#include<bits/stdc++.h>
using namespace std;
using ll = long long;
const int N=2e5+5;
const ll INF=1e18;
int n,m,s,t,l;
ll k;
vector<pair<int,ll>> adj[N];
ll ds[N],dt[N];
vector<ll> v1,v2;
ll ans,cnt;
void dijk(ll *dist,int s){
for(int i=1;i<=n;i++)dist[i]=INF;
priority_queue<pair<ll,int>,vector<pair<ll,int>>,greater<pair<ll,int>>> pq;
dist[s]=0;
pq.emplace(0,s);
while(!pq.empty()){
auto [d,u]=pq.top();
pq.pop();
if(d>dist[u])continue;
for(auto [v,w]:adj[u])if(d+w<dist[v]){
dist[v]=d+w;
pq.emplace(d+w,v);
}
}
}
int main(){
cin.tie(nullptr)->sync_with_stdio(false);
cin >> n >> m;
cin >> s >> t >> l >> k;
for(int i=1;i<=m;i++){
int u,v,w;
cin >> u >> v >> w;
adj[u].emplace_back(v,w);
adj[v].emplace_back(u,w);
}
dijk(ds,s);
if(ds[t]<=k)cout << 1LL*n*(n-1)/2,exit(0);
dijk(dt,t);
for(int i=1;i<=n;i++)v1.emplace_back(ds[i]);
for(int i=1;i<=n;i++)v2.emplace_back(dt[i]);
sort(v1.begin(),v1.end());
sort(v2.begin(),v2.end());
for(auto x:v1){
while(!v2.empty()&&x+v2.back()+l>k)v2.pop_back();
ans+=v2.size();
}
cout << ans;
}
