#include "bits/stdc++.h"
using namespace std;
#ifdef duc_debug
#include "bits/debug.h"
#else
#define debug(...)
#endif
const int maxn = 2e5 + 5;
int n, m, l;
long long k;
int s, t;
vector<pair<int, int>> g[maxn];
long long d[maxn], rev[maxn];
long long org[maxn];
void dijkstra(int src, long long d[]) {
for(int i = 1; i <= n; ++i) {
d[i] = 1e18;
}
priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<pair<long long, int>>> pq;
d[src] = 0;
pq.push(make_pair(0, src));
while(!pq.empty()) {
int u = pq.top().second;
long long dist = pq.top().first;
pq.pop();
if(dist > d[u]) continue;
for(auto e:g[u]) {
int v = e.first, w = e.second;
if(d[v] > d[u] + w) {
d[v] = d[u] + w;
pq.push(make_pair(d[v], v));
}
}
}
}
void solve() {
cin >> n >> m >> s >> t >> l >> k;
for(int i = 1; i <= m; ++i) {
int u, v, w; cin >> u >> v >> w;
g[u].emplace_back(v, w);
g[v].emplace_back(u, w);
}
dijkstra(s, d);
dijkstra(t, rev);
if(d[t] <= k) {
cout << 1ll * n * (n - 1) / 2;
return;
}
for(int i = 1; i <= n; ++i) {
org[i] = rev[i];
}
long long res = 0;
sort(rev + 1, rev + n + 1);
for(int i = 1; i <= n; ++i) {
int x = upper_bound(rev + 1, rev + n + 1, k - l - d[i]) - rev - 1;
res += x;
if(d[i] + org[i] <= k - l) {
--res;
}
}
cout << res;
}
signed main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
solve();
return 0;
}
