#include <bits/stdc++.h>
using namespace std;
int32_t main(){
ios::sync_with_stdio(0);
cin.tie(0);
int n,m;
cin >> n >> m;
int s,t;
long long l,k;
cin >> s >> t >> l >> k;
vector<pair<int,long long> > adj[n+1];
for(int i=0; i<m; i++){
int a,b;
long long c;
cin >> a >> b >> c;
adj[a].push_back({b,c});
adj[b].push_back({a,c});
}
priority_queue<pair<long long,int>,vector<pair<long long,int> >,greater<pair<long long,int> > > pq;
long long dist[2][n+1];
memset(dist,-1,sizeof(dist));
pq.push({0,s});
while(!pq.empty()){
long long a=pq.top().first;
int b=pq.top().second;
pq.pop();
if(dist[0][b]!=-1) continue;
dist[0][b]=a;
for(auto i:adj[b]){
if(dist[0][i.first]!=-1) continue;
pq.push({a+i.second,i.first});
}
}
pq.push({0,t});
while(!pq.empty()){
long long a=pq.top().first;
int b=pq.top().second;
pq.pop();
if(dist[1][b]!=-1) continue;
dist[1][b]=a;
for(auto i:adj[b]){
if(dist[1][i.first]!=-1) continue;
pq.push({a+i.second,i.first});
}
}
for(int i=1; i<=n; i++){
if(dist[0][i]==-1) dist[0][i]=1e16;
if(dist[1][i]==-1) dist[1][i]=1e16;
}
if(dist[0][t]<=k){
cout << (long long)n*(n-1)/2ll;
return 0;
}
vector<long long> yey;
for(int i=1; i<=n; i++) yey.push_back(dist[0][i]);
sort(yey.begin(),yey.end());
long long ans=0;
for(int i=1; i<=n; i++){
ans+=upper_bound(yey.begin(),yey.end(),k-l-dist[1][i])-yey.begin();
}
cout << ans;
}
