#include <bits/stdc++.h>
using namespace std;
#define ll long long int
vector<pair<ll, int>> adj[200005];
int v1[200005];
int v2[200005];
int main()
{
cin.tie(0);
ios_base::sync_with_stdio(NULL);
ll N,M,S,T;
ll L,K;
cin>>N>>M>>S>>T>>L>>K;
S--;T--;
ll d1[N];
ll d2[N];
for (int i=0;i<N;i++) {
d1[i] = LLONG_MAX/2;
d2[i] = LLONG_MAX/2;
}
for (int i=0;i<M;i++) {
int i1,i2;
ll i3;
cin>>i1>>i2>>i3;
i1--;i2--;
adj[i1].push_back(make_pair(i3,i2));
adj[i2].push_back(make_pair(i3,i1));
}
d1[S] = 0;
priority_queue<pair<ll,int>, vector<pair<ll, int>>, greater<pair<ll,int>>> pq;
pq.push(make_pair(0,S));
while (!pq.empty()) {
ll l = pq.top().first;
ll u = pq.top().second;
pq.pop();
if (v1[u]) {continue;}
for (auto pp:adj[u]) {
if (d1[pp.second]>d1[u]+pp.first) {
d1[pp.second] = d1[u]+pp.first;
pq.push(make_pair(d1[u]+pp.first, pp.second));
}
}
}
pq.push(make_pair(0,T));
d2[T] = 0;
while (!pq.empty()) {
ll l = pq.top().first;
ll u = pq.top().second;
pq.pop();
if (v2[u]) {continue;}
for (auto pp:adj[u]) {
if (d2[pp.second]>d2[u]+pp.first) {
d2[pp.second] = d2[u]+pp.first;
pq.push(make_pair(d2[u]+pp.first, pp.second));
}
}
}
sort(d2, d2+N);
ll ans=0;
if (d1[T]<=K) {
cout << (N*(N-1))/2LL;
return 0;
}
for (int i=0;i<N;i++) {
ans+=max(upper_bound(d2,d2+N, K-L-d1[i])-d2, 0L);
}
cout << ans;
return 0;
}
/*
6 4
2 5 10 1
1 2 10
2 3 10
2 4 10
5 6 10
*/
