#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#define fst first
#define snd second
#define pb push_back
#define SZ(x) (int)x.size()
#define ALL(x) x.begin(),x.end()
#define forn(i,a,b) for(int i = a; i<b; i++)
#define mset(a,v) memset(a,v,sizeof(a))
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
template< typename T >
using iset = tree<T,null_type,less<T>,rb_tree_tag,tree_order_statistics_node_update>;
ll actualres(multiset<ll> &s){
ll mini = *s.begin();
ll maxi = *(--s.end());
ll res = maxi-mini;
return res;
}
const int MAXN = 200000+5;
vector<pair<ll,ll>> adj[MAXN];
ll n;
bool vis[MAXN];
vector<ll> dijkstra(ll ini){
vector<ll> dist(n,10000000000000000);
dist[ini]=0;
priority_queue<pair<ll,ll>> pq; pq.push({0,ini});
while(!pq.empty()){
ll nd = pq.top().snd;
ll cost = pq.top().fst*-1;
pq.pop();
vis[nd]=true;
if(dist[nd]!=cost) continue;
for(auto i:adj[nd]){
if(dist[i.fst]==-1 || dist[i.fst]>cost+i.snd){
dist[i.fst]=cost+i.snd;
pq.push({dist[i.fst]*-1,i.fst});
}
}
}
return dist;
}
int main(){
ll m;
ll s,t,l,k;
cin>>n>>m;
cin>>s>>t>>l>>k; s--; t--;
ll u,v,c;
forn(i,0,m){
cin>>u>>v>>c; u--; v--;
adj[u].pb({v,c});
adj[v].pb({u,c});
}
vector<ll> Sto = dijkstra(s);
vector<ll> Tto = dijkstra(t);
if(Sto[t]<=k) cout<<(n*(n-1))/2<<'\n';
else{
iset<pair<ll,ll>> Ttoms;
forn(i,0,n) Ttoms.insert({Tto[i],i});
ll res = 0;
forn(i,0,n){
Ttoms.erase(Ttoms.find({Tto[i],i}));
//cout<<Sto[i]<<" "<<l<<'\n';
ll obj = k-(Sto[i]+l);
//cout<<i<<" -> "<<obj<<" "<<Ttoms.order_of_key({obj,5*n})<<'\n';
res+=Ttoms.order_of_key({obj,5*n});
}
iset<pair<ll,ll>> Stoms;
forn(i,0,n) Stoms.insert({Sto[i],i});
forn(i,0,n){
Stoms.erase(Stoms.find({Sto[i],i}));
//cout<<Sto[i]<<" "<<l<<'\n';
ll obj = k-(Tto[i]+l);
//cout<<i<<" -> "<<obj<<" "<<Ttoms.order_of_key({obj,5*n})<<'\n';
res+=Stoms.order_of_key({obj,5*n});
}
cout<<res<<'\n';
}
return 0;
}
