#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 power[MAX_K], 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, 66);
power[0] = 1.0;
for (int i = 1; i <= K; i++) power[i] = power[i - 1] / 2.0;
arr[0] = 0;
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;
pq.emplace(0, 0, H);
dist[H][0] = 0;
while (!pq.empty()) {
auto [d, k, u] = pq.top();
pq.pop();
if (dist[u][k] < -d) continue;
if (arr[u] == 0) return -d;
for (auto [v, c] : graph[u]) {
if (visited[v] == false) continue;
if (dist[u][k] + power[k] * c < dist[v][k]) {
dist[v][k] = dist[u][k] + power[k] * c;
pq.emplace(-dist[v][k], k, v);
}
if (arr[v] == 2 and k < K and dist[u][k] + power[k] * c < dist[v][k + 1]) {
dist[v][k + 1] = dist[u][k] + power[k] * c;
pq.emplace(-dist[v][k + 1], k + 1, v);
}
}
}
return -1;
}
