#include <iostream>
#include <vector>
#include <algorithm>
#include <queue>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define forn(i,n) for(int i=0;i<(int)n;++i)
#define SZ(v) (int)v.size()
#define ALL(v) v.begin(),v.end()
using namespace std;
using namespace __gnu_pbds;
template<typename T>
using iset = tree<T,null_type,less<T>,rb_tree_tag,tree_order_statistics_node_update>;
typedef long long ll;
const int MAXN = 200005;
const ll INF = 1000000000000000000;
int n;
vector<pair<int,int>> g[MAXN];
vector<ll> dijkstra(int s){
vector<ll> dist(n, INF);
dist[s] = 0;
priority_queue<pair<ll,int>> pq;
pq.push({0,s});
while(SZ(pq)){
int u = pq.top().second;
ll d = -pq.top().first;
pq.pop();
if(dist[u] != d) continue;
for(auto [v, w]: g[u]){
ll nd = d + w;
if(nd < dist[v]){
dist[v] = nd;
pq.push({-nd, v});
}
}
}
return dist;
}
struct P{
ll a, b;
int i;
bool operator<(const P&o)const{
return a-b<o.a-o.b;
}
};
int main(){
cin.tie(0);
ios::sync_with_stdio(0);
int m, s, t, l;
ll k;
cin>>n>>m>>s>>t>>l>>k;
--s, --t;
while(m--){
int u, v, w;
cin>>u>>v>>w;
--u, --v;
g[u].push_back({v, w});
g[v].push_back({u, w});
}
auto fromS = dijkstra(s);
auto fromT = dijkstra(t);
/*forn(i,n) cerr<<fromS[i]<<" ";
cerr<<endl;
forn(i,n) cerr<<fromT[i]<<" ";
cerr<<endl;*/
vector<P> ps(n);
forn(i,n) ps[i] = {fromS[i],fromT[i],i};
sort(ALL(ps));
iset<pair<ll,int>> pre;
ll ans = 0;
forn(i,n){
ll aux = k - ps[i].b - l + 1;
ans += pre.order_of_key({aux,-1});
pre.insert({ps[i].a,i});
}
cout<<ans<<"\n";
return 0;
}
