#include <bits/stdc++.h>
using namespace std;
#define int long long
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define pb push_back
#define all(a) a.begin(), a.end()
#define endl "\n"
void printVector(vector<int> a){
for (auto x: a) cout << x << " ";
cout << endl;
}
vector<vector<pair<int, int>>> graph;
vector<int> dijkstra(int x, int n){
vector<int> dist(n+1, 1e16);
dist[0] = 1e17;
using T = pair<long long, int>;
priority_queue<T, vector<T>, greater<T>> pq;
dist[x] = 0;
pq.push({0, x});
while (!pq.empty()){
auto [cdist, node] = pq.top();
pq.pop();
if (cdist != dist[node]) continue;
for (auto [item, d]: graph[node]){
if (cdist+d < dist[item]){
pq.push({dist[item] = cdist+d, item});
}
}
}
return dist;
}
void solve(){
int n, m; cin >> n >> m;
int s, t, l, k; cin >> s >> t >> l >> k;
graph.resize(n+1);
FOR(i,0,m){
int a, b, c; cin >> a >> b >> c;
graph[a].pb({b, c});
graph[b].pb({a, c});
}
vector<int> from_s = dijkstra(s, n);
vector<int> from_t = dijkstra(t, n);
if (from_s[t] <= k){
cout << (n*(n-1))/2 << endl;
return;
}
sort(all(from_s));
sort(all(from_t));
int ans = 0;
FOR(i,0,n){
auto o = upper_bound(all(from_t), k-from_s[i]-l);
if (o == from_s.begin()) continue;
o--;
int ind = o-from_t.begin();
ans += ind+1;
}
cout << ans << endl;
}
int32_t main(){
ios::sync_with_stdio(false);cin.tie(nullptr);
int t = 1; // cin >> t;
while (t--) solve();
}
