#include<bits/stdc++.h>
#define int long long
using namespace std;
const int INF=1e18;
int n;
vector<vector<pair<int, int>>> adj;
vector<int> dijk(int st) {
vector<bool> vis(n+1, false);
vector<int> dis(n+1, INF); dis[st]=0;
priority_queue<pair<int, int>> q; q.push({0, st});
while(!q.empty()) {
int node=q.top().second; q.pop();
if(vis[node]) continue;
vis[node]=true;
for(auto [child, w] : adj[node]) {
if(dis[child] > dis[node]+w) {
dis[child]=dis[node]+w;
q.push({-dis[child], child});
}
}
}
return dis;
}
signed main() {
int m, s, t, l, k; cin >> n >> m >> s >> t >> l >> k;
adj=vector<vector<pair<int, int>>>(n+1);
for(int i=0; i<m; i++) {
int a, b, c; cin >> a >> b >> c;
adj[a].push_back({b, c});
adj[b].push_back({a, c});
}
vector<int> disS=dijk(s), disT=dijk(t);
if(disS[t] <= k) {
cout << n*(n-1)/2;
return 0;
}
map<int, int> cum;
for(int i=1; i<=n; i++) {
if(disT[i] == INF) continue;
cum[disT[i]]++;
}
int prev=0;
for(auto x : cum) {
cum[x.first]+=prev;
prev=cum[x.first];
}
//for(auto x : cum) cout << x.first << ' ' << x.second << endl;
int ans=0;
for(int i=1; i<=n; i++) {
int otherD=k-(disS[i]+l);
if(otherD >= 0) {
auto it = cum.upper_bound(otherD);
it--;
ans+=it->second;
if(disT[i] <= otherD) ans--;
}
}
cout << ans;
return 0;
}
