#include <bits/stdc++.h>
#define int long long
#define pii pair <int, int>
using namespace std;
const int maxN = 2e5 + 5;
const int inf = 1e18 + 7;
struct Edge {
int u, v, w;
};
int n, m;
int S, T, l, K;
vector <pii> adj[maxN];
vector <Edge> allE;
namespace sub3 {
int L[maxN][2];
inline void dijkstra (int st, int t) {
priority_queue <pii, vector <pii>, greater <pii>> pq;
for (int i = 1; i <= n; i ++) {
L[i][t] = inf;
}
L[st][t] = 0;
pq.push ({L[st][t], st});
while (!pq.empty ()) {
auto [c, u] = pq.top ();
pq.pop ();
if (c > L[u][t]) {
continue;
}
for (auto [v, w] : adj[u]) {
if (L[v][t] > L[u][t] + w) {
L[v][t] = L[u][t] + w;
pq.push ({L[v][t], v});
}
}
}
return;
}
inline void sol () {
dijkstra (S, 0);
dijkstra (T, 1);
int minDist = L[T][0];
if (minDist <= K) {
cout << n * (n - 1) / 2;
return;
}
int res = 0;
for (int i = 1; i <= n; i ++) {
for (int j = i + 1; j <= n; j ++) {
if (min (L[i][0] + L[j][1] + l, L[i][1] + L[j][0] + l) <= K) {
res ++;
}
}
}
cout << res;
return;
}
}
namespace sub4 {
int L[maxN][2];
inline void dijkstra (int st, int t) {
priority_queue <pii, vector <pii>, greater <pii>> pq;
for (int i = 1; i <= n; i ++) {
L[i][t] = inf;
}
L[st][t] = 0;
pq.push ({L[st][t], st});
while (!pq.empty ()) {
auto [c, u] = pq.top ();
pq.pop ();
if (c > L[u][t]) {
continue;
}
for (auto [v, w] : adj[u]) {
if (L[v][t] > L[u][t] + w) {
L[v][t] = L[u][t] + w;
pq.push ({L[v][t], v});
}
}
}
return;
}
inline void sol () {
dijkstra (S, 0);
dijkstra (T, 1);
int minDist = L[T][0];
if (minDist <= K) {
cout << n * (n - 1) / 2;
return;
}
int res = 0;
vector <int> d0, d1;
for (int i = 1; i <= n; i ++) {
d0.push_back (L[i][0]);
}
sort (d0.begin (), d0.end ());
for (int i = 1; i <= n; i ++) {
auto it = upper_bound (d0.begin (), d0.end (), L[i][1] + l - K) - d0.begin ();
res += it;
}
cout << res;
return;
}
}
signed main () {
ios_base :: sync_with_stdio (0);
cin.tie (0);
cin >> n >> m;
cin >> S >> T >> l >> K;
for (int i = 1; i <= m; i ++) {
int u, v, c;
cin >> u >> v >> c;
adj[u].push_back ({v, c});
adj[v].push_back ({u, c});
allE.push_back ({u, v, c});
}
sub4 :: sol ();
}
