#include <bits/stdc++.h>
using namespace std;
#define int long long
const int maxn = 2e5 + 5;
vector<pair<int, int>> g[maxn];
vector<int> dijkstra(int source, int n){
vector<int> dist(n + 1, 1e18);
dist[source] = 0;
priority_queue<array<int, 2>, vector<array<int, 2>>, greater<array<int, 2>>> pq;
pq.push({0, source});
while(pq.size()){
auto [d, u] = pq.top();
pq.pop();
if(d > dist[u]) continue;
for(auto [v, w]: g[u]){
if(dist[v] > d + w){
dist[v] = d + w;
pq.push({dist[v], v});
}
}
}
return dist;
}
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
int n, m, s, t, l, k; cin >> n >> m >> s >> t >> l >> k;
for(int i = 1; i <= m; i++){
int u, v, w; cin >> u >> v >> w;
g[u].push_back({v, w});
g[v].push_back({u, w});
}
vector<int> dists = dijkstra(s, n);
vector<int> distt = dijkstra(t, n);
if(dists[t] <= k) cout << n * (n - 1) / 2;
else{
sort(dists.begin() + 1, dists.end());
int ans = 0;
for(int i = 1; i <= n; i++){
int c = k - (distt[i] + l);
ans += upper_bound(dists.begin() + 1, dists.end(), c) - dists.begin() - 1;
}
cout << ans;
}
}
