#include <bits/stdc++.h>
using namespace std;
#define int long long
int n, m, s, t, l, k;
vector<pair<int, int>> g[200005];
int ds[200005], dt[200005];
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
vector<int> d, e;
int32_t main() {
ios::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
cin >> n >> m >> s >> t >> l >> k;
for (int i = 0; i < m; i++) {
int u, v, w; cin >> u >> v >> w;
g[u].emplace_back(v, w);
g[v].emplace_back(u, w);
}
fill(ds, ds + n + 1, 1e18);
fill(dt, dt + n + 1, 1e18);
ds[s] = 0;
pq.emplace(0, s);
while (!pq.empty()) {
auto c = pq.top(); pq.pop();
if (ds[c.second] != c.first) continue;
for (auto u : g[c.second]) {
if (ds[u.first] > c.first + u.second) {
ds[u.first] = c.first + u.second;
pq.emplace(ds[u.first], u.first);
}
}
}
dt[t] = 0;
pq.emplace(0, t);
while (!pq.empty()) {
auto c = pq.top(); pq.pop();
if (dt[c.second] != c.first) continue;
for (auto u : g[c.second]) {
if (dt[u.first] > c.first + u.second) {
dt[u.first] = c.first + u.second;
pq.emplace(dt[u.first], u.first);
}
}
}
if (ds[t] <= k) { cout << (n * (n - 1)) / 2; return 0;}
int ans = 0;
for (int i = 1; i <= n; i++) d.push_back(dt[i]);
for (int i = 1; i <= n; i++) e.push_back(ds[i]);
sort(d.begin(), d.end());
sort(e.begin(), e.end());
for (int i = 1; i <= n; i++) {
int c = k - l - ds[i];
int it = upper_bound(d.begin(), d.end(), c) - d.begin();
ans += it;
int it2 = upper_bound(e.begin(), e.end(), k - l - dt[i]) - e.begin();
ans += it2;
}
cout << ans / 2;
}
