#include <bits/stdc++.h>
using i64 = long long;
#ifdef DEBUG
#include "debug.h"
#else
#define debug(...) void(23)
#endif
constexpr i64 inf = i64(1E18);
bool chmin(i64& a, i64 b) {
if (a > b) {
a = b;
return true;
}
return false;
}
int main() {
std::ios_base::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<std::pair<int, int>>> adj(N);
for (int i = 0; i < M; ++i) {
int A, B, C;
std::cin >> A >> B >> C;
--A, --B;
adj[A].emplace_back(B, C);
adj[B].emplace_back(A, C);
}
std::vector<i64> ds(N, inf), dt(N, inf);
std::priority_queue<std::pair<i64, int>, std::vector<std::pair<i64, int>>, std::greater<>> pq;
pq.emplace(ds[S] = 0, S);
while (!pq.empty()) {
auto[d, v] = pq.top();
pq.pop();
if (ds[v] != d) {
continue;
}
for (auto[u, w] : adj[v]) {
if (chmin(ds[u], d + w)) {
pq.emplace(ds[u], u);
}
}
}
pq.emplace(dt[T] = 0, T);
while (!pq.empty()) {
auto[d, v] = pq.top();
pq.pop();
if (dt[v] != d) {
continue;
}
for (auto[u, w] : adj[v]) {
if (chmin(dt[u], d + w)) {
pq.emplace(dt[u], u);
}
}
}
debug(ds);
debug(dt);
if (ds[T] <= K) {
i64 all_edges = 1LL * N * (N - 1) / 2;
std::cout << all_edges << '\n';
return 0;
}
std::vector<i64> vv;
for (int v = 0; v < N; ++v) {
if (dt[v] != -1) {
vv.emplace_back(dt[v]);
}
}
std::sort(vv.begin(), vv.end());
i64 ans = 0;
for (int v = 0; v < N; ++v) {
if (ds[v] == -1) {
continue;
}
i64 new_ds = ds[v] + L;
if (new_ds <= K) {
auto it = std::upper_bound(vv.begin(), vv.end(), K - new_ds);
ans += it - vv.begin();
}
}
std::cout << ans << '\n';
return 0;
}
