#include<bits/stdc++.h>
#define int long long
using namespace std;
vector<pair<int,int>>adj[200005];
int diss[200005];
int dist[200005];
int inf=1e18;
int32_t main(){
ios_base::sync_with_stdio(false);
cin.tie(0);
int n,m;cin>>n>>m;
int s,t,l,k;cin>>s>>t>>l>>k;
for(int i=0;i<m;i++){
int a,b,c;cin>>a>>b>>c;
adj[a].push_back({b,c});
adj[b].push_back({a,c});
}
for(int i=1;i<=n;i++)diss[i]=dist[i]=inf;
priority_queue<pair<int,int>,vector<pair<int,int>>,greater<pair<int,int>>>pq;
pq.push({0,s});
while(!pq.empty()){
auto [dis,x]=pq.top();
pq.pop();
if(diss[x]!=inf)continue;
diss[x]=dis;
for(auto v:adj[x])pq.push({dis+v.second,v.first});
}
pq.push({0,t});
while(!pq.empty()){
auto [dis,x]=pq.top();
pq.pop();
if(dist[x]!=inf)continue;
dist[x]=dis;
for(auto v:adj[x])pq.push({dis+v.second,v.first});
}
if(diss[t]<=k){
cout<<n*(n-1)/2;
return 0;
}
vector<int>v;
for(int i=1;i<=n;i++)v.push_back(dist[i]);
sort(v.begin(),v.end());
int ans=0;
for(int i=1;i<=n;i++){
int dis=k-(diss[i]+l);
//cerr<<dis<<"\n";
int id=upper_bound(v.begin(),v.end(),dis)-v.begin();
ans+=id;
}
cout<<ans;
}
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