#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
#define g0(x) get<0>(x)
#define g1(x) get<1>(x)
#define g2(x) get<2>(x)
#define pb push_back
#define int long long
#define f first
#define s second
#define pll pair<long long, long long>
vector<vector<pll>> al(200005);
int n,m,s,t,l,k;
int fw[200005];
int pitr[200005];
vector<pll> dists(200005,{LLONG_MAX, LLONG_MAX}), distt(200005, {LLONG_MAX, LLONG_MAX});
void upd(int x, int v){
while(x<=n){
fw[x]+=v;
x+=(x&-x);
}
}
int qry(int x){
int ret=0;
while(x){
ret+=fw[x];
x-=(x&-x);
}
return ret;
}
void dijkstra(int x, vector<pll> & dist){
for(int i=1; i<=n;i++)dist[i].f=1e16, dist[i].s=i;
dist[x].f=0;
priority_queue<pll,vector<pll>,greater<pll>> pq;
pq.push({0, x});
while(!pq.empty()){
auto [d,c]=pq.top();
//~ printf("at %lld \n", c);
pq.pop();
if(dist[c].f<d)continue;
for(auto [u, v]:al[c]){
if(dist[u].f<d+v)continue;
dist[u].f=d+v;
pq.push({dist[u].f,u});
}
}
}
signed main(){
cin>>n>>m>>s>>t>>l>>k;
for(int i=0;i<m;i++){
int a,b,c;cin>>a>>b>>c;
al[a].pb({b,c});
al[b].pb({a,c});
}
dijkstra(s, dists);
dijkstra(t, distt);
if(dists[t].f <= k){
cout<<(n*(n-1))/2;
return 0;
}
sort(dists.begin(), dists.end());
sort(distt.begin(),distt.end());
for(int i=0;i<n;i++){
pitr[distt[i].s]=i+1;
}
//~ for(int i=0;i<n;i++){
//~ cout<<dists[i].f<<" "<<dists[i].s<<" |";
//~ }cout<<endl;
//~ for(int i=0;i<n;i++){
//~ cout<<distt[i].f<<" "<<distt[i].s<<" |";
//~ }cout<<endl;
//~ for(int i=1;i<=n;i++){
//~ cout<<pitr[i]<<" ";
//~ }cout<<endl;
for(int i=1;i<=n;i++){
upd(i, 1);
}
int ans=0;
for(int i=0;i<n;i++){
//~ cout<<k-l-dists[i].f<<endl;
int av=upper_bound(distt.begin(),distt.end(),make_pair(k-l-dists[i].f, LLONG_MAX)) - distt.begin();
int non=qry(av);
ans+=non;
//~ printf("i %lld, av %lld, non %lld, pitr[dists[i].s] %lld\n",i,av,non,pitr[dists[i].s]);
upd(pitr[dists[i].s], -1);
}
cout<<ans;
}
