#include <bits/stdc++.h>
#define int long long
using namespace std;
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
int32_t main() {
ios_base::sync_with_stdio(false);
cout.tie(0); cin.tie(0);
int n, m, s, t, L, k, ans = 0;
cin >> n >> m >> s >> t >> L >> k;
vector<pii> graph[n+1];
for(int i=0; i<m; i++) {
int a, b, w;
cin >> a >> b >> w;
graph[a].push_back({ b, w });
graph[b].push_back({ a, w });
}
auto dijkstra = [&](int start) {
vector<bool> vis(n+1);
vector<ll> dist(n+1, 1e18);
priority_queue<pll, vector<pll>, greater<pll> > pq;
dist[start] = 0;
pq.push({ 0, start });
while(!pq.empty()) {
int u = pq.top().second; pq.pop();
if(vis[u]) continue;
vis[u] = 1;
for(auto &[v, w] : graph[u]) {
if(dist[v] > dist[u] + w) {
dist[v] = dist[u] + w;
pq.push({ dist[v], v });
}
}
}
return dist;
};
vector<ll> D1 = dijkstra(s);
vector<ll> D2 = dijkstra(t);
if(D1[t] <= k) {
cout << 1ll * n * (n - 1) / 2 << '\n';
return 0;
}
vector<pll> D;
for(int i=1; i<=n; i++) D.push_back({ D2[i], D1[i] });
sort(D.begin(), D.end());
for(int i=1; i<n; i++) {
int l=0, r=i-1, p=-1;
while(l <= r) {
int mid = (l + r) / 2;
if(D[i].second + L + D[mid].first <= k) p = mid, l = mid + 1;
else r = mid - 1;
}
ans += p + 1;
}
cout << ans << '\n';
return 0;
}
