#include "cyberland.h"
#include <bits/stdc++.h>
using namespace std;
#define node tuple<double, int, int>
const int nx=1e5+5, kx=70;
double dp[nx][kx], p[kx];
int dsu[nx];
int find(int x)
{
if (dsu[x]==x) return x;
return dsu[x]=find(dsu[x]);
}
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) {
K=min(K, 70);
priority_queue<node, vector<node>, greater<node>> pq;
vector<vector<pair<int, double>>> d(nx);
vector<vector<double>> dp(N, vector<double>(K, DBL_MAX));
for (int i=0; i<N; i++) dsu[i]=i;
for (int i=0; i<M; i++)
{
d[x[i]].push_back({y[i], c[i]});
d[y[i]].push_back({x[i], c[i]});
int px=find(x[i]), py=find(y[i]);
if (px!=py) dsu[px]=py;
}
if (find(0)!=find(H)) return -1;
p[0]=1;
for (int i=1; i<K; i++) p[i]=p[i-1]/2;
dp[H][0]=0; arr[0]=0;
pq.push({0, H, 0});
while (!pq.empty())
{
auto [cw, cl, ck]=pq.top();
pq.pop();
if (arr[cl]==0) return cw;
for (auto [v, w]:d[cl])
{
double nw=cw+w*p[ck];
if (nw<dp[v][ck]) dp[v][ck]=nw, pq.push({nw, v, ck});
if (arr[v]==2&&ck<K&&nw<dp[v][ck+1]) dp[v][ck+1]=nw, pq.push({nw, v, ck+1});
}
}
return -1;
}
