#include <bits/stdc++.h>
#define int long long
#define fi first
#define se second
#define pii pair<int, int>
#define all(a) a.begin(), a.end()
using namespace std;
#ifdef LOCAL
#include "C:\Users\Dell\Downloads\template\template\icpc-notebook\Utilities\debug.h"
#else
#define debug(...) 42
#endif
const int mn = 5e5 + 5, mod = 1e9 + 7, inf = 2e18;
int n, m, s, t, l, k, d[2][mn];
vector <pii> a[mn];
map <pii, int> mp;
void dijkstra(int st, int kc[]){
fill(kc, kc + mn, inf);
priority_queue <pii, vector <pii>, greater<pii>> pq;
kc[st] = 0; pq.push({kc[st], st});
while(pq.size()){
auto [c, u] = pq.top(); pq.pop();
if(c > kc[u]) continue;
for(auto [v, w] : a[u]){
if(kc[v] > kc[u] + w){
kc[v] = kc[u] + w;
pq.push({kc[v], v});
}
}
}
}
void solve() {
cin >> n >> m >> s >> t >> l >> k;
for(int i = 1; i <= m; i++){
int u, v, c; cin >> u >> v >> c;
a[u].push_back({v, c});
a[v].push_back({u, c});
}
dijkstra(s, d[0]); dijkstra(t, d[1]);
if(d[0][t] <= k){
cout << n * (n - 1) / 2 << '\n';
return;
}
vector <int> val;
for(int i = 1; i <= n; i++) val.push_back(d[1][i]);
sort(all(val));
int res = 0;
for(int i = 1; i <= n; i++){
int kc = k - d[0][i] - l;
debug(kc, *upper_bound(all(val), kc));
res += upper_bound(all(val), kc) - val.begin();
}
cout << res << '\n';
}
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(nullptr); cout.tie(nullptr);
#define task "Kawabata"
if (fopen(task".INP", "r")) {
freopen(task".INP", "r", stdin);
freopen(task".OUT", "w", stdout);
}
int t = 1;
// cin >> t;
while (t--) solve();
return 0;
}
// Don't wanna lose anymore T_T
// Never let me go - Kazuo Ishiguro
