#include<bits/stdc++.h>
#define pb push_back
using namespace std;
double solve (int N, int M, int K, int H, vector<int> x, vector<int> y, vector<int> c, vector<int> arr) {
vector<vector<pair<int, double>>> edge(N);
for (int i = 0; i < M; i ++) {
edge[x[i]].pb({y[i], c[i]});
edge[y[i]].pb({x[i], c[i]});
}
vector<bool> visited(N, false);
queue<int> q;
q.push(0);
while (!q.empty()) {
int v = q.front(); q.pop();
if (v == H) continue;
for (auto [u, w] : edge[v]) {
if (visited[u]) continue;
visited[u] = true;
q.push(u);
}
}
priority_queue<pair<double, pair<int, int>>> pq;
vector<vector<double>> dist(N, vector<double>(K+1, 1e19));
dist[0][0] = 0;
pq.push({0, {0, 0}}); // {-w, {v, k}}
// cout << "zeros: ";
for (int i = 0; i < N; i ++) {
if (arr[i] == 0 && visited[i]) {
// cout << i << " ";
pq.push({0, {i, 0}});
dist[i][0] = 0;
}
}
// cout << endl;
visited.clear();
visited.resize(N, false);
// vector<vector<double>> dist(N, vector<double>(31, 1e19));
// dp[i][t] = min cost to reach to node i with t times of power 2 ability used
while (!pq.empty()) {
int v = pq.top().second.first, k = pq.top().second.second; pq.pop();
// cout << v << endl;
visited[v] = true;
// priority_queue<pair<double, int>> pq_temp = pq;
// while (!pq_temp.empty()) {
// cout << pq_temp.top().first << " " << pq_temp.top().second << endl;
// pq_temp.pop();
// }
// cout << endl;
// for (auto i : visited) {cout << i << " ";} cout << endl;
for (auto [u, w] : edge[v]) {
if (visited[u]) continue;
if (dist[v][k] + w < dist[u][k]) {
dist[u][k] = dist[v][k] + w;
// if (arr[u] == 0) {dist[u] = 0;}
pq.push({ (dist[u][k]*(-1)) , {u, k}});
}
if (arr[u] == 2 && k+1 <= K) {
if ( (dist[v][k] + w)/2 < dist[u][k+1]) {
dist[u][k+1] = (dist[v][k] + w)/2;
pq.push({ (dist[u][k+1]*(-1)), {u, k+1}});
}
}
}
}
// if (dist[0] == 1e19) {return (double)-1;}
// return (double)dist[0];
double mn = 1e19;
// cout << "dist[H]: " << endl;
for (int i = 0; i <= K; i ++) {
// cout << dist[H][i] << " ";
mn = min(mn, dist[H][i]);
}
// cout << endl;
if (mn == 1e19) {return (double)-1;}
return (double)mn;
}
