#include "cyberland.h"
#include <vector>
#include <queue>
#include <iostream>
#include <math.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
const ld INF = 9e18;
struct T {
ld cdist;
int k;
int node;
bool operator>(const T &other) const {
if (cdist != other.cdist) return cdist > other.cdist;
if (k != other.k) return k > other.k;
return node > other.node;
}
};
ld divByPow2(int x, int k) {
return x / (ull)pow(2, k);
}
void checkReal(int start, int H, vector<vector<pair<int, int>>> &adj, vector<bool> &real) {
real[start] = true;
if (start == H) return;
for (const pair<int, int> &i : adj[start]) {
if (!real[i.first]) {
checkReal(i.first, H, adj, real);
}
}
}
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) {
vector<vector<pair<int, int>>> adj(N);
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]});
}
// find "real" nodes
vector<bool> real(N, false);
checkReal(0, H, adj, real);
if (!real[H]) return -1;
// real[H] = false;
// start djikstra's from H
ld mn = INF;
vector<vector<ld>> dist(N, vector<ld>(K + 1, INF));
dist[H][0] = 0;
priority_queue<T, vector<T>, greater<T>> pq;
pq.push({0, 0, H});
while (!pq.empty()) {
const auto [cdist, k, node] = pq.top();
pq.pop();
if (cdist > dist[node][k]) continue;
if ((arr[node] == 0 || node == 0) && real[node]) {
mn = min(mn, cdist);
continue;
}
if (cdist != dist[node][k]) continue;
for (const pair<int, int> &i : adj[node]) {
// if (i.first == H) continue;
if (!real[i.first]) continue;
if (cdist + divByPow2(i.second, k) < dist[i.first][k]) {
dist[i.first][k] = cdist + divByPow2(i.second, k);
pq.push({dist[i.first][k], k, i.first});
}
// power-up 2
if (arr[i.first] == 2 && cdist + divByPow2(i.second, k + 1) < dist[i.first][k+1] && k < K && node != H) {
dist[i.first][k+1] = cdist + divByPow2(i.second, k + 1);
pq.push({dist[i.first][k+1], k + 1, i.first});
}
}
}
return mn == INF ? -1 : mn;
}
