#include <bits/stdc++.h>
using namespace std;
using ll = long long;
class DisjointUnionSets {
vector<ll> rank, parent;
public:
DisjointUnionSets(ll n) {
rank.resize(n, 0);
parent.resize(n);
for (ll i = 0; i < n; i++) {
parent[i] = i;
}
}
ll find(ll i) {
ll root = parent[i];
if (parent[root] != root) {
return parent[i] = find(root);
}
return root;
}
void unionSets(int x, int y) {
ll xRoot = find(x);
ll yRoot = find(y);
if (xRoot == yRoot) return;
if (rank[xRoot] < rank[yRoot]) {
parent[xRoot] = yRoot;
}
else if (rank[yRoot] < rank[xRoot]) {
parent[yRoot] = xRoot;
}
else {
parent[yRoot] = xRoot;
rank[xRoot]++;
}
}
};
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) {
vector<vector<pair<ll,ll>>> adj(N);
DisjointUnionSets dsu(N);
for (int i = 0; i < M; ++i) {
if (x[i] != H && y[i] != H) dsu.unionSets(x[i], y[i]);
adj[x[i]].emplace_back(y[i],c[i]);
adj[y[i]].emplace_back(x[i], c[i]);
}
K = min(K, 100);
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, 0, H);
dist[H][0] = 0;
while(!q.empty()) {
double curDistance = get<0>(q.top());
ll curK = get<1>(q.top());
ll curNode = get<2>(q.top());
q.pop();
if(dist[curNode][curK] < curDistance) continue;
if((arr[curNode] == 0 || curNode == 0)) return curDistance;
for(auto [newNode, distance] : adj[curNode]) {
if (dsu.find(newNode) != dsu.find(0)) continue;
double newDistance = curDistance + (double(distance)/pow(2, curK));
if(newDistance < dist[newNode][curK]) {
dist[newNode][curK] = newDistance;
q.emplace(newDistance, curK, newNode);
}
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, curK + 1, newNode);
}
}
}
}
}
return -1;
}
