#include <bits/stdc++.h>
using namespace std;
#define endl '\n'
#define f first
// #define s second
#define pb(x) push_back(x)
#define int long long
/*
ORDERED SET PDBS
#include <bits/extc++.h>
using namespace __gnu_pbds;
typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;
*/
const int MOD = 1e9+7;
const int inf = 1e9;
const int INF = 1e18+20;
const int LOG = 25;
void solve() {
int n, m;
cin>>n>>m;
int s, t, l, k;
cin>>s>>t>>l>>k;
s--; t--;
vector<vector<pair<int, int>>> adj(n);
for (int i=0; i<m; i++) {
int u, v, w;
cin>>u>>v>>w;
u--; v--;
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
vector<int> d1(n, INF);
d1[s]=0;
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
pq.push({0, s});
while (!pq.empty()) {
auto [d, u] = pq.top();
pq.pop();
if (d1[u]!=d) continue;
for (auto [v, w] : adj[u]) {
if (d1[v] > d+w) {
d1[v] = d+w;
pq.push({d1[v], v});
}
}
}
if (d1[t] <= k) {
cout<<n*(n-1)/2<<endl;
return;
}
vector<int> d2(n, INF);
d2[t]=0;
pq.push({0, t});
while (!pq.empty()) {
auto [d, u] = pq.top();
pq.pop();
if (d2[u]!=d) continue;
for (auto [v, w] : adj[u]) {
if (d2[v] > d+w) {
d2[v] = d+w;
pq.push({d2[v], v});
}
}
}
int cnt=0;
sort(d1.begin(), d1.end());
sort(d2.begin(), d2.end());
int K = k-l;
for (int i = 0; i<n; i++) {
int left = K - d1[i];
auto it = upper_bound(d2.begin(), d2.end(), left);
cnt += (it - d2.begin());
}
cout<<cnt<<endl;
}
bool multi=false;
int32_t main()
{
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int t=1;
if (multi) cin>>t;
while (t--) solve();
return 0;
}
