#include <bits/stdc++.h>
using namespace std;
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
#define int long long
typedef pair<int,int> pii;
typedef vector<int> vi;
typedef vector<pii> vii;
typedef vector<bool> vb;
typedef tree<pii,null_type,less<pii>,rb_tree_tag,
tree_order_statistics_node_update> oset;
#define fi first
#define se second
#define pb push_back
#define pf push_front
#define mid (l+r)/2
#define all(x) x.begin(),x.end()
#define FOR(i,a) for(int i=0;i<(a);i++)
#define FORE(i,a,b) for(int i=(a);i<(b);i++)
#define cont(x) for(auto el:x) cout<<el<<' ';cout<<endl;
#define contp(x) for(auto el:x) cout<<el.fi<<'-'<<el.se<<' ';cout<<endl;
#define sp <<" "<<
#define DEBUG(x) cout<<(#x) sp x<<endl
#define carp(a,b) (((a%MOD)*(b%MOD))%MOD)
#define topla(a,b) (((a%MOD)+(b%MOD))%MOD)
const int INF=1e18;
const int MAXN=2e5+5;
const int MOD=998244353;
int n,m,s,t,l,k;
vii adj[MAXN];
int d[MAXN];
vi vec;
int ans;
void dij(int bas){
set<pii> ss;
FORE(i,1,n+1) d[i]=INF;
d[bas]=0;
ss.insert({0,bas});
while(!ss.empty()){
auto el=*ss.begin();
ss.erase(el);
int nd=el.se;
for(auto [kom,cost]:adj[nd]){
if(d[kom]>d[nd]+cost){
if(d[kom]!=INF) ss.erase({d[kom],kom});
d[kom]=d[nd]+cost;
ss.insert({d[kom],kom});
}
}
}
if(bas==t){
FORE(i,1,n+1) vec.pb(d[i]);
sort(all(vec));
}
else{
FORE(i,1,n+1){
int kalan=k-(d[i]+l);
if(kalan<0) continue;
auto it=upper_bound(all(vec),kalan)-vec.begin();
ans+=it;
}
}
}
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
cin>>n>>m;
cin>>s>>t>>l>>k;
FOR(i,m){
int a,b,c;
cin>>a>>b>>c;
adj[a].pb({b,c});
adj[b].pb({a,c});
}
ans=0;
dij(t);
dij(s);
if(d[t]<=k) ans=n*(n-1)/2;
//eğer sden tye zaten <=k da gidiyosam hepsi
cout<<ans<<endl;
}
