#include <bits/stdc++.h>
using namespace std;
#define ff first
#define ss second
#define pb push_back
#define int long long
#define pint pair<int, int>
#define vint vector<pair<int, int>>
const int mod = 1e9 + 7;
const int shrek = 5e5 + 5;
const int say = INT_MAX / 2;
const int gex = INT_MIN / 2;
const long long oo = 1e9;
signed main(){
ios::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
int n, m; cin >> n >> m;
int s, t, l, k;
cin >> s >> t >> l >> k;
vector<vector<pair<int, int>>> adj(n + 1);
bool vis1[n + 1];
int diss[n + 1], dist[n + 1];
for(int i = 0; i < m; i++) {
int a, b, c;
cin >> a >> b >> c;
adj[a].pb({b, c});
adj[b].pb({a, c});
}
for(int i = 1; i <= n; i++) diss[i] = oo;
diss[s] = 0;
priority_queue<pair<int, int>> q1;
q1.push({0, s});
while(!q1.empty()) {
int a = q1.top().second;
q1.pop();
if(vis1[a]) continue;
vis1[a] = true;
for(auto u : adj[a]) {
int b = u.first, w = u.second;
if(diss[a] + w < diss[b]) {
diss[b] = diss[a] + w;
q1.push({-diss[b], b});
}
}
}
priority_queue<pair<int, int>> q2;
q2.push({0, s});
while(!q2.empty()) {
int a = q2.top().second;
q2.pop();
if(vis1[a]) continue;
vis1[a] = true;
for(auto u : adj[a]) {
int b = u.first, w = u.second;
if(dist[a] + w < dist[b]) {
dist[b] = dist[a] + w;
q1.push({-dist[b], b});
}
}
}
if(diss[t] <= k) {
cout << n * (n - 1) / 2 << '\n';
return 0;
}
sort(diss + 1, diss + n + 1);
sort(dist + 1, dist + n + 1);
int ans = 0;
for(int i = 1; i <= n; i++) {
ans += upper_bound(dist + 1, dist + n + 1, k - l - diss[i]) - (dist + 1);
}
cout << ans << '\n';
return 0;
}
