// In honor of El Psy Congroo
//#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
#include <random>
#include <chrono>
using namespace std;
#pragma GCC optimize("O3")
// variables
using ld = long double;
using ll = long long;
using ull = unsigned long long;
template<typename T>
using min_heap = priority_queue<T, vector<T>, greater<T>>;
// bitwise operations
#define cnt_bit(n) __builtin_popcountll(n)
#define low_bit(n) ((n) & (-(n)))
#define bit(n, i) (((n) >> (i)) & 1)
#define set_bit(n, i) ((n) | (1ll << (i)))
#define reset_bit(n, i) ((n) & ~(1ll << (i)))
#define flip_bit(n, i) ((n) ^ (1ll << (i)))
// math
#define sqr(n) ((n) * (n))
int log2_floor(ull n) {
return n ? __builtin_clzll(1) - __builtin_clzll(n) : -1;
}
// vector
#define len(x) (int) x.size()
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
template <typename T>
istream& operator>>(istream& is, vector<T>& v) {
for(auto& el : v) {
is >> el;
}
return is;
}
template <typename T>
ostream& operator<<(ostream& os, const vector<T>& v) {
for (int i = 0; i < len(v); i++) {
if (i) os << ' ';
os << v[i];
}
return os;
}
template<class... Args>
auto create(size_t n, Args&&... args) {
if constexpr(sizeof...(args) == 1) {
return vector(n, args...);
}
else {
return vector(n, create(args...));
}
}
template<typename T>
void remove_dups(vector<T>& v) {
sort(v.begin(), v.end());
v.erase(unique(v.begin(), v.end()), v.end());
}
// random
mt19937 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
//////solution start//////
void solve() {
int n, m;
cin >> n >> m;
int s, t, l;
ll k;
cin >> s >> t >> l >> k;
s--, t--;
vector<vector<pair<int, int>>> g(n);
for (int i = 0; i < m; i++) {
int v, u, w;
cin >> v >> u >> w;
v--, u--;
g[v].emplace_back(u, w);
g[u].emplace_back(v, w);
}
auto dijkstra = [&] (int start) {
vector<optional<ll>> dist(n);
vector<ll> val;
dist[start] = 0;
min_heap<pair<ll, int>> pq;
pq.emplace(*dist[start], start);
while (!pq.empty()) {
auto [dist_v, v] = pq.top();
pq.pop();
if (dist[v] != dist_v) continue;
val.push_back(*dist[v]);
for (auto [u, w] : g[v]) {
if (dist[u].has_value() && *dist[u] < *dist[v] + w) continue;
dist[u] = *dist[v] + w;
pq.emplace(*dist[u], u);
}
}
return make_pair(dist, val);
};
auto [dist_s, val_s] = dijkstra(s);
auto [dist_t, val_t] = dijkstra(t);
if (dist_s[t].has_value() && dist_s[t] <= k) {
cout << n * 1ll * (n - 1) / 2;
return;
}
ll ans = 0;
int i = 0, j = len(val_t);
while (i < len(val_s)) {
while (j > 0 && val_s[i] + val_t[j - 1] + l > k) {
j--;
}
ans += j;
i++;
}
cout << ans << '\n';
}
//////solution end//////
signed main() {
ios_base::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
int tt = 1;
//cin >> tt;
for (int i = 1; i <= tt; i++) {
solve();
}
}
