#include "cyberland.h"
#include <bits/stdc++.h>
#define ll long long
#define inf 1e18
#define dbg(x) cerr<<#x<<' '<<x<<endl;
using namespace std;
vector<bool> vis;
vector<ll> zeros;
vector<ll> tws;
vector<vector<pair<ll,long double>>> adj;
void dfs(ll node, vector<int>& arr, ll h)
{
vis[node]=true;
if(node==h) return;
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,h);
}
}
}
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.assign(N,false);
adj.assign(N,vector<pair<ll,long double>>());
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,H);
if(!vis[H]) return -1;
vector<long double> dist(N,inf);
priority_queue<pair<long double,int>,vector<pair<long double,int>>,greater<pair<long double,int>>> pq;
for (auto &&e : zeros)
{
dist[e]=0;
pq.push({0,e});
}
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;
if(e.first!=H)pq.push({dist[e.first],e.first});
}
}
}
};
dij();
for (int i=0;i<min(62,K);i++)
{
vector<long double> prev=dist;
for (auto &&e : tws)
{
long double val = prev[e]/2;
for (auto &&ei : adj[e])
{
dist[ei.first]=min(dist[ei.first],val+ei.second);
if(ei.first!=H)
pq.push({dist[ei.first],ei.first});
}
}
dij();
}
return dist[H];
}
