#include <bits/stdc++.h>
using namespace std;
#define int long long
int32_t main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int n,m,s,t,l,k;
cin >> n >> m >> s >> t >> l >> k;
vector<vector<pair<int,int>>> adj(n+1);
for(int i=1;i<=m;i++) {
int a,b,c;cin>>a>>b>>c;
adj[a].emplace_back(b,c);
adj[b].emplace_back(a,c);
}
auto dijkastra = [&](int x,vector<int> &ans) {
priority_queue<pair<int,int>> pq;
pq.emplace(0,x);
vector<bool> visited(n+1);
while(!pq.empty()) {
auto [dist,curr] = pq.top();pq.pop();dist=-dist;
if(visited[curr])continue;
visited[curr]=true;
ans[curr]=dist;
for(auto&[x,c]:adj[curr])if(!visited[x])pq.emplace(-dist-c,x);
}
};
vector<int> distFromS(n+1,1e16);
dijkastra(s,distFromS);
vector<int> distFromT(n+1,1e16);
dijkastra(t,distFromT);
if(distFromS[t]<=k) {
cout << n*(n-1)/2 << '\n';
return 0;
}
distFromT.erase(distFromT.begin());
sort(distFromT.begin(), distFromT.end());
int ans = 0;
for(int i=1;i<=n;i++) {
int allowed = k-distFromS[i]-l;
ans+=upper_bound(distFromT.begin(), distFromT.end(), allowed)-distFromT.begin();
}
cout << ans << '\n';
}
