#include <bits/stdc++.h>
using namespace std;
typedef long long int i64;
#define int long long
typedef pair<int, int> pii;
#define ff first
#define ss second
#define MP make_pair
const i64 inf = 1e18 + 10;
const int mxn = 2e5 + 10;
vector<i64> st, en;
vector<pii> adj[mxn];
int n, m, s, e, len;
i64 lim;
void djkstra(int st, vector<i64> &dis) {
dis.resize(n + 1, inf);
priority_queue<pii> pq;
pq.push(MP(0, st));
while(pq.size()) {
int d = -pq.top().ff;
int u = pq.top().ss;
pq.pop();
if(dis[u] < inf) continue;
dis[u] = d;
for(pii p : adj[u]) {
int v = p.ff;
int c = p.ss + d;
if(dis[v] == inf)
pq.push(MP(-c, v));
}
}
}
int32_t main() {
cin >> n >> m;
cin >> s >> e >> len >> lim;
for(int i = 0; i < m; i++) {
int a, b, c;
cin >> a >> b >> c;
adj[a].push_back(MP(b, c));
adj[b].push_back(MP(a, c));
}
djkstra(s, st);
djkstra(e, en);
if(st[e] <= lim) {
i64 ans = 1LL * n * (n - 1) / 2;
cout << ans << endl;
return 0;
}
st[0] = en[0] = -1;
sort(st.begin(), st.end());
sort(en.begin(), en.end());
i64 ans = 0LL;
for(int i = 1; i <= n; i++) {
i64 sus = lim - len - st[i];
if(sus < 0) continue;
i64 add = upper_bound(en.begin(), en.end(), sus) - en.begin() - 1;
ans += add;
}
cout << ans << endl;
return 0;
}
