#include <bits/stdc++.h>
#define L(i,j,k) for(int i=(j);i<=(k);i++)
#define R(i,j,k) for(int i=(j);i>=(k);i--)
#define all(x) x.begin(),x.end()
#define sz(a) ((int)a.size())
#define pb push_back
using namespace std;
typedef long long ll;
const int N=2e5+5;
const ll INF=1e18+5;
vector<pair<int,int>>adj[N];
int n;
ll gauss(ll n){
return (n*(n-1))/2;
}
vector<ll>distances(ll s){
vector<ll>dist(n+1,INF),parent(n+1);
priority_queue<pair<int,int>,vector<pair<int,int>>,greater<pair<int,int>>>q;
q.push({0,s});
dist[s]=0;
while(sz(q)){
auto [d,u]=q.top();q.pop();
if(d!=dist[u])continue;
for(auto [v,c]:adj[u]){
if(dist[v]>dist[u]+c){
dist[v]=dist[u]+c;
parent[v]=u;
q.push({dist[v],v});
}
}
}
return dist;
}
int main(){
ll m;cin>>n>>m;
ll s,t,l,k;cin>>s>>t>>l>>k;
L(i,0,m-1){
ll a,b,c;cin>>a>>b>>c;
adj[a].pb({b,c});
adj[b].pb({a,c});
}
auto ds=distances(s),dt=distances(t);
if(ds[t]<=k){
cout<<gauss(n)<<endl;
return 0;
}
vector<ll>nodes;
L(i,1,n){
nodes.pb(dt[i]);
}
sort(all(nodes));
ll ans=0;
L(i,0,n-1){
if(k<ds[i])continue;
ll ll=-1,rr=sz(nodes);
while(rr-ll>1){
int mm=(rr+ll)/2;
if(ds[i]+l+nodes[mm]<=k){
ll=mm;
}else{
rr=mm;
}
}
ans+=ll+1;
}
cout<<ans<<endl;
}
