#include "cyberland.h"
#include <bits/stdc++.h>
using namespace std;
#define node tuple<double, int, int>
const int nx=1e5+5, kx=70;
double p[kx+2];
bool can[nx];
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(N+2);
vector<vector<double>> dp(N, vector<double>(K+2, DBL_MAX));
vector<vector<bool>> vs(N, vector<bool>(K+2, 0));
queue<int> q;
for (int i=0; i<N; i++) can[i]=0;
for (int i=0; i<M; i++)
{
d[x[i]].emplace_back(y[i], c[i]);
d[y[i]].emplace_back(x[i], c[i]);
}
q.emplace(0);
can[H]=1;
while (!q.empty())
{
int x=q.front();
q.pop();
if (can[x]) continue;
can[x]=1;
for (auto [y, z]:d[x]) if (!can[y]) q.push(y);
}
p[0]=1;
for (int i=1; i<=K; i++) p[i]=p[i-1]/2;
dp[H][0]=0; arr[0]=0;
pq.emplace(0, H, 0);
while (!pq.empty())
{
auto [cw, cl, ck]=pq.top();
pq.pop();
if (vs[cl][ck]) continue;
vs[cl][ck]=1;
if (arr[cl]==0&&can[cl]) return cw;
for (auto [v, w]:d[cl])
{
if (!can[v]||v==H) continue;
double nw=cw+w*p[ck];
if (nw<dp[v][ck]) dp[v][ck]=nw, pq.emplace(nw, v, ck);
if (arr[v]==2&&ck<K&&nw<dp[v][ck+1]) dp[v][ck+1]=nw, pq.emplace(nw, v, ck+1);
}
}
return -1;
}
