#include "bits/stdc++.h"
using namespace std;
#define vec vector
#define all(x) (x).begin(), (x).end()
double solve(int N, int M, int K, int H, vec<int> X, vec<int> Y, vec<int> C, vec<int> S) {
using pii = pair<int, int>;
map<pii, int> edges;
vec<vec<pii>> adj(N);
for (int i = 0; i < M; i++) {
int u = X[i], v = Y[i], cost = C[i];
adj[u].push_back({v, cost});
adj[v].push_back({u, cost});
edges[{u, v}] = cost;
edges[{v, u}] = cost;
}
vec<int> dist(N, INT_MAX);
dist[0] = 0;
priority_queue<pii, vec<pii>, greater<pii>> pq;
pq.push({0, 0});
while (!pq.empty()) {
auto [d, u] = pq.top();
pq.pop();
if (d > dist[u]) continue;
for (auto [v, cost] : adj[u]) {
if (dist[v] > d + cost) {
dist[v] = d + cost;
pq.push({dist[v], v});
}
}
}
if (dist[H] == INT_MAX) return -1;
if (N == 2) {
return dist[H];
}
// Subtask O1
if (N == 3) {
int other = (H == 1 ? 2 : 1);
double result = INT_MAX;
if (edges.count({0, H})) {
result = edges[{0, H}];
}
if (edges.count({0, other}) && edges.count({other, H})) {
if (S[other] == 0)
result = min(result, (double)edges[{other, H}]);
if (S[other] == 1)
result = min(result, (double)dist[H]);
if (S[other] == 2)
result = min(result, (double)edges[{0, other}] / 2.0 + edges[{other, H}]);
}
return result;
}
vec<int> backdist(N, INT_MAX);
backdist[H] = 0;
priority_queue<pii, vec<pii>, greater<pii>> backpq;
backpq.push({0, H});
while (!backpq.empty()) {
auto [d, u] = backpq.top();
backpq.pop();
if (d > backdist[u]) continue;
for (auto [v, cost] : adj[u]) {
if (backdist[v] > d + cost) {
backdist[v] = d + cost;
backpq.push({backdist[v], v});
}
}
}
if (backdist[0] == INT_MAX) return -1;
return backdist[H];
}
