#include <bits/stdc++.h>
#define all(x) x.begin(), x.end()
#define ar array
using namespace std;
typedef long long ll;
const int N = 2e5 + 5;
const ll inf = 1e18;
vector <ar <int, 2>> g[N];
void go(int s, vector <ll> &dis) {
dis[s] = 0;
priority_queue <ar <ll, 2>> pq;
pq.push({0, s});
while (!pq.empty()) {
auto now = pq.top(); pq.pop();
int x = now[1];
ll ds = -now[0];
if (dis[x] < ds) continue;
for (auto u : g[x]) {
if (dis[u[0]] > dis[x] + u[1]) {
dis[u[0]] = dis[x] + u[1];
pq.push({-dis[u[0]], u[0]});
}
}
}
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
ll n, m, s, t, l, k;
cin >> n >> m >> s >> t >> l >> k;
for (int i = 1; i <= m; i++) {
int a, b, c;
cin >> a >> b >> c;
g[a].push_back({b, c});
g[b].push_back({a, c});
}
vector <ll> ds(n + 1, inf), dt(n + 1, inf), sv(n + 1);
go(s, ds);
go(t, dt);
if (ds[t] <= k)
return cout << n * (n - 1) / 2 << '\n', 0;
for (int i = 1; i <= n; i++)
sv[i] = dt[i];
dt[0] = 0;
sort(all(dt));
ll res = 0;
for (int i = 1; i <= n; i++) {
ll cur = ds[i] + l;
cur = k - cur;
if (cur < 0)
continue;
int j = upper_bound(all(dt), cur) - dt.begin() - 1;
res += j - (sv[i] <= cur);
}
cout << res << '\n';
}
