#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<int, int>;
#define FOR(i, a, b) for (int i = a; i < (b); i++)
#define F0R(i, a) for (int i = 0; i < (a); i++)
#define F0R1(i, a) for (int i = 1; i <= (a); i++)
#define FORd(i, a, b) for (int i = (b)-1; i >= a; i--)
#define F0Rd(i, a) for (int i = (a)-1; i >= 0; i--)
#define F0Rd1(i, a) for (int i = a; i > 0; i--)
#define SORT(vec) sort(vec.begin(), vec.end())
#define S0RT(arr, n) sort(arr, arr + n)
#define pA first
#define pB second
#define MOD 1000000007
#define nl "\n"
#define pb push_back
int n, m, k;
vector<int> exits;
int pathInd = 0; // index each path to make sure we don't duplicate paths
class cmp {
public:
bool operator()(vector<int> a, vector<int> b) { return a[1] > b[1]; }
};
pair<pii, pii> dist[100000]; // 2 smallest distances to each node
vector<pii> adj[100000];
bool shortestVis[100000]; // whether the shortest path for each node has already been taken
void dijkstra() { // traceback
for (int i = 0; i < n; i++) {
dist[i] = {{1e18, -1}, {1e18, -1}};
shortestVis[i] = false;
}
priority_queue<vector<int>, vector<vector<int>>, cmp> nodes;
for (int root : exits) {
dist[root] = {{0, pathInd}, {0, -1}};
nodes.push({root, 0, pathInd++});
shortestVis[root] = true;
}
while (!nodes.empty()) {
int node = nodes.top()[0];
int minDist = nodes.top()[1];
int pathInd = nodes.top()[2];
nodes.pop();
if (!shortestVis[node]) {
shortestVis[node] = true;
continue;
} else if (pathInd != dist[node].pB.pB) {
continue;
}
for (pii i : adj[node]) {
int neighbor = i.pA;
int length = i.pB;
if (minDist + length < dist[neighbor].pA.pA) {
dist[neighbor].pB = dist[neighbor].pA;
dist[neighbor].pA = {minDist + length, pathInd};
nodes.push({neighbor, dist[neighbor].pA.pA, pathInd++});
} else if (minDist + length < dist[neighbor].pB.pA) {
dist[neighbor].pB = {minDist + length, pathInd};
nodes.push({neighbor, dist[neighbor].pB.pA, pathInd++});
}
}
}
}
int travel_plan(int n1, int m1, int (*r1) [2], int* L, int k1, int* P) {
n = n1;
m = m1;
k = k1;
for (int i = 0; i < m; i++) {
int a, b, c;
a = r1[i][0];
b = r1[i][1];
c = L[i];
adj[a].pb(pii(b, c));
adj[b].pb(pii(a, c));
}
FOR(i, 0, k) {
exits.pb(P[i]);
}
dijkstra();
return dist[0].pB.pA;
}
