#include <bits/stdc++.h>
using namespace std;

struct edge {
	int t, n, w;
} e[500100];
int T, cnt = 0, hd[500100], k;
int lv[500100], d[500100];
int ans = 0x3f3f3f3f;

bool v[500100] = {0};

void add(int x, int y, int z) {
	e[++cnt].t = y;
	e[cnt].w = z;
	e[cnt].n = hd[x];
	hd[x] = cnt;
}

void spfa(int s) {
	queue<int>q;
	memset(d, 0x3f, sizeof(d));
	memset(v, 0, sizeof(v));
	v[s] = 1;
	q.push(s);
	d[s] = 0;
	while (!q.empty()) {
		int u = q.front();
		q.pop();
		v[u] = 0;
		for (int i = hd[u]; i; i = e[i].n) {
			int ver = e[i].t;
			if (d[ver] > d[u] + e[i].w) {
				d[ver] = d[u] + e[i].w;
				if (v[ver] == 0) {
					q.push(ver);
					v[ver] = 1;
				}
			}
		}
	}
	for (int i = 1; i <= k; i++) {
		if (s != lv[i])
			ans = min(ans, d[lv[i]]);
	}
}

int main() {
	freopen("WAW.in", "r", stdin);
	freopen("WAW.out", "w", stdout);
	cin >> T;
	while (T--) {
		int n, m;
		cin >> n >> m >> k;
		ans = 0x3f3f3f3f;
		cnt = 0;
		memset(hd, 0, sizeof(hd));
		for (int i = 1; i <= m; i++) {
			int x, y, z;
			cin >> x >> y >> z;
			add(x, y, z);
		}
		for (int i = 1; i <= k; i++) {
			int x;
			cin >> x;
			lv[i] = x;
		}
		for (int i = 1; i <= k; i++) {
			spfa(lv[i]);
		}
		cout << ans << endl;
	}
	return 0;
}