#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define fi first
#define se second
#define pii pair<int,int>
#define pll pair<long long,long long>
#define pb push_back
#define debug(x) cerr<<#x<<"="<<x<<endl
#define pq priority_queue
#define inf 1ll<<60
#define rep(i,a,b) for (ll i=a;i<(b);i++)
#define MP make_pair
#define SZ(x) (int(x.size()))
#define mod 1000000007
#define ALL(x) x.begin(),x.end()
#define endl "\n"
void inc(ll &a,ll b) {a=(a+b)%mod;}
void dec(ll &a,ll b) {a=(a-b+mod)%mod;}
int prod(ll a,ll b) {return ll(a)*ll(b)%mod;}
int lowbit(ll x) {return x&(-x);}
ll p0w(ll base,ll p) {ll ret=1;while(p>0){if (p%2ll==1ll) ret=ret*base%mod;base=base*base%mod;p/=2ll;}return ret;}
ll n,m;
const ll maxn=222222;
vector<pll>alist[maxn];
ll dist[2][maxn];
void dijkstra(ll st,ll id){
priority_queue<pll,vector<pll>,greater<pll>>s;
s.push(MP(0ll,st));
dist[id][st]=0;
while(!s.empty()){
auto u=s.top();
s.pop();
if(dist[id][u.se]!=u.fi)continue;
for(auto x:alist[u.se]){
if(dist[id][x.se]>dist[id][u.se]+x.fi){
dist[id][x.se]=dist[id][u.se]+x.fi;
s.push(MP(dist[id][x.se],x.se));
}
}
}
}
signed main(){
ios::sync_with_stdio(0);
cin.tie(0);
memset(dist,63,sizeof dist);
cin>>n>>m;
ll s,t,l,k;cin>>s>>t>>l>>k;
rep(i,1,m+1){
ll a,b,c;cin>>a>>b>>c;
alist[a].pb(MP(c,b));
alist[b].pb(MP(c,a));
}
dijkstra(s,0);
dijkstra(t,1);
if(dist[0][t]<=k){
cout<<n*(n-1)/2<<endl;
return 0;
}
//debug(11);
ll ans=0,pp=n;
sort(dist[0]+1,dist[0]+n+1);
sort(dist[1]+1,dist[1]+n+1);
/*
rep(i,1,n+1)cout<<dist[0][i]<<" ";
cout<<endl;
rep(i,1,n+1)cout<<dist[1][i]<<" ";
cout<<endl;
*/
rep(i,1,n+1){
ll goal=k-dist[0][i]-l;
while(dist[1][pp]>goal and pp>0)pp--;
ans+=pp;
}
cout<<ans<<endl;
return 0;
}
