#include <bits/stdc++.h>
#define fast cin.tie(0)->sync_with_stdio(0);
#define int long long
#define inf ((int)1e18)
using namespace std;
int32_t main() {
fast
int n, m;
cin >> n >> m;
int s, t, l, k;
cin >> s >> t >> l >> k;
s--, t--;
vector <vector<pair<int, int> > > adj(n);
for(int i = 0; i < m; i++) {
int a, b, w;
cin >> a >> b >> w;
a--, b--;
adj[a].push_back({b, w});
adj[b].push_back({a, w});
}
auto dij = [&](int st) {
vector <int> dist(n, inf);
vector <bool> vis(n);
priority_queue <pair<int, int> > pq;
pq.push({0, st});
dist[st] = 0;
while(!pq.empty()) {
auto [d, node] = pq.top();
d = -d;
pq.pop();
if(vis[node]) continue;
vis[node] = 1;
for(auto [to, w]:adj[node]) {
if(d + w < dist[to]) {
dist[to] = d + w;
pq.push({-(d + w), to});
}
}
}
return dist;
};
vector <int> from = dij(s), to = dij(t);
// for(auto it:from) {
// cout << it << ' ';
// }
// cout << '\n';
// for(auto it:to) {
// cout << it << ' ';
// }
// cout << '\n';
if(from[t] <= k) {
cout << n * (n - 1) / 2 << '\n';
return 0;
}
int ans = 0;
sort(from.begin(), from.end());
sort(to.begin(), to.end());
k -= l;
for(int i = 0; i < n; i++) {
int v = k - from[i];
ans += upper_bound(to.begin(), to.end(), v) - to.begin();
}
cout << ans << '\n';
}
