#include <vector>
#include <algorithm>
#include <map>
using namespace std;
long long const MAXN=1e5+10;
vector<pair<int,int>>nei[MAXN]={};
bool ex[MAXN]={};
bool vis1[MAXN]={};
map<pair<int,int>,long long>vis,value;
bool comp(pair<int,int>a,pair<int,int>b)
{
return (a.second<=b.second);
}
long long dfs(long long n,long long val)
{
if (ex[n])
return val;
vis1[n]=1;
vector<int>g;
long long mn1=1e15+10,mn2=1e15+10;
for (auto [i,w1]:nei[n])
{
if (!vis1[i])
{
long long z;
if (vis[{i,n}]==0)
{
z=dfs(i,val+w1);
value[{i,n}]=z-val;
vis[{i,n}]=1;
}
else
{
z=value[{i,n}]+val;
}
if (z<mn1)
{
mn2=mn1;
mn1=z;
}
else if (mn2>z)
mn2=z;
}
}
vis1[n]=0;
return mn2;
}
int travel_plan(int N, int M, int R[][2], int L[], int K, int P[])
{
for (int i=0;i<M;i++)
{
nei[R[i][0]].push_back({R[i][1],L[i]});
nei[R[i][1]].push_back({R[i][0],L[i]});
}
for (int i=0;i<K;i++)
ex[P[i]]=1;
for (int i=0;i<N;i++)
sort(begin(nei[i]),end(nei[i]),comp);
return dfs(0,0);
}
