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)

#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")
#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#define ll long long
#define ull unsigned long long
#define ld long double
#define pii pair<int,int>
#define pll pair<ll,ll>
#define xx first
#define yy second
#define sci(n) scanf("%d",&n)
#define scii(n,m) scanf("%d%d",&n,&m)
#define sciii(n,m,w) scanf("%d%d%d",&n,&m,&w)
#define scl(n) scanf("%lld",&n)
#define scll(n,m) scanf("%lld%lld",&n,&m)
#define sclll(n,m,w) scanf("%lld%lld%lld",&n,&m,&w)
#define pf(a)   printf("%d\n",a)
#define CASE(a) printf("Case %d:\n",a)
#define dbg(i) printf("yo %lld\n", i)
#define endl '\n'
#define READ  freopen("input.txt","r",stdin)
#define WRITE freopen("output.txt","w",stdout);
#define pi acos(-1)
#define mem(a,b) memset(a,b,sizeof(a))
#define SQR(a) (a)*(a)
#define all(v) v.begin(),v.end()
#define pb push_back
#define pri priority_queue<int>
#define rev_pri priority_queue<int,vector<int>,greater<int> >
#define IOS ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
#define mod 1000000007
#define inf INT_MAX
#define eps 1e-9
#define FOR(i, a, b) for (int i=a; i<(b); i++)
#define F0R(i, a) for (int i=0; i<(a); i++)
#define FORd(i,a,b) for (int i = (b)-1; i >= a; i--)
#define F0Rd(i,a) for (int i = (a)-1; i >= 0; i--)
#define snuke(c,itr) for(__typeof((c).begin()) itr=(c).begin();itr!=(c).end();itr++)

using namespace __gnu_pbds;
using namespace std;

int dx[] = {0,1,0,-1,1,1,-1,-1};
int dy[] = {1,0,-1,0,1,-1,-1,1};
//ll ncr(ll n,ll r){
    //if(n==r)return 1;
    //if(r==1)return n;
    //if(dp[n][r]!=-1)return dp[n][r];
    //return dp[n][r]=ncr(n-1,r)+ncr(n-1,r-1);
//}

bool checkbit(int mask,int bit){
    return mask & (1<<bit);
}
int setbit(int mask,int bit){
    return mask | (1<<bit) ;
}
int clearbit(int mask,int bit){
    return mask & ~(1<<bit);
}
int togglebit(int mask,int bit){
    return mask ^ (1<<bit);
}
int topbit(signed t){
	return t==0?-1:31-__builtin_clz(t);
}
int topbit(ll t){
	return t==0?-1:63-__builtin_clzll(t);
}
int botbit(signed a){
	return a==0?32:__builtin_ctz(a);
}
int botbit(ll a){
	return a==0?64:__builtin_ctzll(a);
}
int popcount(signed t){
	return __builtin_popcount(t);
}
int popcount(ll t){
	return __builtin_popcountll(t);
}
bool ispow2(int i){
	return i&&(i&-i)==i;
}

//#define CAPITAL
void yes(bool ex=true){
	#ifdef CAPITAL
	cout<<"YES"<<"\n";
	#else
	cout<<"Yes"<<"\n";
	#endif
	if(ex)exit(0);
}
void no(bool ex=true){
	#ifdef CAPITAL
	cout<<"NO"<<"\n";
	#else
	cout<<"No"<<"\n";
	#endif
	if(ex)exit(0);
}
void possible(bool ex=true){
	#ifdef CAPITAL
	cout<<"POSSIBLE"<<"\n";
	#else
	cout<<"Possible"<<"\n";
	#endif
	if(ex)exit(0);
}
void impossible(bool ex=true){
	#ifdef CAPITAL
	cout<<"IMPOSSIBLE"<<"\n";
	#else
	cout<<"Impossible"<<"\n";
	#endif
	if(ex)exit(0);
}

template <typename T> T BigMod (T b,T p,T m){
    if (p == 0) return 1;if (p%2 == 0){T s = BigMod(b,p/2,m);return ((s%m)*(s%m))%m;}return ((b%m)*(BigMod(b,p-1,m)%m))%m;
}
template <typename T> T ModInv (T b,T m){
    return BigMod(b,m-2,m);
}
template <typename T> T in(){
    char ch;T n = 0;bool ng = false;while (1){ch = getchar();if (ch == '-'){ng = true;ch = getchar();break;}
    if (ch>='0' && ch<='9')     break;}
    while (1){n = n*10 + (ch - '0');ch = getchar();if (ch<'0' || ch>'9')   break;}return (ng?-n:n);
}
template <typename T> T POW(T B,T P){
    if(P==0) return 1; if(P&1) return B*POW(B,P-1);  else return SQR(POW(B,P/2));
}
template <typename T> T Bigmod(T b,T p,T m){
    if(p==0) return 1; else if (!(p&1)) return SQR(Bigmod(b,p/2,m)) % m;else return ((b % m) * Bigmod(b,p-1,m)) % m;
}
template <typename T> T Dis(T x1,T y1,T x2, T y2){
    return sqrt( SQR(x1-x2) + SQR(y1-y2) );
}
template <typename T> T Angle(T x1,T y1,T x2, T y2){
    return atan( double(y1-y2) / double(x1-x2));
}
template <typename T> T DIFF(T a,T b) {
    T d = a-b;if(d<0)return -d;else return d;
}
template <typename T> T ABS(T a) {
    if(a<0)return -a;else return a;
}
template <typename T> T euclide(T a,T b,T &x,T &y) {
    if(a<0){T d=euclide(-a,b,x,y);x=-x;return d;}
    if(b<0){T d=euclide(a,-b,x,y);y=-y;return d;}
    if(b==0){x=1;y=0;return a;}
    else{T d=euclide(b,a%b,x,y);T t=x;x=y;y=t-(a/b)*y;return d;}
}
template <typename T> void ia (T a[],int n){for (int i=0; i<n; i++) cin >> a[i];}
template <typename T> void pa (T a[],int n){for (int i=0; i<n-1; i++) cout << a[i] << " ";cout << a[n-1] << endl;}
template <typename T> ll isLeft(T a,T b,T c) { return (a.x-b.x)*(b.y-c.y)-(b.x-c.x)*(a.y-b.y);}
template <typename T> T gcd(T a,T b){
    if(a<0)return gcd(-a,b);if(b<0)return gcd(a,-b);return (b==0)?a:gcd(b,a%b);
}
template <typename T> T lcm(T a,T b) {
    if(a<0)return lcm(-a,b);if(b<0)return lcm(a,-b);return a*(b/gcd(a,b));
}

