#include "cyberland.h"
#include <iostream>
#include <vector>
#include <queue>
#include <array>
#define ll long long
#define ld long double
using namespace std;
vector <array<ll, 2>> adj[100000];
ll h;
bool visited[100000];
priority_queue<array<ld, 3>, vector<array<ld, 3>>, greater<array<ld, 3>>> pq;
ld dp[100000][61];
void dfs(ll u) {
visited[u] = 1;
for (auto [v, x] : adj[u]) {
if (v != h && !visited[v]) {
dfs(v);
}
}
}
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) {
K = min(K, 60), h = H;
for (int i=0; i<N; ++i) {
for (int j=0; j<=K; ++j) {
dp[i][j] = 1e18;
}
}
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]});
}
dfs(0);
for (int i=0; i<N; ++i) {
if (visited[i] && (!arr[i] || !i)) {
dp[i][K] = 0;
pq.push({0, (ld)i, (ld)K});
}
}
while (!pq.empty()) {
auto [w, du, dy] = pq.top();
pq.pop();
ll u = (ll)du, y = (ll)dy;
if (dp[u][y] != w || u == H) continue;
for (auto [v, x] : adj[u]) {
if (dp[v][y] > w+x) {
dp[v][y] = w+x;
pq.push({dp[v][y], (ld)v, (ld)y});
}
else if (y && arr[v] == 2 && dp[v][y-1] > (w+(ld)x)/2) {
dp[v][y-1] = (w+(ld)x)/2;
pq.push({dp[v][y-1], (ld)v, (ld)(y-1)});
}
}
}
ld f = 1e18;
for (int i=0; i<=K; ++i) {
f = min(f, dp[H][i]);
}
return f;
}
