#include <bits/stdc++.h>
using namespace std;
#define int long long
std::vector <vector<pair<int, int>>> adj(500005);
std::vector <vector<int>> dist(2, vector <int> (500005, LLONG_MAX/2));
std::vector <bool> vis_s(500005, false), vis_t(500005, false);
//nvm dijkstra cannot dfs this
void dijk_s(int idx, int source) {
using T = pair<long long, int>;
priority_queue<T, vector<T>, greater<T>> pq;
dist[idx][source] = 0;
pq.push({0, source});
while (!pq.empty()) {
const auto [cdist, cur] = pq.top(); // 'cur' is the current node
pq.pop();
if (cdist != dist[idx][cur]) { continue; }
for (auto &edge : adj[cur]) {
int next = edge.first;
int weight = edge.second;
if (cdist + weight < dist[idx][next]) {
dist[idx][next] = cdist + weight;
pq.push({dist[idx][next], next});
}
}
}
}
int32_t main(){
int n, m, s, t, l, k;
std::cin >> n >> m >> s >> t >> l >> k;
for(int i=0; i<m; i++){
int a, b, c;
std::cin >> a >> b >> c;
adj[a].push_back({b, c});
adj[b].push_back({a, c});
}
//dfs from s then dfs from t
//just put in array and upper bound or smth to query how much can
dijk_s(0, s);
dijk_s(1, t);
std::vector <int> dist_s, dist_t;
for(int i=1; i<=n; i++){
dist_s.push_back(dist[0][i]);
dist_t.push_back(dist[1][i]);
//std::cout << dist[0][i] << " ";
}
if(dist_s[t-1]<=k){
std::cout << (n * (n - 1)) / 2;
return 0;
}
sort(dist_s.begin(), dist_s.end());
sort(dist_t.begin(), dist_t.end());
int ans=0;
for(int i=0; i<n; i++){
int mx=k-l-dist_s[i];//dist_t gotta be <=t to make it
int ind=upper_bound(dist_t.begin(), dist_t.end(), mx)-dist_t.begin();
//std::cout << ind << " ";
ans+=ind;
}
std::cout << ans;
}
