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