#include <bits/stdc++.h>
using namespace std;
const int N = 10005;
const int K = 105;
const double INF = 1e18;
const double EPS = 1e-9;
double solve(int n, int m, int k, int T,
vector<int> type,
vector<int> u,
vector<int> v,
vector<int> w) {
vector<vector<pair<int, int>>> graph(n);
for (int i = 0; i < m; i++) {
graph[u[i]].emplace_back(v[i], w[i]);
graph[v[i]].emplace_back(u[i], w[i]);
}
vector<vector<vector<double>>> dist(n, vector<vector<double>>(k + 1, vector<double>(2, INF)));
priority_queue<tuple<double, int, int, int>, vector<tuple<double, int, int, int>>, greater<>> pq;
dist[0][k][0] = 0.0;
pq.emplace(0.0, 0, k, 0);
double ans = INF;
while (!pq.empty()) {
auto [d, u, r, used] = pq.top(); pq.pop();
if (d > dist[u][r][used] + EPS) continue;
if (u == n - 1) {
ans = min(ans, d);
}
if (used == 0 && type[u] == 1 && r > 0) {
if (d < dist[u][r - 1][1] - EPS) {
dist[u][r - 1][1] = d;
pq.emplace(d, u, r - 1, 1);
}
}
for (auto [v, wgt] : graph[u]) {
double nd = d + (used == 0 ? (double)wgt : (double)wgt / 2.0);
if (nd < dist[v][r][0] - EPS) {
dist[v][r][0] = nd;
pq.emplace(nd, v, r, 0);
}
}
}
return (ans == INF ? -1.0 : ans);
}
