#include "cyberland.h"
#define go(a,b,c,d) if(dis[a][b][c]>d) dis[a][b][c] = d, pq.push({b, {d, a, c}});
#include <bits/stdc++.h>
using namespace std;
double dis[100000][100][2], ans;
bool vis[100000];
vector<pair<int, int>> adj[100000];
void dfs(int n, int h) {
if(vis[n]) return;
vis[n] = 1;
if(n==h) return;
for(auto i: adj[n])
dfs(i.first, h);
}
double solve(int N, int M, int K, int H, vector<int> x, vector<int> y, vector<int> c, vector<int> arr) {
K = min(K, 100);
arr[0] = 0, ans = 1e18;
for(int i = 0; i < N; i++)
for(auto &j: dis[i])
j[0] = j[1] = 1e18;
for(int i = 0; i < N; i++)
adj[i].clear(), vis[i] = 0;
for(int i = 0; i < M; i++)
adj[x[i]].push_back({y[i], c[i]}), adj[y[i]].push_back({x[i], c[i]});
dfs(0, H);
if(!vis[H]) return -1;
priority_queue<pair<int, tuple<double, int, int>>, vector<pair<int, tuple<double, int, int>>>, greater<>> pq;
for(int i = 0; i < N; i++)
if(vis[i]&&!arr[i])
pq.push({0, {0, i, 0}});
while(pq.size()) {
double dist;
int node, halves, halved;
tie(dist, node, halved) = pq.top().second;
halves = pq.top().first, pq.pop();
if(node==H) {ans = min(ans, dist); continue;}
if(!halved&&halves<K&&arr[node] == 2) go(node, halves+1, 1, dist/2);
for(auto i: adj[node])
go(i.first, halves, 0, dist+i.second);
}
return ans;
}
