#include <bits/stdc++.h>
#define ll long long
using namespace std;
ll n;
vector<vector<pair<ll,ll>>> adj;
vector<ll> dijkstra(ll s) {
vector<ll> dist(n, 1e18);
dist[s] = 0;
priority_queue<pair<ll,ll>, vector<pair<ll,ll>>, greater<pair<ll,ll>>> pq;
pq.push({0, s});
while(!pq.empty()) {
auto [d,u] = pq.top();
pq.pop();
if (d>dist[u]) continue;
for (auto [v,w] : adj[u]) {
if (dist[v]>dist[u]+w) {
dist[v] = dist[u]+w;
pq.push({dist[v],v});
}
}
}
return dist;
}
vector<ll> T;
void update(ll idx, ll val) {
for (; idx<=n; idx+=idx & -idx) {
T[idx]+=val;
}
}
ll sum(ll idx) {
ll res = 0;
for (; idx>0; idx-=idx & -idx) {
res+=T[idx];
}
return res;
}
bool comp(pair<ll,ll> a, pair<ll,ll>b) {
return a.first-a.second<=b.first-b.second;
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
ll m,s,t,l,k;
cin >> n >> m >> s >> t >> l >> k;
s--; t--;
adj.resize(n);
for (int i=0; i<m; i++) {
ll a,b,c;
cin >> a >> b >> c;
a--; b--;
adj[a].push_back({b,c});
adj[b].push_back({a,c});
}
vector<ll> dists = dijkstra(s);
vector<ll> distt = dijkstra(t);
if (dists[t]<=k) {
cout << (n*(n-1))/2;
return 0;
}
ll res = 0;
vector<pair<ll,ll>> v(n);
for (int i=0; i<n; i++) {
v[i] = {dists[i], distt[i]};
}
sort(v.begin(), v.end(), comp);
map<ll,ll> mp;
vector<ll> b;
for (int i=0; i<n; i++) {
b.push_back(v[i].first);
b.push_back(k-l-v[i].second);
}
sort(b.begin(), b.end());
b.erase(unique(b.begin(), b.end()), b.end());
ll j = 1;
for (int i=0; i<b.size(); i++) {
if (i==0 || b[i]>b[i-1]) {
mp[b[i]] = j++;
}
}
T.resize(b.size()+2, 0);
for (int i=0; i<n; i++) {
ll k1 = sum(mp[k-l-v[i].second]);
res+=k1;
update(mp[v[i].first], 1);
}
cout << res;
}
