#include "cyberland.h"
// START
#include <bits/stdc++.h>
#define IOS ios_base::sync_with_stdio(false);cin.tie();cout.tie();
#define all(x) x.begin(), x.end()
#define vi vector<int>
#define pi pair<int, int >
#define lb lower_bound
#define ub upper_bound
#define pb push_back
#define eb emplace_back
#define mset multiset
#define F first
#define S second
#define pid pair<int, double>
#define pdi pair<double, int>
using namespace std;
vector<pid> adj[100005];
double mindis[100005];
bool reach[100005];
int h, n;
void dfs(int u) {
reach[u] = 1;
if (u == h) return;
for (auto [v, w]: adj[u]) {
if (!reach[v]) dfs(v);
}
}
void dij(vector<int> &arr) {
priority_queue<pdi, vector<pdi>, greater<pdi>> 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().S;
pq.pop();
if (vis[u]) continue;
vis[u] = 1;
if (u == h) continue;
for (auto [v, w]: adj[u]) {
if (reach[v] && !vis[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 != h) mn = min(mn, (mindis[v] + w) / 2.0);
}
}
if(mn < mindis[u]) tmp.pb({u, mn});
}
for (auto [u, dis]: tmp) {
mindis[u] = min(mindis[u], dis);
}
}
double solve(int N, int M, int K, int H, vector<int> x, vector<int> y, vector<int> c, vector<int> arr) {
h = H; n = N;
K = min(K, 70);
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]].pb({y[i], (double)c[i]});
adj[y[i]].pb({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];
}
//END
