#include<bits/stdc++.h>
#define ii pair<int,int>
#define f first
#define s second
#define mp make_pair
#define int long long
using namespace std;
int32_t main(){
int N,M;
cin>>N>>M;
vector<ii> A[N+1];
int S,T,L,K;
cin>>S>>T>>L>>K;
while(M--){
int x,y,z;
cin>>x>>y>>z;
A[x].push_back(mp(z,y));
A[y].push_back(mp(z,x));
}
vector<int> dist1(N+1,LLONG_MAX);
priority_queue<ii,vector<ii>,greater<ii>> PQ;
dist1[S]=0;
PQ.push(mp(0,S));
while(!PQ.empty()){
int node=PQ.top().s;
int d=PQ.top().f;
PQ.pop();
if(dist1[node]!=d)continue;
for(auto i:A[node])
if(dist1[i.s]>d+i.f){
dist1[i.s]=d+i.f;
PQ.push(mp(d+i.f,i.s));
}
}
if(dist1[T]<=K){cout<<(N*(N-1))/2; return 0;}
vector<int> dist2(N+1,LLONG_MAX);
dist2[T]=0;
PQ.push(mp(0,T));
while(!PQ.empty()){
int node=PQ.top().s;
int d=PQ.top().f;
PQ.pop();
if(dist2[node]!=d)continue;
for(auto i:A[node])
if(dist2[i.s]>d+i.f){
dist2[i.s]=d+i.f;
PQ.push(mp(d+i.f,i.s));
}
}
vector<int> V;
for(int i=1;i<=N;i++){
if(dist2[i]!=LLONG_MAX)V.push_back(dist2[i]);
}
sort(V.begin(),V.end());
int c=0;
for(int i=1;i<=N;i++){
if(dist1[i]==LLONG_MAX)continue;
int quota=K-dist1[i]-L;
auto itr=upper_bound(V.begin(),V.end(),quota);
c+=itr-V.begin();
}
cout<<c;
}
