#include "cyberland.h"
#include <bits/stdc++.h>
#include <queue>
using namespace std;
using ll = long long;
const ll INF = 1e18;
vector<vector<array<int, 2>>> adj;
vector<ll> dijkstra(vector<int> starts, int N) {
vector<ll> dist(N, INF);
priority_queue<pair<ll, int>> pq;
for (auto v: starts) {
dist[v] = 0;
pq.push({0, v});
}
while (!pq.empty()) {
auto [d, v] = pq.top(); pq.pop();
d = - d;
if (d>dist[v]) continue;
for (auto [u, w]: adj[v]) {
if (dist[v]+w<dist[u]) {
dist[u] = dist[v]+w;
pq.push({-dist[u], u});
}
}
}
return dist;
}
double solve(int N, int M, int K, int H, std::vector<int> x, std::vector<int> y, std::vector<int> c, std::vector<int> arr) {
adj.assign(N, {});
for (int i=0; i<M; i++) {
int u = x[i], v=y[i], w=c[i];
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
double ans = INF;
vector<char> vis(N);
vis[0] = true;
queue<int> q;
q.push(0);
while (!q.empty()) {
int v= q.front(); q.pop();
for (auto [u, _]: adj[v]) {
if (!vis[u] && u!=H) {
vis[u] = true;
q.push(u);
}
}
};
vector<int> starts = {0};
for (int i=1; i<N; i++) if (vis[i] && arr[i]==0) starts.push_back(i);
vector<ll> d0 = dijkstra(starts, N), d1 = dijkstra({H}, N);
if (d1[0]==INF) return -1;
for (auto v: starts) ans = min(ans, (double)d1[v]);
for (int i=0; i<N; i++) {
if (arr[i]!=2 || d0[i]==INF || d1[i]==INF) continue;
int cnt = K;
double dist = d0[i];
while (dist>1e-9 && cnt) {
dist /= 2;
cnt--;
}
ans = min(ans, dist+d1[i]);
}
return ans;
}
