#pragma GCC optimize("O3")
#include <bits/stdc++.h>
using namespace std;
constexpr long double inf = 1e16 + 100;
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, int>>> g(n);
for (int i = 0; i < m; ++i) {
g[x[i]].emplace_back(y[i], c[i]);
g[y[i]].emplace_back(x[i], c[i]);
}
vector<int> used(n);
used[0] = 1;
queue<int> q;
q.push(0);
while (!q.empty()) {
int v = q.front();
q.pop();
if (v == h) {
continue;
}
for (auto [u, w] : g[v]) {
if (!used[u]) {
used[u] = 1;
q.push(u);
}
}
}
if (!used[h]) {
return -1;
}
k = min(k, 67);
vector<vector<long double>> dist(k + 1, vector<long double>(n, inf));
priority_queue<pair<long double, int>> s_nw, s_nxt;
dist[0][0] = 0;
s_nxt.push({-dist[0][0], 0});
for (int i = 0; i < n; ++i) {
if (used[i] && arr[i] == 0) {
dist[0][i] = 0;
s_nxt.push({-dist[0][i], i});
}
}
used.assign(n, -1);
for (int i = 0; i <= k; ++i) {
s_nw.swap(s_nxt);
while (!s_nw.empty()) {
int v = s_nw.top().second;
s_nw.pop();
if (used[v] == i) {
continue;
}
used[v] = i;
if (v == h) {
continue;
}
if (dist[i][v] >= inf - 10) {
continue;
}
for (auto [u, w] : g[v]) {
if (dist[i][u] > dist[i][v] + w) {
dist[i][u] = dist[i][v] + w;
s_nw.push({-dist[i][u], u});
}
if (arr[v] == 2 && i + 1 <= k && dist[i + 1][u] > dist[i][v] / 2.0 + w) {
dist[i + 1][u] = dist[i][v] / 2.0 + w;
s_nxt.push({-dist[i + 1][u], u});
}
}
}
}
long double ans = inf;
for (int i = 0; i <= k; ++i) {
ans = min(ans, dist[i][h]);
}
return ans;
}
