#include <bits/stdc++.h>
using namespace std;
using ll = long long;
vector<bool> isReachable;
void dfs(ll v, ll H, vector<vector<pair<ll,ll>>>& adj) {
isReachable[v] = true;
if(v == H) return;
for(auto u : adj[v]) {
if(!isReachable[u.first]){
dfs(u.first, H, adj);
}
}
}
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) {
cout << fixed << setprecision(12);
vector<vector<pair<ll,ll>>> adj(N);
isReachable.clear();
isReachable.resize(N);
for (int i = 0; i < M; ++i) {
adj[x[i]].emplace_back(y[i],c[i]);
adj[y[i]].emplace_back(x[i], c[i]);
}
dfs(0, H, adj);
if(!isReachable[H]) return -1;
K = min(K, 60);
vector<vector<double>> dist(N + 10, vector<double>(K + 10, 1e18));
priority_queue<tuple<double, ll, ll>, vector<tuple<double, ll, ll>>, greater<>> q;
q.emplace(0, H, 0);
dist[H][0] = 0;
double ans = 1e18;
while(!q.empty()) {
double curDistance = get<0>(q.top());
ll curNode = get<1>(q.top());
ll curK = get<2>(q.top());
q.pop();
if(dist[curNode][curK] < curDistance) continue;
if((arr[curNode] == 0 || curNode == 0) && isReachable[curNode]) {
ans = min(ans, curDistance);
continue;
}
for(auto [newNode, distance] : adj[curNode]) {
if(isReachable[newNode]) {
double newDistance = curDistance + double(distance)/pow(2, curK);
if(newDistance < dist[newNode][curK]) {
dist[newNode][curK] = newDistance;
q.emplace(newDistance, newNode, curK);
}
if(arr[curNode] == 2) {
if(curK < K) {
double betterDistance = curDistance + double(distance)/pow(2, curK + 1);
if(betterDistance < dist[newNode][curK + 1]) {
dist[newNode][curK + 1] = betterDistance;
q.emplace(betterDistance, newNode, curK + 1);
}
}
}
}
}
}
return ans;
}
