#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define int ll
using P = pair<int, int>;
#define all(x) x.begin(), x.end()
#define rep(i, l, n) for (int i = l; i < (n); ++i)
#define sz(x) (int)x.size()
const char nl = '\n';
const int mod = 998244353;
const int NMAX = 2e5+10;
const int inf = NMAX*1e9;
vector<P> g[NMAX];
int n, m, s, t, l, k;
vector<int> djk(int src) {
vector<int> d(n+1, inf); d[src] = 0;
priority_queue<P, vector<P>, greater<P>> pq;
pq.push(P(0, src));
while (!pq.empty()) {
auto [dist, nd] = pq.top(); pq.pop();
if (d[nd] != dist)continue;
for (auto [ch, w]: g[nd])
if (dist+w < d[ch])
d[ch] = dist+w,
pq.push(P(dist+w, ch));
}
return d;
}
void solve() {
cin >> n >> m >> s;
cin >> t >> l >> k;
rep(i, 0, m) {
int a, b, c; cin >> a >> b >> c;
g[a].push_back(P(b, c));
g[b].push_back(P(a, c));
}
vector<int> ds = djk(s);
vector<int> dt = djk(t);
int res = 0;
rep(v, 2, n+1) {
rep(u, 1, v)
if (ds[u]+l+dt[v] <= k || dt[u]+l+ds[v] <= k || ds[t] <= k)res += 1;
}
cout << res;
}
int32_t main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
solve();
return 0;
}
