#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define st first
#define nd second
#define pb push_back
#define all(a) a.begin(), a.end()
#define sz(a) int(a.size())
#define f(i, a, b) for (int i = a; i < b; i++)
#define rep(i, a) f(i, 0, a)
#define int ll
#define tv(a, x) for (auto& a : x)
#define DUZO 1000000000000000000LL
using pii = pair<int, int>;
using vi = vector<int>;
using vvi = vector<vi>;
int n;
vvi dist;
vector<vector<pii>> g;
void dijkstra(int s) {
dist[s].resize(n + 1, DUZO);
priority_queue<pii> pq;
pq.push({0, s});
while (!pq.empty()) {
int d = -pq.top().st;
int u = pq.top().nd;
pq.pop();
if (dist[s][u] != DUZO) continue;
dist[s][u] = d;
tv(e, g[u]) {
int v = e.st;
int w = e.nd;
if (dist[s][v] == DUZO) {
pq.push({-(d + w), v});
}
}
}
}
void solve() {
int m, s, t, l, k;
cin >> n >> m >> s >> t >> l >> k;
g.resize(n + 1);
rep(i, m) {
int a, b, c;
cin >> a >> b >> c;
g[a].pb({b, c});
g[b].pb({a, c});
}
dist.resize(n + 1);
dijkstra(s);
dijkstra(t);
if (dist[s][t] <= k) {
cout << (n * (n - 1)) / 2 << "\n";
return;
}
vi a;
f(i, 1, n + 1) a.pb(dist[s][i]);
sort(all(a));
vi b;
f(i, 1, n + 1) b.pb(dist[t][i]);
b.pb(-DUZO);
sort(all(b));
int ans = 0;
int j = sz(b) - 1;
tv(x, a) {
while (j > 0 && x + b[j] + l > k) j--;
ans += j;
}
cout << ans << "\n";
}
int32_t main() {
ios::sync_with_stdio(0);
cin.tie(0);
int q = 1;
//cin >> q;
while (q--) {
solve();
}
return 0;
}
