#include <bits/stdc++.h>
#define F first
#define S second
#define speed ios_base::sync_with_stdio(0);cin.tie(0)
#define all(x) x.begin()+1, x.end()
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
template<class T>
using vvector = vector<vector<T>>;
const ll oo =0x3f3f3f3f3f3f3f3f;
void DJ(ll st,ll n,vvector<pll> &G,vector<ll> &dis) {
vector<bool> vis(n+1);
priority_queue<pll> Q;
Q.push({0ll,st});
dis[st]=0;
while (!Q.empty()) {
while (!Q.empty() and vis[Q.top().S]) Q.pop();
if (Q.empty()) break;
auto [dd,v]=Q.top();
Q.pop();
vis[v]=true;
for (auto [i,w]:G[v]) {
if (dis[i]>dis[v]+w) {
dis[i]=dis[v]+w;
Q.push({-dis[i],i});
}
}
}
}
int main() {
speed;
ll n,m;
cin>>n>>m;
ll s,t,l,k;
cin>>s>>t>>l>>k;
vvector<pll> G(n+1);
for (int i=1;i<=m;i++) {
ll a,b,w;
cin>>a>>b>>w;
G[a].emplace_back(b,w);
G[b].emplace_back(a,w);
}
vector<ll> d1(n+1,oo);
DJ(s,n,G,d1);
vector<ll> d2(n+1,oo);
DJ(t,n,G,d2);
if (d1[t]<=k) {
cout<<n*(n-1)/2<<"\n";
return 0;
}
ll ans=0;
sort(all(d1));
sort(all(d2));
// for (int i=1;i<=n;i++) cout<<d1[i]<<" ";
// cout<<"\n";
// for (int i=1;i<=n;i++) cout<<d2[i]<<" ";
// cout<<"\n";
ll id2=n;
for (ll i=1;i<=n;i++) {
while (id2>=1 and d2[id2]+d1[i]+l>k) id2--;
ans+=id2;
}
cout<<ans<<"\n";
return 0;
}
/*
3 2
1 3 1 1
1 2 1
2 3 1
*/
