#include <iostream>
#include <vector>
#include <queue>
#include "crocodile.h"
using namespace std;
vector <vector <pair <int, int>>> g(1e5);
vector <int> o1(1e5, 2e9);
vector <int> o2(1e5, 2e9);
vector <bool> done(1e5, false);
priority_queue <pair <int, int>> pq;
bool update(int i, int val) {
if (val < o1[i]) { o2[i] = o1[i]; o1[i] = val; return true; }
if (val < o2[i]) { o2[i] = val; return true; }
return false;
}
int travel_plan(int N, int M, int R[][2], int L[], int K, int P[]) {
int a, b, w;
for (int i = 0; i < M; i++) {
a = R[i][0]; b = R[i][1]; w = L[i];
g[a].push_back({ b,w });
g[b].push_back({ a,w });
}
for (int i = 0; i < K; i++) {
o1[P[i]] = o2[P[i]] = 0;
pq.push({ 0,P[i] });
}
while (!done[0]) {
a = pq.top().second; pq.pop();
if (done[a]) continue;
done[a] = true;
for (auto p : g[a]) {
b = p.first; w = p.second;
if (update(b, o2[a] + w)) pq.push({ -o2[b], b });
}
}
return o2[0];
}
