#pragma GCC opmize("Ofast", unroll-loops)
#pragma GCC target("arch=skylake")
#include <bits/stdc++.h>
using namespace std;
#define name "TENBAI"
#define fi first
#define se second
#define endl '\n'
#define setmin(x, y) x = min((x), (y))
#define setmax(x, y) x = max((x), (y))
#define sqr(x) ((x) * (x))
#define all(x) x.begin(), x.end()
mt19937 hdp(chrono::high_resolution_clock::now().time_since_epoch().count());
int rand(int l, int r){return l + ((hdp() % (r - l + 1)) + r - l + 1) % (r - l + 1);}
const double inf = 1 / .0;
const int NM = 1e5 + 5;
double dist[NM][71];
double solve(int N, int M, int K, int H, vector<int> x, vector<int> y, vector<int> c, vector<int> a)
{
setmin(K, 70);
fill(dist[0], dist[0] + N * 71, inf);
vector<vector<pair<int, int>>> g(N);
for (int i = 0; i < M; i++)
g[x[i]].push_back({y[i], c[i]}), g[y[i]].push_back({x[i], c[i]});
vector<int> st(1, 0);
vector<bool> vis(N, 0);
priority_queue<tuple<int, double, int>, vector<tuple<int, double, int>>, greater<>> pq;
while (st.size())
{
int u = st.back();
st.pop_back();
if (u == H)
continue;
vis[u] = 1;
if (!a[u] || !u)
{
for (int i = 0; i <= K; i++)
dist[u][i] = 0;
pq.push({0, 0, u});
}
for (auto v : g[u])
if (!vis[v.fi])
{
st.push_back(v.fi);
vis[v.fi] = 1;
}
}
while (pq.size())
{
auto u = get<2>(pq.top()), t = get<0>(pq.top());
double d = get<1>(pq.top());
pq.pop();
if (dist[u][t] != d || u == H)
continue;
for (pair<int, int> v : g[u])
{
if (dist[v.fi][t] > d + v.se)
{
dist[v.fi][t] = d + v.se;
pq.push({t, dist[v.fi][t], v.fi});
}
if (a[v.fi] == 2 && t + 1 <= K && dist[v.fi][t + 1] > (d + v.se) / 2.0)
{
dist[v.fi][t + 1] = (d + v.se) / 2.0;
pq.push({t + 1, dist[v.fi][t + 1], v.fi});
}
}
}
double res = inf;
for (int i = 0; i <= K; i++)
setmin(res, dist[H][i]);
if (res == inf)
res = -1;
return res;
}
