//#pragma GCC optimize("Ofast,unroll-loops,O3")
//#pragma GCC target("avx,avx2,sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,fma,tune=native")
#include <bits/stdc++.h>
#define int long long
#define pii pair<int, int>
#define x first
#define y second
#define N 200015
using namespace std;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int n, m, s, t, l, k, ans = 0;
vector<pii> G[N];
vector<int> dijkstra(int st){
priority_queue<pii, vector<pii>, greater<pii> > pq;
vector<int> dis;
dis.resize(n + 1, 1e18);
dis[st] = 0;
pq.push({dis[st], st});
while (!pq.empty()){
pii now = pq.top(); pq.pop();
if (now.x != dis[now.y])
continue;
for (auto [i, c] : G[now.y]){
if (dis[i] > now.x + c){
dis[i] = now.x + c;
pq.push({dis[i], i});
}
}
}
return dis;
}
signed main(){
ios::sync_with_stdio(0);
cin.tie(0);
cin >> n >> m >> s >> t >> l >> k;
for (int i = 1; i <= m; i++){
int a, b, c;
cin >> a >> b >> c;
G[a].push_back({b, c});
G[b].push_back({a, c});
}
vector<int> dis1 = dijkstra(s);
vector<int> dis2 = dijkstra(t);
vector<int> dis3 = dis2;
if (dis1[t] <= k){
cout << n * (n - 1) / 2 << '\n';
return 0;
}
sort(dis2.begin(), dis2.end());
for (int i = 1; i <= n; i++){
int need = k - dis1[i] - l;
int can = upper_bound(dis2.begin(), dis2.end(), need) - dis2.begin();
ans += can;
if (dis3[i] <= need)
ans--;
}
cout << ans << '\n';
}
