#include <iostream>
#include <bits/stdc++.h>
#define ll long long
using namespace std;
const ll maxn = 2*1e5+5, INF = 4e18+9;
vector<ll> dijkstra(int n, int s, vector<vector<pair<ll, ll>>> &adj){
vector<ll> dist(n+1, INF);
dist[s] = 0;
vector<bool> vis(n+1, false);
priority_queue<pair<ll, ll>, vector<pair<ll, ll>>, greater<pair<ll, ll>>> pq;
pq.push({0, s});
while(!pq.empty()){
ll d_u = pq.top().first;
int u = pq.top().second;
pq.pop();
if(vis[u]){
continue;
}
vis[u] = true;
for(auto it : adj[u]){
int v = it.first;
ll w = it.second;
if(vis[v]) continue;
if(dist[v] > d_u+w){
dist[v] = d_u+w;
pq.push({dist[v], v});
}
}
}
return dist;
}
void solve(){
int n, m;
cin >> n >> m;
ll S, T, L, K;
cin >> S >> T >> L >> K;
vector<vector<pair<ll, ll>>> adj(n+1);
for(int i = 1; i <= m; i++){
int u, v, w;
cin >> u >> v >> w;
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
vector<ll> dS = dijkstra(n, S, adj), dT = dijkstra(n, T, adj);
if(dS[T] <= K){
cout << (ll)n*(n-1)/2;
return;
}
vector<ll> tv;
for(int i = 1; i <= n; i++){
tv.push_back(dT[i]);
}
sort(tv.begin(), tv.end());
tv.push_back(INF);
K -= L;
ll ans = 0;
for(int i = 1; i <= n; i++){
int p = upper_bound(tv.begin(), tv.end(), K-dS[i]) - tv.begin() - 1;
p++;
ans += p;
}
cout << ans;
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
solve();
}
