#include<bits/stdc++.h>
#define int long long
#define fi first
#define se second
#define pb push_back
#define ii pair<int, int>
#define sz(v) (int)v.size()
#define all(v) v.begin(), v.end()
using namespace std;
const int N=1e5+5, mod = 1e9+7, inf = 1e18;
int n, m;
int s, t, l, k;
vector<ii> adj[N];
int d1[N], d2[N];
signed main() {
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
cin >> n >> m >> s >> t >> l >> k;
for (int i=1; i<=m; i++) {
int u, v, w; cin >> u >> v >> w;
adj[u].pb({v, w});
adj[v].pb({u, w});
}
for (int i=1; i<=n; i++) d1[i] = d2[i] = inf;
priority_queue<ii, vector<ii>, greater<ii>> pq;
d1[s] = 0;
pq.push({0, s});
while(!pq.empty()) {
auto [d, u] = pq.top(); pq.pop();
for (auto [v, w]: adj[u]) {
if(d1[v]>d1[u]+w) {
d1[v] = d1[u]+w;
pq.push({d1[v], v});
}
}
}
if(d1[t]<=k) {
cout << n*(n-1)/2;
return 0;
}
sort(d1+1, d1+n+1, greater<int>());
int ans = 0;
d2[t] = 0;
pq.push({0, t});
int idx = 1;
while(!pq.empty()) {
auto [d, u] = pq.top(); pq.pop();
while(idx<=n && d1[idx]+l+d>k) idx++;
ans += n-idx+1;
for (auto [v, w]: adj[u]) {
if(d2[v]>d2[u]+w) {
d2[v] = d2[u]+w;
pq.push({d2[v], v});
}
}
}
cout << ans;
}
