#include <bits/stdc++.h>

#define int int64_t

const int kMaxN = 2e5 + 5;

int n, m, s, t, l, k;
int dis1[kMaxN], dis2[kMaxN];
std::vector<std::pair<int, int>> G[kMaxN];

void dijkstra(int s, int *dis) {
  static bool vis[kMaxN];
  for (int i = 1; i <= n; ++i)
    dis[i] = 1e18, vis[i] = 0;
  std::priority_queue<std::pair<int, int>> q;
  q.emplace(0, s), dis[s] = 0;
  for (; !q.empty();) {
    int u = q.top().second; q.pop();
    if (vis[u]) continue;
    vis[u] = 1;
    for (auto [v, w] : G[u]) {
      if (dis[v] > dis[u] + w) {
        dis[v] = dis[u] + w;
        q.emplace(-dis[v], v);
      }
    }
  }
}

void dickdreamer() {
  std::cin >> n >> m >> s >> t >> l >> k;
  for (int i = 1; i <= m; ++i) {
    int u, v, w;
    std::cin >> u >> v >> w;
    G[u].emplace_back(v, w), G[v].emplace_back(u, w);
  }
  dijkstra(s, dis1), dijkstra(t, dis2);
  if (dis1[t] <= k) return void(std::cout << 1ll * n * (n - 1) / 2 << '\n');
  int ans = 0;
  for (int i = 1; i <= n; ++i)
    for (int j = i + 1; j <= n; ++j)
      if (dis1[i] + dis2[j] + l <= k || dis1[j] + dis2[i] + l <= k)
        ++ans;
  std::cout << ans << '\n';
}

int32_t main() {
#ifdef ORZXKR
  freopen("in.txt", "r", stdin);
  freopen("out.txt", "w", stdout);
#endif
  std::ios::sync_with_stdio(0), std::cin.tie(0), std::cout.tie(0);
  int T = 1;
  // std::cin >> T;
  while (T--) dickdreamer();
  // std::cerr << 1.0 * clock() / CLOCKS_PER_SEC << "s\n";
  return 0;
}