#include <bits/stdc++.h>
using namespace std;
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
int n,m,s,t,c0,a,b,c;
cin >> n >> m;
long long k, odl[n+1][2], odp = 0;
cin >> s >> t >> c0 >> k;
vector<pair<int,int>> g[n+1];
for (int i = 0; i < m; i++)
cin >> a >> b >> c, g[a].push_back({b,c}), g[b].push_back({a,c});
bool odw[n+1];
for (int i = 1; i <= n; i++)
odw[i] = false, odl[i][0] = odl[i][1] = 1000000000000000000;
priority_queue<pair<long long,int>,vector<pair<long long,int>>,greater<pair<long long,int>>> q;
odl[s][0] = odl[t][1] = 0, q.push({0,s});
while (!q.empty()) {
long long d = q.top().first;
int v = q.top().second; q.pop();
if (odw[v])
continue;
odw[v] = true;
for (auto e : g[v])
if (odl[e.first][0] > d+e.second)
odl[e.first][0] = d+e.second, q.push({d+e.second,e.first});
}
if (odl[t][0] <= k)
odp = 1ll*n*(n-1)/2;
else {
fill(odw,odw+n+1,false), q.push({0,t});
while (!q.empty()) {
long long d = q.top().first;
int v = q.top().second; q.pop();
if (odw[v])
continue;
odw[v] = true;
for (auto e : g[v])
if (odl[e.first][1] > d+e.second)
odl[e.first][1] = d+e.second, q.push({d+e.second,e.first});
}
vector<long long> v;
for (int i = 1; i <= n; i++)
v.push_back(odl[i][1]);
sort(v.begin(),v.end());
for (int i = 1; i <= n; i++) {
int l = 0, r = n-1;
while (l < r) {
int mid = (l+r)/2;
if (odl[i][0]+v[mid]+c0 > k)
r = mid;
else
l = mid+1;
}
odp += l;
}
}
cout << odp << endl;
return 0;
}
