#include <bits/stdc++.h>
using namespace std;
#define int long long
#define endl '\n'
const int N = 2e5 + 5;
int n, m, s, t, l, k, dists[N], distt[N], vis[N];
vector<pair<int, int>> adj[N];
signed main(){
cin >> n >> m >> s >> t >> l >> k;
for (int i = 1; i <= m; i++){
int u, v, w; cin >> u >> v >> w;
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> q;
q.push({0, s});
for (int i = 1; i < N; i++) dists[i] = 1e18;
dists[s] = 0;
while (q.size()){
auto [c, u] = q.top();
q.pop();
if (vis[u]) continue;
vis[u] = 1;
for (auto [v, w] : adj[u]){
if (dists[u] + w < dists[v]){
dists[v] = dists[u] + w;
q.push({dists[v], v});
}
}
}
for (int i = 1; i < N; i++) {vis[i] = 0;}
q.push({0, t});
for (int i = 1; i < N; i++) distt[i] = 1e18;
distt[t] = 0;
while (q.size()){
auto [c, u] = q.top();
q.pop();
if (vis[u]) continue;
vis[u] = 1;
for (auto [v, w] : adj[u]){
if (distt[u] + w < distt[v]){
distt[v] = distt[u] + w;
q.push({distt[v], v});
}
}
}
vector<int> bs;
for (int i = 1; i <= n; i++) bs.push_back(distt[i]);
sort(bs.begin(), bs.end());
if (dists[t] <= k){
cout << (n * (n - 1)) / 2 << endl;
return 0;
}
int ans = 0;
for (int i = 1; i <= n; i++){
int left = k - (dists[i] + l);
int le = -1, r = bs.size();
while (r - le > 1){
int mid = (r + le) / 2;
if (bs[mid] <= left) le = mid;
else r = mid;
}
ans += le + 1;
}
//
cout << ans << endl;
return 0;
}
