///NotIsora
///This is my last dance
#include<bits/stdc++.h>
#define modulo 1000000007
#define fi first
#define se second
#define sq(x) (x)*(x)
#define ll long long
#define ld long double
#define el '\n'
#define pb push_back
///#define int long long
using namespace std;
const int N=1e5+5;
const ll INF=1e18;
int n,m;
int st,ed,l;
ll k;
ll d[2][N];
vector<pair<int,int>>adj[N];
struct State{
int s,type;
ll dis;
bool operator < (const State&other) const{
return dis>other.dis;
}
};
signed main(){
ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
///freopen("i.INP","r",stdin);
cin>>n>>m;
cin>>st>>ed>>l>>k;
for(int i=1;i<=m;i++){
int a,b,w;
cin>>a>>b>>w;
adj[a].pb({b,w});
adj[b].pb({a,w});
}
for(int i=1;i<=n;i++){
d[0][i]=d[1][i]=INF;
}
priority_queue<State>pq;
d[0][st]=0;
d[1][ed]=0;
pq.push({st,0,0LL});
pq.push({ed,1,0LL});
while(!pq.empty()){
int s=pq.top().s;
int t=pq.top().type;
ll dis=pq.top().dis;
pq.pop();
if (dis>d[t][s]) continue;
for(pair<int,int>&pr:adj[s]){
int u=pr.fi;
int w=pr.se;
if (d[t][u]>d[t][s]+(ll)w){
d[t][u]=d[t][s]+(ll)w;
pq.push({u,t,d[t][u]});
}
}
}
ll ans=0;
for(int u=1;u<=n;u++){
for(int v=u+1;v<=n;v++){
if (d[0][u]+(ll)l+d[1][v]<=k) ans++;
if (d[1][u]+(ll)l+d[0][v]<=k) ans++;
}
}
cout<<ans;
}
