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

vector<pair<int, ll>> g[200005];
const ll inf = 1e18;

vector<ll> dijkstra (int n, int s) {
	vector<ll> dist (n+1, inf);
	priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<>> pq;
	dist[s] = 0;
	pq.push({0, s});
	while (!pq.empty()) {
		auto [d, u] = pq.top();
		pq.pop();
		if (dist[u] != d) continue;
		for (auto& [v, w] : g[u]) if (d+w < dist[v]) {
			dist[v] = d+w;
			pq.push({d+w, v});
		}
	}
	return dist;
}

int main () {
	ios::sync_with_stdio(false);
	cin.tie(0);
	int n, m, s, t;
	ll l, k;
	cin >> n >> m >> s >> t >> l >> k;
	while (m--) {
		int a, b, c;
		cin >> a >> b >> c;
		g[a].push_back({b, c});
		g[b].push_back({a, c});
	}
	vector<ll> d1 = dijkstra(n, s);
	if (d1[t] <= k) {
		cout << ll(n)*(n-1)/2 << '\n';
		return 0;
	}
	vector<ll> dn = dijkstra(n, t);
	sort(d1.begin(), d1.end());
	sort(dn.begin(), dn.end());
	d1.pop_back();
	dn.pop_back();
	ll ans = 0;
	for (int i = 0, j = n-1; i < n && j >= 0; i++) {
		while (j >= 0 && d1[i]+dn[j]+l > k) j--;
		ans += j+1;
	}
	cout << ans << '\n';
	return 0;
}