// #ifndef khos
// #pragma GCC optimize ("Ofast")
// #pragma GCC optimize ("unroll-loops")
// #endif
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#ifdef khos
#include "t_debug.cpp"
#else
#define debug(...) 42
#endif
using namespace std;
using namespace __gnu_pbds;
template<typename T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T> using indexed_multiset = tree<pair<int,int>, null_type, less<pair<int,int>>, rb_tree_tag, tree_order_statistics_node_update>;
// #define int int64_t
#define vi vector
#define ss second
#define ff first
#define TESTCASES
#define all(x) (x).begin(), (x).end()
const int mod = 1e9+7;
const int MAXN=4e6;
const int inf=1e9;
vi<int> dx={1, -1, 0, 0};
vi<int> dy={0, 0, 1, -1};
// ... (sarlavha va includes o'zi kabi)
void solution() {
int n,s;
cin >> n >> s;
vi<string> a(n);
const int INF = 1e9;
vi<vi<int>> dist(n, vi<int> (n, INF));
queue<pair<int,int>> q;
int sx=-1, sy=-1, ex=-1, ey=-1;
for(int i=0; i<n; i++){
cin >> a[i];
for(int j=0; j<n; j++){
if(a[i][j]=='H'){
dist[i][j]=0;
q.push({i, j});
}
if(a[i][j]=='M'){
sx=i; sy=j;
}
if(a[i][j]=='D'){
ex=i; ey=j;
}
}
}
auto isvalid = [&](int nx, int ny) -> bool {
if(nx<0 || ny<0) return false;
if(nx>=n || ny>=n) return false;
if(a[nx][ny]!='G' && a[nx][ny]!='M') return false;
return true;
};
while(!q.empty()){
auto [x,y]=q.front(); q.pop();
for(int i=0;i<4;i++){
int nx=x+dx[i], ny=y+dy[i];
if(isvalid(nx, ny) && dist[nx][ny]==INF){
dist[nx][ny]=dist[x][y]+1;
q.push({nx, ny});
}
}
}
int l=-1, r=n*n;
while(l<r){
int mid=(l+r+1)/2;
queue<pair<int,int>> qq;
bool ok = false;
// if bees already at start at or before mid -> impossible
if (dist[sx][sy] <= mid) {
ok = false;
} else {
qq.push({sx, sy});
vi<vi<char>> vis(n, vi<char>(n,0));
vi<vi<int>> mt(n, vi<int>(n,0));
vis[sx][sy]=1; mt[sx][sy]=0;
while(!qq.empty() && !ok){
auto [x,y]=qq.front(); qq.pop();
for(int i=0;i<4;i++){
int nx=x+dx[i], ny=y+dy[i];
// if stepping straight into home
if(nx==ex && ny==ey){
int needed = (mt[x][y] + 1 + s - 1) / s;
if (dist[ex][ey] > mid + needed) { ok = true; break; }
else continue;
}
if(!isvalid(nx, ny)) continue;
if(vis[nx][ny]) continue;
int needed = (mt[x][y] + 1 + s - 1) / s;
if(dist[nx][ny] > mid + needed){
vis[nx][ny]=1;
mt[nx][ny]=mt[x][y]+1;
qq.push({nx, ny});
}
}
}
}
if(ok) l = mid;
else r = mid-1;
}
cout << l << '\n';
}
int32_t main(){
clock_t tStart = clock();
// freopen("atlarge.in", "r", stdin);
// freopen("atlarge.out", "w", stdout);
#ifdef khos
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
#endif
std::ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
int q = 1;
#ifdef TESTCASES
// cin >> q;
#endif
while(q--) {
solution();
cout << '\n';
}
cerr<<fixed<<setprecision(3)<<"\nTime Taken: "<<(double)(clock()- tStart)/CLOCKS_PER_SEC<<endl;
}
