#include<bits/stdc++.h>
#define s second
#define f first
#define plli pair<long long, int>
#define pill pair<int, long long>
using namespace std;
using ll = long long;
int n, m, s, t;
ll l, k;
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
cin >> n >> m >> s >> t >> l >> k;
s--, t--;
vector<plli> adj[n];
for(int i = 0; i < m; i++) {
int a, b;
ll c;
cin >> a >> b >> c;
a--, b--;
adj[a].push_back({b, c});
adj[b].push_back({a, c});
}
priority_queue<plli, vector<plli>, greater<plli>> pq;
vector<ll> dis(n, 1e18);
dis[s] = 0;
pq.push({0, s});
while(!pq.empty()) {
ll dist = pq.top().f;
int a = pq.top().s;
pq.pop();
if(dist != dis[a]) continue;
for(plli p : adj[a]) {
ll c = p.s;
int b = p.f;
if(dist + c < dis[b]) {
dis[b] = dist + c;
pq.push({dis[b], b});
}
}
}
if(dis[t] <= k) {
cout << 1LL * n * (n - 1) / 2 << '\n';
return 0;
}
vector<ll> dis1(n, 1e18);
dis1[t] = 0;
pq.push({0, t});
while(!pq.empty()) {
ll dist = pq.top().f;
int a = pq.top().s;
pq.pop();
if(dist != dis1[a]) continue;
for(plli p : adj[a]) {
ll c = p.s;
int b = p.f;
if(dist + c < dis1[b]) {
dis1[b] = dist + c;
pq.push({dis1[b], b});
}
}
}
sort(dis1.begin(), dis1.end());
ll ans = 0;
for(int i = 0; i < n; i++) {
ans += max(0ll, ll(upper_bound(dis1.begin(), dis1.end(), k - l - dis[i]) - dis1.begin()));
}
cout << ans << '\n';
return 0;
}
