#include <bits/stdc++.h>
#pragma GCC optimize("Ofast,O3,unroll-loops")
#pragma GCC target("avx2")
#define all(v) ((v).begin(), (v).end())
#define F first
#define S second
typedef long long ll;
#define pii pair<ll, double>
using namespace std;
const ll mod = 1e9 + 7;
const ll mxN = 1e6 + 5;
struct path
{
ll i, k;
double val;
};
bool operator<(path a, path b)
{
return a.val < b.val;
}
bool operator>(path a, path b)
{
return a.val > b.val;
}
double solve(int N, int M, int K, int H, vector<int> x, vector<int> y, vector<int> c, vector<int> arr)
{
vector<vector<double>>dp;
vector<int>vis;
vector<vector<pii>> v;
dp.resize(N + 3);
vis.resize(N + 3);
v.resize(N + 3);
K = min(K,70);
for (int i = 0; i < M; i++)
{
v[x[i]].push_back({y[i], (double)c[i]});
v[y[i]].push_back({x[i], (double)c[i]});
}
for(int i = 0;i < N;i++){
dp[i].resize(K + 3);
for(int j = 0;j <= K;j++){
dp[i][j] = 1e18;
}
}
priority_queue<path,vector<path>,greater<path>>q;
q.push({0,0,0});
dp[0][0] = 0;
while(q.size()){
auto u = q.top();
q.pop();
if(u.val < dp[u.i][u.k] || u.i == H) continue;
for(auto x : v[u.i]){
if (arr[x.F] == 0 && dp[x.F][u.k] != (double)0)
{
dp[x.F][u.k] = (double)0;
q.push({x.F, u.k, (double)0});
}
if(dp[x.F][u.k] > dp[u.i][u.k] + x.S){
dp[x.F][u.k] = dp[u.i][u.k] + x.S;
q.push({x.F,u.k,dp[x.F][u.k]});
}
if(u.k != K && arr[u.i] == 2 && dp[x.F][u.k + 1] > dp[u.i][u.k] / 2 + x.S){
dp[x.F][u.k + 1] = dp[u.i][u.k] / 2 + x.S;
q.push({x.F,u.k + 1,dp[x.F][u.k + 1]});
}
}
}
double ans = 1e18;
for(int i = 0;i <= K;i++){
ans = min(ans,dp[H][i]);
}
return ans == 1e18 ? -1 : ans;
}
// int main()
// {
// int T;
// assert(1 == scanf("%d", &T));
// while (T--)
// {
// int N, M, K, H;
// assert(4 == scanf("%d %d %d\n%d", &N, &M, &K, &H));
// vector<int> x(M);
// vector<int> y(M);
// vector<int> c(M);
// vector<int> arr(N);
// for (int i = 0; i < N; i++)
// assert(1 == scanf("%d", &arr[i]));
// for (int i = 0; i < M; i++)
// assert(3 == scanf("%d %d %d", &x[i], &y[i], &c[i]));
// printf("%.12lf\n", solve(N, M, K, H, x, y, c, arr));
// }
// }
