#include<bits/stdc++.h>
using namespace std;
#define int long long
#define ii pair<int,int>
#define fir first
#define sec second
const int maxn=2e5;
int n,m,s,t,l,k;
vector<ii>adj[maxn+2];
int bia[maxn+2],blk[maxn+2];
signed main(){
ios_base::sync_with_stdio(0);
cin.tie(0);cout.tie(0);
cin>>n>>m>>s>>t>>l>>k;
for(int q=1;q<=m;q++){
int u,v,w;
cin>>u>>v>>w;
adj[u].push_back({v,w});
adj[v].push_back({u,w});
}
for(int q=1;q<=n;q++){
bia[q]=blk[q]=1e18;
}
priority_queue<ii,vector<ii>,greater<ii> >pq;
pq.push({0,s}); bia[s]=0;
while(pq.size()){
ii cur=pq.top(); pq.pop();
if(cur.fir!=bia[cur.sec])continue;
for(auto [v,w] : adj[cur.sec]){
if(bia[v]>cur.fir+w){
bia[v]=cur.fir+w;
pq.push({bia[v],v});
}
}
}
pq.push({0,t}); blk[t]=0;
while(pq.size()){
ii cur=pq.top(); pq.pop();
if(cur.fir!=blk[cur.sec])continue;
for(auto [v,w] : adj[cur.sec]){
if(blk[v]>cur.fir+w){
blk[v]=cur.fir+w;
pq.push({blk[v],v});
}
}
}
if(bia[t]<=k){
cout<<n*(n-1)/2<<endl;
return 0;
}
vector<int>cek;
for(int q=1;q<=n;q++){
cek.push_back(blk[q]);
}
sort(cek.begin(),cek.end());
int ans=0;
for(int q=1;q<=n;q++){
int sisa=k-l-bia[q];
int idx=upper_bound(cek.begin(),cek.end(),sisa)-cek.begin();
ans+=idx;
}
cout<<ans<<endl;
}
