#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;

template <typename T> pair<T, vector<int>>
weighted_matching(vector<vector<T>> &C) {
    int i = sz(C), m = sz(C[0]), c, j, s, r;
    vector<T> dist(m), potential(m);
    vi row_match(i), col_match(m, -1), cols(m), prev(m);
    T d, nd, cost = 0;
    for (; i--;) {
        rep(c, 0, m) dist[c] = C[i][c], cols[c] = c, prev[c] = i;
        for (s = 0;;) {
            for (j = s; j < m; j++) if (c = cols[j],
                nd = dist[c] - potential[c], j == s || d > nd)
                d = nd, swap(cols[s], cols[j]);
            if (!~(r = col_match[c = cols[s++]])) break;
            rep(j, 0, m) if (dist[j] > (nd = C[r][j] - C[r][c] +
                dist[c])) dist[j] = nd, prev[j] = r;
        }
        for (cost += dist[c]; s--;) j = cols[s],
            potential[j] = dist[j] - d;
        for (; r != i; swap(c, row_match[r]))
            r = col_match[c] = prev[c];
    }
    return {cost, row_match};
}

const double inf = 1e10;
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++;
		}
	}

	auto [c, _] = weighted_matching(cost);
	if (c >= inf) cout << "IMPOSSIBLE";
	else cout << fixed << setprecision(15) << c;
}