#include<bits/stdc++.h>
using namespace std;
#define int long long
vector<pair<int,long long> > adj[200005];
long long d1[200005],d2[200005],k,ans=0;
int s,t,l,m,n,a,b,c;
#define oo 10000000000000001
priority_queue<pair<long long,int> > pq;
bitset<200005> vis;
signed main(){
ios::sync_with_stdio(0),cin.tie(0);
cin>>n>>m>>s>>t>>l>>k;
for(int i=1;i<=m;i++){
cin>>a>>b>>c;
adj[a].push_back({b,c});
adj[b].push_back({a,c});
}
for(int i=1;i<=n;i++){
d1[i]=oo;
d2[i]=oo;
}
pq.push({d1[s]=0,s});
while(!pq.empty()){
auto p=pq.top();
pq.pop();
int v=p.second;
if(vis[v]) continue;
vis[v]=1;
for(auto e:adj[v]){
int u=e.first;
long long w=e.second;
if(d1[u]>d1[v]+w){
d1[u]=d1[v]+w;
pq.push({-d1[u],u});
}
}
}
pq.push({d2[t]=0,t});
vis.reset();
while(!pq.empty()){
auto p=pq.top();
pq.pop();
int v=p.second;
if(vis[v]) continue;
vis[v]=1;
for(auto e:adj[v]){
int u=e.first;
long long w=e.second;
if(d2[u]>d2[v]+w){
d2[u]=d2[v]+w;
pq.push({-d2[u],u});
}
}
}
if(d1[t]<=k){
cout<<n*(n-1)/2<<'\n';
return 0;
}
sort(d1+1,d1+n+1),sort(d2+1,d2+n+1);
/*int x=1,y=n;
while(x<=n){
while(d1[x]+d2[y]+l>k&&y>0) y--;
x++;
if(y<=0) break;
ans+=y;
}
*/
for(int i=1;i<=n;i++){
ans+=upper_bound(d2+1,d2+n+1,k-l-d1[i])-(d2+1);
}
cout<<ans<<'\n';
}
