// File construcproj2.cpp created on 28.09.2025 at 19:27:47
#include <bits/stdc++.h>
using i64 = long long;
#ifdef DEBUG
#include "/home/ahmetalp/Desktop/Workplace/debug.h"
#else
#define debug(...) void(23)
#endif
constexpr i64 inf = i64(1E18);
template<typename T>
bool chmin(T& a, T b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template<typename T>
using min_pq = std::priority_queue<T, std::vector<T>, std::greater<T>>;
int main() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
int N, M;
std::cin >> N >> M;
int S, T, L;
i64 K;
std::cin >> S >> T >> L >> K;
--S, --T;
std::vector<std::vector<int>> adj(N);
std::vector<std::array<int, 3>> E(M);
for (int i = 0; i < M; ++i) {
std::cin >> E[i][0] >> E[i][1] >> E[i][2];
--E[i][0], --E[i][1];
adj[E[i][0]].emplace_back(i);
adj[E[i][1]].emplace_back(i);
}
auto dijsktra = [&](int st) -> std::vector<i64> {
min_pq<std::pair<int, int>> pq;
std::vector<i64> dis(N, inf);
pq.emplace(dis[st] = 0, st);
while (!pq.empty()) {
auto[d, v] = pq.top();
pq.pop();
if (dis[v] != d) {
continue;
}
for (auto i : adj[v]) {
int u = E[i][0] ^ E[i][1] ^ v;
if (chmin(dis[u], dis[v] + E[i][2])) {
pq.emplace(dis[u], u);
}
}
}
return dis;
};
auto dS = dijsktra(S);
auto dT = dijsktra(T);
if (dS[T] <= K) {
i64 ans = 1LL * N * (N - 1) / 2;
std::cout << ans << '\n';
return 0;
}
i64 ans = 0;
std::sort(dS.begin(), dS.end());
std::sort(dT.begin(), dT.end());
debug(dS);
debug(dT);
int p = N - 1;
for (int i = 0; i < N; ++i) {
while (p != -1 && dT[p] + dS[i] + L > K) {
p--;
}
ans += p + 1;
}
std::cout << ans << '\n';
return 0;
}
