#include <bits/stdc++.h>
using namespace std;
using ll = long long;
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
int n, m;
cin >> n >> m;
int s, t, l;
ll k;
cin >> s >> t >> l >> k;
vector<vector<pair<int, int>>> adj(n + 1);
for (int i = 0; i < m; ++i) {
int a, b, w;
cin >> a >> b >> w;
adj[a].push_back({b, w});
adj[b].push_back({a, w});
}
auto dijikstra = [&](int st, vector<ll>& dist) -> void {
priority_queue<array<ll, 2>> pq;
pq.push({0, st});
dist[st] = 0;
while (pq.size()) {
ll d = -pq.top()[0];
int v = pq.top()[1];
pq.pop();
if (dist[v] != d) continue;
for (auto& [u, w] : adj[v]) {
if (dist[u] > dist[v] + w) {
dist[u] = dist[v] + w;
pq.push({-dist[u], u});
}
}
}
};
const ll INF = 1e18;
vector<ll> dist1(n + 1, INF), dist2(n + 1, INF);
dijikstra(s, dist1);
dijikstra(t, dist2);
ll res = 0;
if (dist1[t] <= k) {
cout << 1LL * n * (n - 1) / 2 << "\n";
return 0;
}
vector<array<ll, 2>> tot_dist1, tot_dist2;
for (int i = 1; i <= n; ++i) {
tot_dist2.push_back({dist2[i], i});
}
for (int i = 1; i <= n; ++i) {
tot_dist1.push_back({dist1[i], i});
}
sort(begin(tot_dist1), end(tot_dist1));
sort(begin(tot_dist2), end(tot_dist2));
int ptr = (int)tot_dist2.size() - 1;
vector<int> in(n + 1);
for (auto& [_, i] : tot_dist2) in[i] = 1;
for (int i = 0; i < (int)tot_dist1.size(); ++i) {
ll total = tot_dist1[i][0] + l;
while (ptr >= 0) {
ll now = min(total, dist1[tot_dist2[ptr][1]]) + tot_dist2[ptr][0];
if (now > k) {
in[tot_dist2[ptr][1]] = 0;
ptr -= 1;
} else {
break;
}
}
res += ptr + 1 - in[tot_dist1[i][1]];
}
cout << res << "\n";
}
