#include<bits/stdc++.h>
using namespace std;
typedef unsigned long long ll;
const int MAXN = 2000 * 1000;
vector<pair<int, ll>> graf[MAXN + 1];
ll odl[MAXN + 1];
priority_queue<pair<ll, int>> pq;
vector<ll> v1;
vector<ll> v2;
int n;
void djikstra(int start) {
for (int i = 1; i <= n; i ++) {
odl[i] = LLONG_MAX/100;
}
odl[start] = 0;
pq.push({0, start});
while (pq.size() > 0) {
int v = pq.top().second;
ll dist = pq.top().first;
dist *= (-1);
pq.pop();
if (dist > odl[v]) {
continue;
}
for (auto u : graf[v]) {
if (odl[v] + u.second < odl[u.first]) {
odl[u.first] = odl[v] + u.second;
pq.push({-odl[u.first], u.first});
}
}
}
}
int main () {
ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
int m, s, t, a, b;
ll c, k, w;
cin >> n >> m >> s >> t >> c >> k;
for (int i = 0; i < m; i ++) {
cin >> a >> b >> w;
graf[a].push_back({b, w});
graf[b].push_back({a, w});
}
djikstra(s);
for (int i = 1; i <= n ; i ++) {
v1.push_back(odl[i]);
}
if (odl[t] <= k) {
cout << (ll(n) * ll(n - 1))/ 2 << "\n";
return 0;
}
djikstra(t);
for (int i = 1; i <= n ; i ++) {
v2.push_back(odl[i]);
}
sort(v1.begin(), v1.end());
sort(v2.begin(), v2.end());
int kon = n - 1;
ll wyn = 0;
for (int pocz = 0; pocz < n; pocz ++) {
while (kon >= 0 && (v2[kon] + v1[pocz] + c > k)) {
kon --;
}
wyn += ll(kon + 1);
}
cout << wyn << "\n";
return 0;
}
