#include <bits/stdc++.h>
#define int long long
using namespace std;
signed main() {
int n, m, s, t, l, k; cin >> n >> m >> s >> t >> l >> k; s--, t--;
vector<vector<pair<int,int>>> adj(n);
for(int i=0;i<m;i++) {
int x, y, z; cin >> x >> y >> z; x--, y--;
adj[x].push_back({y,z}), adj[y].push_back({x,z});
}
vector<int> ds(n,1e18), dt(n,1e18); vector<bool> ps(n), pt(n);
ds[s] = 0, dt[t] = 0; priority_queue<pair<int,int>> q; q.push({0,s});
while(!q.empty()) {
int a = q.top().second; q.pop();
if(ps[a]) continue; ps[a] = true;
for(auto u:adj[a]) {
int b = u.first, w = u.second;
if(ds[a]+w < ds[b]) {ds[b] = ds[a]+w; q.push({-ds[b],b});}
}
}
q.push({0,t}); while(!q.empty()) {
int a = q.top().second; q.pop();
if(pt[a]) continue; pt[a] = true;
for(auto u:adj[a]) {
int b = u.first, w = u.second;
if(dt[a]+w < dt[b]) {dt[b] = dt[a]+w; q.push({-dt[b],b});}
}
}
if(ds[t] <= k) {cout << n*(n-1)/2; return 0;}
sort(begin(ds),end(ds)), sort(begin(dt),end(dt));
int ans = 0, y = n-1;
for(int i=0;i<n;i++) {while(y >= 0 && dt[y]+ds[i] > k-l) y--; ans += y+1;}
cout << ans;
}
