#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
#define g0(x) get<0>(x)
#define g1(x) get<1>(x)
#define g2(x) get<2>(x)
#define pb push_back
#define int long long
#define f first
#define s second
#define pll pair<long long, long long>
vector<vector<pll>> al(200005);
int n,m,s,t,l,k;
//~ int fw[200005];
int pitr[200005];
vector<pll> dists(200005,{LLONG_MAX, LLONG_MAX}), distt(200005, {LLONG_MAX, LLONG_MAX});
//~ void upd(int x, int v){
//~ if(x==0)assert(false);
//~ while(x<=n){
//~ fw[x]+=v;
//~ x+=(x&-x);
//~ }
//~ }
//~ int qry(int x){
//~ int ret=0;
//~ while(x>0){
//~ ret+=fw[x];
//~ x-=(x&-x);
//~ }
//~ return ret;
//~ }
void dijkstra(int x, vector<pll> & dist){
//~ for(int i=1; i<=n;i++)dist[i].f=1e16, dist[i].s=i;
//~ dist[x].f=0;
//~ queue<int> q;
//~ q.push(x);
//~ while(!q.empty()){
//~ int c=q.front();
//~ q.pop();
//~ cout<<c<<endl;
//~ for(auto it:al[c]){
//~ if(dist[it.f].f>dist[c].f+1){
//~ dist[it.f].f=dist[c].f+1;
//~ q.push(it.f);
//~ }
//~ }
//~ }
for(int i=1; i<=n;i++)dist[i].f=1e16, dist[i].s=i;
dist[x].f=0;
priority_queue<pll,vector<pll>,greater<pll>> pq;
pq.push({0, x});
while(!pq.empty()){
auto [d,c]=pq.top();
//~ printf("at %lld \n", c);
pq.pop();
if(dist[c].f<d)continue;
for(auto [u, v]:al[c]){
if(dist[u].f<=d+v)continue;
dist[u].f=d+v;
pq.push({dist[u].f,u});
}
}
}
signed main(){
ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
cin>>n>>m>>s>>t>>l>>k;
for(int i=0;i<m;i++){
int a,b,c;cin>>a>>b>>c;
al[a].pb({b,c});
al[b].pb({a,c});
}
dijkstra(s, dists);
dijkstra(t, distt);
if(dists[t].f <= k){
cout<<(n*(n-1))/2;
return 0;
}
sort(dists.begin(), dists.end());
sort(distt.begin(),distt.end());
for(int i=0;i<n;i++){
pitr[distt[i].s]=i+1;
}
//~ for(int i=0;i<n;i++){
//~ cout<<dists[i].f<<" "<<dists[i].s<<" |";
//~ }cout<<endl;
//~ for(int i=0;i<n;i++){
//~ cout<<distt[i].f<<" "<<distt[i].s<<" |";
//~ }cout<<endl;
//~ for(int i=1;i<=n;i++){
//~ cout<<pitr[i]<<" ";
//~ }cout<<endl;
int ans=0, cur=0, ptr=0;
bool tcov[n+1]; fill(tcov, tcov+n+1, false);
bool scov[n+1]; fill(scov, scov+n+1, false);
for(int i=n-1;i>=0;i--){
while(ptr<n and distt[ptr].f + dists[i].f + l <= k){
tcov[distt[ptr].s]=1;
if(!scov[distt[ptr].s])cur++;
ptr++;
}
scov[dists[i].s]=1;
if(tcov[dists[i].s])cur++;
//~ printf("i %lld, ptr %lld, cur %lld\n", i, ptr, cur);
ans+=max(0ll, ptr-cur);
}
cout<<ans;
}
