#include <bits/stdc++.h>
using namespace std;
#define forn(i,n) for(int i=0;i<int(n);i++)
#define forsn(i,s,n) for(int i=int(s);i<int(n);i++)
#define dforn(i,n) for(int i=int(n)-1;i>=0;i--)
#define dforsn(i,s,n) for(int i=int(n)-1;i>=int(s);i--)
#define fst first
#define snd second
#define pb push_back
#define eb emplace_back
#define sz(x) (int)x.size()
#define all(x) x.begin(), x.end()
typedef long long ll;
typedef vector<ll> vll;
typedef vector<int> vi;
typedef pair<int,int> ii;
const ll INF=1e18;
vll dijkstra(int s, const vector<vector<ii>> &adj){
int n=sz(adj);
vector<ll> dist(n,INF);
priority_queue<pair<ll,int>> pq;
pq.emplace(-(dist[s]=0),s);
while(!pq.empty()){
auto[d,u]=pq.top(); pq.pop(); d*=-1;
if(dist[u]!=d) continue;
for(auto[v,w]:adj[u]) if(dist[v]>dist[u]+w) pq.emplace(-(dist[v]=dist[u]+w),v);
}
return dist;
}
int main(){
ios::sync_with_stdio(0);
cin.tie(0);
int n,m,s,t; ll l,k;
cin>>n>>m>>s>>t>>l>>k;
--s,--t;
vector<vector<ii>> adj(n);
forn(i,m){
int u,v,w;
cin>>u>>v>>w;
--u,--v;
adj[u].eb(v,w);
adj[v].eb(u,w);
}
vll dist_s=dijkstra(s,adj);
vll dist_t=dijkstra(t,adj);
if(dist_s[t]<=k){
cout<<n*(n-1LL)/2<<'\n';
return 0;
}
sort(all(dist_t));
ll target=k-l;
ll ans=0;
auto cnt=[&](ll x){
return int(upper_bound(all(dist_t),x)-begin(dist_t));
};
forn(u,n){
ans+=cnt(target-dist_s[u]);
}
cout<<ans<<'\n';
return 0;
}
