#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pb push_back
#define ff first
#define ss second
#define all(s) s.begin(),s.end()
#define rall(s) s.rbegin(),s.rend()
int main(){
ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
ll n,m;
cin>>n>>m;
ll S,T,L,K;
cin>>S>>T>>L>>K;
vector<pair<ll,ll>>g[n+5];
for(ll i=1;i<=m;i++){
ll a,b,c;
cin>>a>>b>>c;
g[a].pb({b,c});
g[b].pb({a,c});
}
vector<ll>dist(n+5,(ll)1e18);
set<pair<ll,ll>>q;
dist[S]=0;
q.insert({0ll,S});
while(!q.empty()){
auto [d,i]=*q.begin();
q.erase(q.begin());
if(dist[i]!=d) continue;
for(auto [j,w]:g[i]){
if(dist[i]+w<dist[j]){
dist[j]=dist[i]+w;
q.insert({dist[j],j});
}
}
}
if(dist[T]<=K){
cout<<n*(n-1)/2;
return 0;
}
vector<vector<ll>>v;
v.pb(dist);
fill(all(dist),(ll)1e18);
dist[T]=0;
q.insert({0ll,T});
while(!q.empty()){
auto [d,i]=*q.begin();
q.erase(q.begin());
if(dist[i]!=d) continue;
for(auto [j,w]:g[i]){
if(dist[i]+w<dist[j]){
dist[j]=dist[i]+w;
q.insert({dist[j],j});
}
}
}
v.pb(dist);
ll l[n+5],r[n+5];
for(ll i=1;i<=n;i++){
l[i]=v[0][i];
r[i]=v[1][i];
}
sort(l+1,l+n+1);
sort(r+1,r+n+1);
ll ans=0;
for(ll i=1;i<=n;i++){
ll x=upper_bound(r+1,r+n+1,K-L-l[i])-r-1;
ans+=x;
// b<=K-L-a
}
cout<<ans;
}
