Bakery

Masha wants to open her own bakery and bake muffins in one of the n cities numbered from 1 to n. There are m bidirectional roads, each of whose connects some pair of cities.

To bake muffins in her bakery, Masha needs to establish flour supply from some storage. There are only k storages, located in different cities numbered a1, a2, …, ak.

Unforunately the law of the country Masha lives in prohibits opening bakery in any of the cities which has storage located in it. She can open it only in one of another n - k cities, and, of course, flour delivery should be paid — for every kilometer of path between storage and bakery Masha should pay 1 ruble.

Formally, Masha will pay x roubles, if she will open the bakery in some city b (ai ≠ b for every 1 ≤ i ≤ k) and choose a storage in some city s (s = aj for some 1 ≤ j ≤ k) and b and s are connected by some path of roads of summary length x (if there are more than one path, Masha is able to choose which of them should be used).

Masha is very thrifty and rational. She is interested in a city, where she can open her bakery (and choose one of k storages and one of the paths between city with bakery and city with storage) and pay minimum possible amount of rubles for flour delivery. Please help Masha find this amount.

Input
The first line of the input contains three integers n, m and k (1 ≤ n, m ≤ 105, 0 ≤ k ≤ n) — the number of cities in country Masha lives in, the number of roads between them and the number of flour storages respectively.

Then m lines follow. Each of them contains three integers u, v and l (1 ≤ u, v ≤ n, 1 ≤ l ≤ 109, u ≠ v) meaning that there is a road between cities u and v of length of l kilometers .

If k > 0, then the last line of the input contains k distinct integers a1, a2, …, ak (1 ≤ ai ≤ n) — the number of cities having flour storage located in. If k = 0 then this line is not presented in the input.

Output
Print the minimum possible amount of rubles Masha should pay for flour delivery in the only line.

If the bakery can not be opened (while satisfying conditions) in any of the n cities, print  - 1 in the only line.

Examples
input
5 4 2
1 2 5
1 2 3
2 3 4
1 4 10
1 5
output
3

input
3 1 1
1 2 3
3
output
-1

题意

在n个城市中，在k个城市中建造仓库的，在剩下的城市中建一个面包店， 仓库和面包店之间必须有一条路相连，求出满足条件的面包店和仓库的最小距离。

思路

把每个边存起来，如果某个边的起点和终点一个是仓库，一个不是，那这条边就可能的情况，在所有情况中找出距离最小的。

#include <map>
#include <set>
#include <queue>
#include <cmath>
#include <stack>
#include <cstdio>
#include <vector>
#include <utility>
#include <cstring>
#include <iostream>
#include <algorithm>
#define eps 1e-8
#define PI acos(-1)
#define INF 0x3f3f3f3f
#define N 100005
#define newmax(a,b) a>b?a:b
#define newmin(a,b) a>b?b:a
#define Lowbit(x) (x&-x)
using namespace std;
typedef long long int LL;
const int dir[4][2]= { {1,0},{0,1},{-1,0},{0,-1} };
struct EDGE
{
    int u,v,l;
}edge[N];
int main()
{
    int ha[N]={0};
    int a,n,m,k,ans=INF;
    scanf("%d%d%d",&n,&m,&k);
    for(int i=0;i<m;i++)
        scanf("%d%d%d",&edge[i].u,&edge[i].v,&edge[i].l);
    for(int i=0;i<k;i++)
    {
        scanf("%d",&a);
        ha[a]=1;
    }
    for(int i=0;i<m;i++)
        if(ha[edge[i].u]+ha[edge[i].v]==1)
            ans=min(edge[i].l,ans);
    if(ans==INF)
        printf("-1\n");
    else
        printf("%d\n",ans);
    return 0;
}