'; __print(x.first); cerr << ','; __print(x.second); cerr << '}';}
template<typename T> void __print(const queue<T> &x)
{queue<T>temp=x;cerr<<"\n-----\n";while(!temp.empty())
{cerr << temp.front() << endl;temp.pop();}cerr<<"-----\n";}
template<typename T> void __print(const stack<T> &x)
{stack<T>temp=x;cerr<<"\n-----\n";while(!temp.empty())
{cerr << temp.top() << endl;temp.pop();}cerr<<"-----\n";}
template<typename T> void __print(const T &x)
{int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? "," : ""), __print(i); cerr << "}";}
void _print() {cerr << "]\n";}
template <typename T, typename... V> void _print(T t, V... v)
{__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}

#ifndef ONLINE_JUDGE
    #define db(x...) cerr << "[" << #x << "] = [", _print(x)
#endif
using ll = long long;
const int N = 100005;
const int MOD = 1000000007;
int dx[]={0,0,1,-1};
int dy[]={1,-1,0,0};
map<pi,bool>vis;
map<pi,int>cost;
int p,q,pp,qq,n,m,k;
string a[N];
bool valid(int x,int y)
{
    if(x>=0 && x<n && y>=0 && y<m && a[x][y]=='.')
        return true;
    return false;
}
void bfs()
{
    int i,j;
    vis[{p,q}]=true;
    cost[{p,q}]=0;
    queue<pi>qqq;
    qqq.push({p,q});
    while(!qqq.empty())
    {
        pi pr=qqq.front();
        int x=pr.fi,y=pr.se;
        if(x==pp && y==qq)
        {
            pf("%d",cost[{pp,qq}]);
            return;
        }
        qqq.pop();
        rep0(i,4)
        {
            rep(j,k)
            {
                int xx=x+dx[i]*j;
                int yy=y+dy[i]*j;
                if(!valid(xx,yy))
                    break;
                if(vis[{xx,yy}]==false)
                {
                    vis[{xx,yy}]=true;
                    cost[{xx,yy}]=cost[{x,y}]+1;
                    if(xx==pp && yy==qq)
                    {
                        pf("%d",cost[{pp,qq}]);
                        return;
                    }
                    qqq.push({xx,yy});
                }
            }
        }
    }
    pf("-1");
}

int main()
{
    #ifndef ONLINE_JUDGE
        //freopen("input.txt", "r", stdin);
        //freopen("output.txt","w",stdout);
    #endif
    sfff(n,m,k);
    sff(p,q);
    sff(pp,qq);
    int i;
    rep0(i,n)
        cin>>a[i];

    if(p==pp && q==qq)
    {
        pf("0");
        return 0;
    }
    p--;q--;pp--;qq--;
    bfs();
}