#include "cyberland.h"
#include <bits/stdc++.h>
#define ll long long
#define inf 1e17
#define dbg(x) cerr<<#x<<' '<<x<<endl;
using namespace std;
vector<bool> vis;
vector<ll> zeros;
vector<ll> tws;
vector<vector<pair<ll,ll>>> adj;
void dfs(ll node, vector<int>& arr)
{
vis[node]=true;
if(arr[node]==0) zeros.push_back(node);
else if(arr[node]==2) tws.push_back(node);
for (auto &&e : adj[node])
{
if(!vis[e.first])
{
dfs(e.first,arr);
}
}
}
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) {
vis.clear();
adj.clear();
vis.assign(N,false);
adj.assign(N,vector<pair<ll,ll>>());
zeros.clear();
tws.clear();
zeros.push_back(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,arr);
if(!vis[H]) return -1;
vector<double> dist(N,inf);
priority_queue<pair<double,int>,vector<pair<double,int>>,greater<pair<double,int>>> pq;
dist[H]=0;
pq.push({0,H});
auto dij=[&]()
{
while(!pq.empty())
{
ll nd=pq.top().second;
pq.pop();
for (auto &&e : adj[nd])
{
if(dist[e.first] > dist[nd]+e.second)
{
dist[e.first]=dist[nd]+e.second;
pq.push({dist[e.first],e.first});
}
}
}
};
dij();
for (int i=0;i<K;i++)
{
for (auto &&e : tws)
{
double val = dist[e]/2;
for (auto &&ei : adj[e])
{
dist[ei.first]=min(dist[ei.first],val+ei.second);
pq.push({dist[ei.first],ei.first});
}
}
dij();
}
double ans=inf;
for (auto &&e : zeros)
{
ans=min(ans,dist[e]);
}
return ans;
}
