#include <bits/stdc++.h>
using namespace std;
#define int long long
#define pb push_back
#define mp make_pair
#define pii pair<int, int>
#define fi first
#define se second
const int maxn = 2e5;
const int inf = 1e16 + 42;
int n, m;
int start, goal;
int len, total;
vector<pii > graph[1 + maxn];
vector<int> dijkstra(int source) {
vector<bool> done(1 + n, false);
vector<int> dist(1 + n, inf);
priority_queue<pii > q;
dist[source] = 0;
q.push(mp(0, source));
while(!q.empty()) {
int cur = q.top().se;
int cur_dist = -q.top().fi;
q.pop();
if(done[cur]) {
continue;
}
done[cur] = true;
for(pii nei : graph[cur]) {
if(dist[nei.fi] > dist[cur] + nei.se) {
dist[nei.fi] = dist[cur] + nei.se;
q.push(mp(-dist[nei.fi], nei.fi));
}
}
}
return dist;
}
void solve() {
cin >> n >> m;
cin >> start >> goal >> len >> total;
for(int i = 1; i <= m; i++) {
int a, b, c;
cin >> a >> b >> c;
graph[a].pb(mp(b, c));
graph[b].pb(mp(a, c));
}
vector<int> U = dijkstra(start), V = dijkstra(goal);
if(U[goal] <= total) {
cout << n * (n - 1) / 2 << "\n";
return;
}
sort(U.begin() + 1, U.end());
priority_queue<int> q;
for(int i = 1; i <= n; i++) {
q.push(V[i]);
}
int ans = 0;
for(int i = 1; i <= n; i++) {
while(!q.empty() && U[i] + q.top() > total - len) {
q.pop();
}
ans += q.size();
}
cout << ans << "\n";
}
signed main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
// int T = 1; cin >> T; while(T--)
solve();
}
