#include "cyberland.h"
#include <bits/stdc++.h>
using namespace std;
#define pid pair<int,double>
#define f first
#define s second
#define A pair<double, int>
vector<pid> adj[100005];
bool reach[100005];
int HH, N;
void dfs(int u) {
reach[u] = 1;
if(u==HH) return;
for(auto [v, w]:adj[u]) {
if(!reach[v]) dfs(v);
}
}
double mindis[100005];
void dij(vector<int> &arr) {
priority_queue<A, vector<A>, greater<A>> pq;
for(int i=0;i<N;i++) {
if(reach[i] && mindis[i]<1e18) pq.push({mindis[i], i});
}
vector<bool> vis(N, 0);
while(!pq.empty()) {
int u = pq.top().second;
pq.pop();
if(vis[u]) continue;
vis[u] = 1;
if(u==HH) continue;
for(auto [v, w]:adj[u]) {
if(reach[v] && mindis[v]>mindis[u]+w) {
mindis[v] = mindis[u]+w;
pq.push({mindis[v], v});
}
}
}
vector<pid> tmp;
for(int u=0;u<N;u++) {
double mn = mindis[u];
if(reach[u] && arr[u]==2) {
for(auto [v, w]:adj[u]) {
if(reach[v] && v!=HH) mn = min(mn, (mindis[v]+w)/2.0);
}
}
if(mn<mindis[u]) tmp.push_back({u, mn});
}
for(auto [u, dis]:tmp) {
mindis[u] = min(mindis[u], dis);
}
}
double solve(int NN, int M, int K, int H, vector<int> x, vector<int> y, vector<int> c, vector<int> arr) {
HH = H; N = NN;
for(int i=0;i<N;i++) {
adj[i].clear();
reach[i] = 0;
mindis[i] = 1e18;
}
for(int i=0;i<M;i++) {
adj[x[i]].push_back({y[i], (double)c[i]});
adj[y[i]].push_back({x[i], (double)c[i]});
}
dfs(0);
if(!reach[H]) return -1;
mindis[0] = 0;
for(int i=1;i<N;i++) {
if(reach[i] && arr[i]==0) {
mindis[i] = 0;
}
}
for(int i=0;i<=K;i++) dij(arr);
return mindis[H];
}
