#include <bits/stdc++.h>
#include "cyberland.h"
using namespace std;
const int MAX_N = 1e5 + 5;
const int MAX_K = 71;
const long long INF = 1e18 + 7;
vector <pair <int, int>> graph[MAX_N];
double dist[MAX_N][MAX_K];
bool visited[MAX_N];
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, 65);
for (int i = 0; i < N; i++) {
graph[i].clear();
visited[i] = false;
for (int k = 0; k <= K; k++) {
dist[i][k] = INF;
}
}
for (int i = 0; i < M; i++) {
graph[x[i]].emplace_back(y[i], c[i]);
graph[y[i]].emplace_back(x[i], c[i]);
}
queue <int> q;
q.push(0);
visited[0] = true;
while (!q.empty()) {
int u = q.front();
q.pop();
for (auto [v, c] : graph[u]) {
if (visited[v] == true or v == H) continue;
visited[v] = true;
q.push(v);
}
}
priority_queue <tuple <double, int, int>> pq;
arr[0] = 0;
for (int i = 0; i < N; i++) {
if (visited[i] == false or arr[i] != 0) continue;
pq.emplace(0, 0, i);
dist[i][0] = 0;
}
while (!pq.empty()) {
auto [d, k, u] = pq.top();
pq.pop();
if (dist[u][k] < d or u == H) continue;
for (auto [v, c] : graph[u]) {
if (dist[u][k] + c < dist[v][k]) {
dist[v][k] = dist[u][k] + c;
pq.emplace(-dist[v][k], k, v);
}
if (arr[v] == 2 and k < K and (dist[u][k] + c) / 2.0 < dist[v][k + 1]) {
dist[v][k + 1] = (dist[u][k] + c) / 2.0;
pq.emplace(-dist[v][k + 1], k + 1, v);
}
}
}
double res = INF;
for (int k = 0; k <= K; k++) res = min(res, dist[H][k]);
if (res == INF) res = -1;
return res;
}
