#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pll pair<ll, ll>
#define pii pair<int, int>
#define fs first
#define sc second
#define pb push_back
const int maxn=2e5;
vector<pll> adj[maxn+1];
void solve() {
ll n,m,s,t,l,k;
cin>>n>>m>>s>>t>>l>>k;
while(m--){
ll u,v,w;
cin>>u>>v>>w;
adj[u].pb({v,w});
adj[v].pb({u,w});
}
ll d1[n+1],d2[n+1];
memset(d1,63,sizeof(d1));
memset(d2,63,sizeof(d2));
priority_queue<pll> pq;
bool vis[n+1];
memset(vis,0,sizeof(vis));
d1[s]=0;
pq.push({0,s});
while(!pq.empty()){
int v=pq.top().sc;
pq.pop();
if(vis[v])continue;
vis[v]=1;
for(auto[u,w]:adj[v])if(!vis[u]){
d1[u]=min(d1[u],d1[v]+w);
pq.push({-d1[u],u});
}
}
if(d1[t]<=k){
cout<<n*(n-1)/2<<'\n';
return;
}
memset(vis,0,sizeof(vis));
d2[t]=0;
pq.push({0,t});
while(!pq.empty()){
int v=pq.top().sc;
pq.pop();
if(vis[v])continue;
vis[v]=1;
for(auto[u,w]:adj[v])if(!vis[u]){
d2[u]=min(d2[u],d2[v]+w);
pq.push({-d2[u],u});
}
}
sort(d2+1,d2+n+1);
ll c=0;
for(int i=1;i<=n;i++){
c+=upper_bound(d2+1,d2+n+1,k-l-d1[i])-d2-1;
}
cout<<c<<'\n';
}
int main() {
#ifdef FPO
freopen("in","r",stdin);
freopen("out","w",stdout);
#endif
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
solve();
}
