#include <bits/stdc++.h>
#include <experimental/random>
#include <random>
//#include <ext/pb_ds/assoc_container.hpp>
//using namespace __gnu_pbds;
using namespace std;
using ld = long double;
using ll = long long;
const ll INF = 1e18, MOD = 1e9 + 7;
void solve();
signed main() {
#ifdef LOCAL
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
#endif
ios::sync_with_stdio(false);
cin.tie(0);
int q = 1;
//cin >> q;
while (q--) {
solve();
}
}
void solve() {
ll n, m;
cin >> n >> m;
ll s, t, l, k;
cin >> s >> t >> l >> k;
s--, t--;
vector<vector<pair<ll, ll>>> g(n);
for (int i = 0; i < m; i++) {
ll a, b, c; cin >> a >> b >> c; a--, b--;
g[a].emplace_back(b, c);
g[b].emplace_back(a, c);
}
vector<ll> d1(n, INF);
d1[s] = 0;
set<pair<ll, ll>> dj;
dj.insert({0, s});
while (!dj.empty()) {
ll v = dj.begin()->second; dj.erase(dj.begin());
for (auto [u, d] : g[v]) {
if (d1[u] > d1[v] + d) {
dj.erase({d1[u], u});
d1[u] = d1[v] + d;
dj.insert({d1[u], u});
}
}
}
if (d1[t] <= k) {
cout << n * (n - 1) / 2;
return;
}
vector<ll> d2(n, INF);
d2[t] = 0;
dj.insert({0, t});
while (!dj.empty()) {
ll v = dj.begin()->second; dj.erase(dj.begin());
for (auto [u, d] : g[v]) {
if (d2[u] > d2[v] + d) {
dj.erase({d2[u], u});
d2[u] = d2[v] + d;
dj.insert({d2[u], u});
}
}
}
sort(d2.begin(), d2.end());
ll ans = 0;
for (auto c : d1) {
ans += upper_bound(d2.begin(), d2.end(), k - l - c) - d2.begin();
}
cout << ans;
}
