#pragma GCC optimize("Ofast")
#pragma GCC optimize("O3,unroll-loops")
#include <bits/stdc++.h>
using namespace std;
#define f0r(i, n) for (auto i = 0; i < (n); ++i)
#define fnr(i, n, k) for (auto i = (n); i < (k); ++i)
#define all(v) (v).begin(), (v).end()
#define pb push_back
#define F first
#define S second
#define ctn(x) cout << x << '\n'
#define forl(a, l) for (auto a : l)
#define ctl(l) for (auto &a : (l)) cout << a << ' '; cout << endl;
#define lb(v, x) (lower_bound(all(v), x) - begin(v))
#define ub(v, x) (upper_bound(all(v), x) - begin(v))
#define pq priority_queue
template <class T>
using V = vector<T>;
using ll = long long;
using vi = V<int>;
using ld = long double;
using vl = V<ld>;
using pi = pair<int, int>;
using pl = pair<ld, int>;
using ti = tuple<int, int, int>;
using Adj = V<V<pair<int, ld>>>;
using vvi = V<vi>;
#include "cyberland.h"
Adj G;
ld djikstra(vi &st, int H, int K, vi &A) {
V<vl> dist(G.size()+1, vl(K+1, 1e15));
using pr = pair<ld, pi>;
priority_queue<pr, V<pr>, greater<pr>> pq;
int s = G.size();
G.pb({});
A.pb(1);
forl(x, st) {
G[s].pb({x, 0});
}
pq.push({0, {s, 0}});
dist[s][0] = 0;
vl p2(K+1);
p2[0] = 1;
fnr(i, 1, K+1) p2[i] = p2[i-1]*2;
while (!pq.empty()) {
auto [d, p] = pq.top();
auto [u, k] = p;
pq.pop();
if (d > dist[u][k]) continue;
if (u == H) continue;
for (auto [c, w]: G[u]) {
if (d + w < dist[c][k]) {
dist[c][k] = d+w;
pq.push({d+w, {c, k}});
}
if (A[c] == 2 && k < K && (d+w)/2 < dist[c][k+1]) {
dist[c][k+1] = (d+w)/2;
pq.push({dist[c][k+1], {c, k+1}});
}
}
}
return *min_element(all(dist[H]));
}
double solve(int N, int M, int K, int H, vi x, vi y, vi c, vi arr) {
K = min(K, 70);
G.assign(N, {});
f0r(i, M) {
G[x[i]].pb({y[i], c[i]});
G[y[i]].pb({x[i], c[i]});
}
queue<int> Q;
Q.push(0);
V<bool> vis(N);
while (!Q.empty()) {
int u = Q.front();
Q.pop();
if (vis[u]) continue;
vis[u] = 1;
if (u == H) continue;
for (auto [c, w]: G[u]) {
Q.push(c);
}
}
arr[0] = 0;
vi st;
f0r(i, N) if (!arr[i] && vis[i]) st.pb(i);
ld mn = djikstra(st, H, K, arr);
//f0r(i, N) if (!arr[i] && vis[i]) mn = min(mn, *min_element(all(dist[i])));
return mn == 1e15 ? -1 : mn;
}
