/* Author : Mychecksdead */
#include<bits/stdc++.h>
using namespace std;
#define ll long long int
#define MOD (1000000000+7)
#define MOD1 (998244353)
#define pb push_back
#define all(x) x.begin(), x.end()
#define en cout << '\n'
#define ff first
#define ss second
#define pii pair<int,int>
#define vi vector<int>
const int N = 1e6+100, M = 1e5+10, K = 52, MX = 30;
ll n, m, s, t, k, l;
vector<pair<int, ll>> g[N];
void solve(){
cin >> n >> m >> s >> t >> l >> k;
--s,--t;
for(int i = 1; i <= m; ++i){
int u, v, w; cin >>u >> v >> w;
--u,--v;
g[u].pb({v, w});
g[v].pb({u, w});
}
priority_queue<pair<ll,int>>Q;
vector<ll> dist(n, (ll)1e18*1ll);
vector<ll> dist2(n, (ll)1e18*1ll);
vector<bool> used(n);
Q.push({0, s});
dist[s] = 0;
while(!Q.empty()){
int v = Q.top().ss; Q.pop();
if(used[v]) continue;
used[v] = 1;
for(auto [u, w]: g[v]){
if(dist[u] > dist[v] + w){
dist[u] = dist[v] + w;
Q.push({-dist[u], u});
}
}
}
fill(all(used), 0);
Q.push({0, t});
dist2[t] = 0;
while(!Q.empty()){
int v = Q.top().ss; Q.pop();
if(used[v]) continue;
used[v] = 1;
for(auto [u, w]: g[v]){
if(dist2[u] > dist2[v] + w){
dist2[u] = dist2[v] + w;
Q.push({-dist2[u], u});
}
}
}
if(dist[t] <= k){
cout << n*(n-1)/2;
}else{
ll ans=0;
sort(all(dist));
sort(all(dist2));
for(ll x: dist){
ans += upper_bound(all(dist2), k - l - x) - dist2.begin();
}
cout<<ans;
}
}
int main(){
cin.tie(0); ios::sync_with_stdio(0);
int tt = 1, aa;
// freopen("in.txt", "r", stdin);
// freopen("out.txt", "w", stdout);
while(tt--){
solve();
en;
}
cerr<<"time taken : "<<(float)clock()/CLOCKS_PER_SEC<<" seconds\n";
return 0;
}