template<class t>
int lwb(const vector<t>&v,const t&a){
	return lower_bound(all(v),a)-v.bg;
}

template<typename A, typename B>
class Dijkstra {
public:
    vector<vector<pair<int, A>>> vertexs;
    B Cost_Function;
    Dijkstra(int n, B cost) : Cost_Function(cost) {
        vertexs = vector<vector<pair<int, A>>>(n, vector<pair<int, A>>{});
    }
    ~Dijkstra() {
        vertexs.clear();
    }
    void add_edge(int a, int b, A c) {
        vertexs[a].push_back(mp(b, c));
    }
    vector<ll> build_result(int StartPoint) {
        vector<ll> dist(vertexs.size(), 2e18);
        dist[StartPoint] = 0;
        priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> next;
        next.push(make_pair(0, StartPoint));
        while (next.empty() == false) {
            pair<ll, int> now = next.top();
            next.pop();
            if (dist[now.second] != now.first) continue;
            for (auto x : vertexs[now.second]) {
                ll now_cost = now.first + Cost_Function(x.second);
                if (dist[x.first] > now_cost) {
                    dist[x.first] = now_cost;
                    next.push(mp(now_cost, x.first));
                }
            }
        }
        return dist;
    }
};

#define mxn 100005

//bool vis[1LL << 19];
const ll nax=1000050;
ll n,w,m;
ll ar[nax];
ll h,k;
vector<char>v[nax];
vector<ll>ds[nax];
pair<ll,pll>pr;
void bfs(ll hn,ll hm,ll sx,ll sy)
{
    priority_queue<pair<ll,pair<ll,ll> > ,vector<pair<ll,pair<ll,ll> > >,greater<pair<ll,pair<ll,ll> > > >pq;
    pq.push({0,{hn,hm}});
    ll crds,x,y,cn;
    while(!pq.empty()){
        pr=pq.top();
        pq.pop();
        crds=pr.xx;
        x=pr.yy.xx; y=pr.yy.yy;
        for(ll i=x+1,cn=1;i<=h&&cn<=k;i++,cn++ ){
            if(v[i][y]=='@')break;
            if(ds[i][y]>crds+1){
                ds[i][y]=crds+1;
                pq.push({ds[i][y],{i,y}});
            }
        }
        for(ll i=x-1,cn=1;i>=1&&cn<=k;i--,cn++){
            if(v[i][y]=='@')break;
            if(ds[i][y]>crds+1){
                ds[i][y]=crds+1;
                pq.push({ds[i][y],{i,y}});
            }
        }
        for(ll i=y+1,cn=1;i<=w&&cn<=k;i++,cn++){
            if(v[x][i]=='@')break;
            if(ds[x][i]>crds+1){
                ds[x][i]=crds+1;
                pq.push({ds[x][i],{x,i}});
            }
        }
        for(ll i=y-1,cn=1;i>=1&&cn<=k;i--,cn++){
            if(v[x][i]=='@')break;
            if(ds[x][i]>crds+1){
                ds[x][i]=crds+1;
                pq.push({ds[x][i],{x,i}});
            }
        }
    }

}
void solve()
{

    ll a,b,c,q,j,l,mx=0,i;
    ll hn,hm,gc,sx,sy,ex=1,ey=-1;
    scll(h,w);
    scl(k);
    FOR(i,0,h+4) {v[i].resize(w+4);ds[i].resize(w+4);}
    scll(hn,hm);
    scll(sx,sy);char cha;scanf("%c",&cha);
    FOR(i,1,h+1) {FOR(j,1,w+1) {scanf("%c",&cha);v[i][j]=cha; ds[i][j]=nax*nax;}scanf("%c",&cha);}
    ds[hn][hm]=0;
    bfs(hn,hm,sx,sy);
    if(ds[sx][sy]==nax*nax) printf("-1\n");
    else printf("%I64d\n",ds[sx][sy]);
}
int main()
{
    //IOS;
    double start_time = clock();
    ll t=1,mex=1;
   //cin>>t;
    while(t--){
        solve();
    }
    double end_time = clock();
    //fprintf(stderr, "Time = %lf\n", (end_time - start_time) / CLOCKS_PER_SEC);
    return 0;
}