#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int N = 2e5+10;
vector<pair<int, ll>> adj[N];
ll dist1[N], dist2[N];
void dijkstra(int st, ll *dist){
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> pq;
pq.push({dist[st] = 0, st});
while(!pq.empty()){
auto [d, u] = pq.top(); pq.pop();
if(dist[u] < d) continue;
for(auto [v, w] : adj[u]){
if(dist[v] > d+w){
pq.push({dist[v] = d+w, v});
}
}
}
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int n, m, st, en, l, k;
cin >> n >> m >> st >> en >> l >> k;
while(m--){
int u, v, w;
cin >> u >> v >> w;
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
memset(dist1, 0x3f, sizeof dist1);
memset(dist2, 0x3f, sizeof dist2);
dijkstra(st, dist1);
dijkstra(en, dist2);
vector<ll> v;
for(int i = 1; i <= n; ++i) v.push_back(dist2[i]);
sort(v.begin(), v.end());
//(st -> u) + l + (v -> en) <= k
//(v -> en) <= k - l - (st -> u)
ll res = 0;
for(int i = 1; i <= n; ++i){
// cerr << "dbg : " << dist1[i] << '\n';
// cerr << "dbg : " << upper_bound(v.begin(), v.end(), k - l - dist1[i]) - v.begin() << '\n';
res += upper_bound(v.begin(), v.end(), k - l - dist1[i]) - v.begin();
if(dist2[i] <= k - l - dist1[i]) res--;
}
cout << res << '\n';
}
