#include <bits/stdc++.h>
using namespace std;
#define int long long
#define ll long long
#define rep(i,a,b) for (int i = a; i <= b; i++)
#define per(i,a,b) for (int i = a; i >= b; i--)
#define fi first
#define se second
#define pii pair<int,int>
#define pb push_back
const int MAXN = 2e5+10;
const int INF = 1e18 + 5;
const int MOD = 1e9+7;
vector<pii> g[MAXN];
int dist[MAXN][2],n;
bool vis[MAXN][2];
void dijkstra(int u, int k) {
rep(i,1,n) dist[i][k] = INF;
priority_queue<pii, vector<pii>, greater<pii>> pq;
pq.push({0,u});
dist[u][k] = 0;
while (!pq.empty()) {
auto [d, cur] = pq.top();pq.pop();
if(vis[cur][k]) continue;
vis[cur][k] = 1;
for(auto &[v,w] : g[cur]) {
if (dist[v][k] <= d+w) continue;
dist[v][k] = d+w;
pq.push({d+w,v});
}
}
}
void solve() {
int m,s,t,l,k;
cin >> n >> m >> s >> t >> l >> k;
rep(i,1,m) {
int u,v,c;cin >> u >> v >> c;
g[u].pb({v,c});
g[v].pb({u,c});
}
dijkstra(s,0);
dijkstra(t,1);
if(dist[t][0] <= k) {
cout << n*(n-1)/2 << '\n';
return;
}
vector<pii> val;
vector<int> bs;
rep(i,1,n) val.pb({dist[i][0], dist[i][1]});
sort(val.begin(),val.end());
int cnt = 0;
for(auto &[du,dv] : val) {
cnt += upper_bound(bs.begin(),bs.end(),k-l-dv) - bs.begin();
//cout << du << ' ' << dv << ' ' << upper_bound(bs.begin(),bs.end(),k-l-dv) - bs.begin() << '\n';
bs.pb(du);
}
cout << cnt << '\n';
}
int32_t main() {
ios_base::sync_with_stdio(0); cin.tie(nullptr);
int tt = 1;
//cin >> tt;
while (tt--) solve();
return 0;
}
