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

#define rep(i, a, b) for(int i = a; i < (b); ++i)
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;

const double inf = 1e10;
const double DIST_INF = 1e14;

pair<double, vi> hungarian(const vector<vector<double>> &a) {
	if (a.empty()) return {0, {}};
	int n = sz(a) + 1, m = sz(a[0]) + 1;
	vector<double> u(n), v(m);
	vi p(m), ans(n - 1);
	rep(i,1,n) {
		p[0] = i;
		int j0 = 0; // add "dummy" worker 0
		vector<double> dist(m, DIST_INF);
		vi pre(m, -1);
		vector<bool> done(m + 1);
		do { // dijkstra
			done[j0] = true;
			int i0 = p[j0], j1 = -1;
			double delta = DIST_INF;
			rep(j,1,m) if (!done[j]) {
				double cur = a[i0 - 1][j - 1] - u[i0] - v[j];
				if (cur < dist[j]) dist[j] = cur, pre[j] = j0;
				if (dist[j] < delta) delta = dist[j], j1 = j;
			}
			rep(j,0,m) {
				if (done[j]) u[p[j]] += delta, v[j] -= delta;
				else dist[j] -= delta;
			}
			j0 = j1;
		} while (p[j0]);
		while (j0) { // update alternating path
			int j1 = pre[j0];
			p[j0] = p[j1], j0 = j1;
		}
	}
	rep(j,1,m) if (p[j]) ans[p[j] - 1] = j - 1;
	return {-v[0], ans}; // min cost
}

int main() {
	cin.tie(0)->sync_with_stdio(0);
	cin.exceptions(cin.failbit);

	ll n, s, t, q;
	cin >> n >> s >> t >> q;
	q *= q;

	vector<vector<double>> cost(t, vector<double>(s, inf));
	vector<pii> pos;
	vi height;
	rep(i, 0, n) {
		int x, y, h;
		cin >> x >> y >> h;
		pos.emplace_back(x, y);
		height.push_back(h);
	}
	vi istown(n);
	vi is_spring(n);
	vi spring_ind(n);
	int ind = 0;
	rep(i, 0, s) {
		int spr_ind;
		cin >> spr_ind;
		spr_ind--;
		is_spring[spr_ind] = 1;
		spring_ind[spr_ind] = ind++;
	}
	rep(i, 0, t) {
		int town_ind;
		cin >> town_ind;
		town_ind--;
		istown[town_ind] = 1;
	}

	ind = 0;
	rep(i, 0, n) {
		if (istown[i]) {
			priority_queue<pair<double, int>> pq;
			vi vis(n);
			pq.emplace(0, i);
			while (pq.size()) {
				double d;
				int u;
				tie(d, u) = pq.top();
				pq.pop();

				if (vis[u]) continue;
				vis[u] = 1;
				if (is_spring[u]) cost[ind][spring_ind[u]] = -d;

				rep(j, 0, n) {
					if (height[u] >= height[j]) continue;
					double dist = pow(pos[u].first - pos[j].first, 2) + pow(pos[u].second - pos[j].second, 2) + pow(height[u] - height[j], 2);
					if (dist > q) continue;
					pq.emplace(d - sqrt(dist), j);
				}
			}
			ind++;
		}
	}

	double c = hungarian(cost).first;
	if (c >= inf) cout << "IMPOSSIBLE";
	else cout << fixed << setprecision(15) << c;
}