#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll, ll> pii;
const ll INF = 1e18 + 7;
int main() {
ll n, m;
cin >> n >> m;
ll s, t, l, k;
cin >> s >> t >> l >> k;
s--; t--;
vector<vector<pii>> csucsok(n, vector<pii>());
for(ll i = 0; i < m; i++){
ll a, b, c;
cin >> a >> b >> c;
a--; b--;
csucsok[a].push_back({b, c});
csucsok[b].push_back({a, c});
}
vector<ll> tTol(n, INF);
vector<bool> bejart(n);
priority_queue<pii/*, vector<pii>, greater<pii>*/> bejar;
bejar.push({0, t});
tTol[t] = 0;
while(!bejar.empty()){
ll akt = bejar.top().second;
bejar.pop();
if(bejart[akt]) continue;
bejart[akt] = 1;
for(pii x : csucsok[akt]){
if(bejart[x.first]) continue;
if(tTol[x.first] > tTol[akt] + x.second){
tTol[x.first] = tTol[akt] + x.second;
bejar.push({-tTol[x.first], x.first});
}
}
}
vector<ll> sTol(n, INF);
bejart.assign(n, 0);
bejar.push({0, s});
sTol[s] = 0;
while(!bejar.empty()){
ll akt = bejar.top().second;
bejar.pop();
if(bejart[akt]) continue;
bejart[akt] = 1;
for(pii x : csucsok[akt]){
if(bejart[x.first]) continue;
if(sTol[x.first] > sTol[akt] + x.second){
sTol[x.first] = sTol[akt] + x.second;
bejar.push({-sTol[x.first], x.first});
}
}
}
if(sTol[t] <= k){
cout << n*(n - 1) / 2 << "\n";
return 0;
}
sort(tTol.begin(), tTol.end(), greater<ll>());
sort(sTol.begin(), sTol.end());
ll ind = 0;
ll ans = 0;
for(ll i = 0; i < n; i++){
while(ind < tTol.size() && sTol[i] + tTol[ind] + l > k){
ind++;
}
ans += n - ind;
}
cout << ans << "\n";
}
