#include <bits/stdc++.h>
using namespace std;
#pragma GCC optimize("Ofast,unroll-loops,no-stack-protector")
#pragma GCC target("avx2")
#define int int64_t
const int inf=1e18;
#ifdef LOCAL
#include "algo/debug.h"
#else
template <typename... Args>
void dummy(Args&&... args){}
#define ps dummy
#endif
#define f first
#define s second
template<class T> using V = vector<T>;
using vi = V<int>;
using vb = V<bool>;
using vs = V<string>;
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define len(x) (int)((x).size())
#define rsz resize
#define ins insert
#define ft front()
#define bk back()
#define pb push_back
#define lb lower_bound
#define ub upper_bound
#define ai2 array<int,2>
#define ai3 array<int,3>
#define ai4 array<int,4>
#define ai5 array<int,5>
template<class T> int lwb(const V<T>& a, const T& b) { return lb(all(a),b)-begin(a); }
template<class T> int upb(const V<T>& a, const T& b) { return ub(all(a),b)-begin(a); }
template<class T> bool ckmin(T& a, const T& b) { return a > b ? a=b, true : false; }
template<class T> bool ckmax(T& a, const T& b) { return a < b ? a=b, true : false; }
#define pct __builtin_popcountll
#define ctz __builtin_ctzll
#define clz __builtin_clzll
constexpr int p2(int x) { return (int)1 << x; }
constexpr int bits(int x) { return x == 0 ? 0 : 63-clz(x); } // floor(log2(x))
template<class T>void UNIQUE(V<T>& v) { sort(all(v)); v.erase(unique(all(v)),end(v)); }
template<class T,class U>void erase(T& t, const U& u) { auto it = t.find(u); assert(it != end(t)); t.erase(it); }
template<class F> struct y_combinator_result {
F f;
template<class T> explicit y_combinator_result(T &&f): f(std::forward<T>(f)) {}
template<class ...Args> decltype(auto) operator()(Args &&...args) { return f(std::ref(*this), std::forward<Args>(args)...); }
};
template<class Fun> decltype(auto) yy(Fun &&fun) { return y_combinator_result<std::decay_t<Fun>>(std::forward<Fun>(fun)); }
template<class T> using pqg = priority_queue<T,vector<T>,greater<T>>;
void solve() {
int n, m; cin >> n >> m;
int s, t, L, K; cin >> s >> t >> L >> K; s--; t--;
V<V<ai2>> g(n);
for (int i = 0; i < m; i++) {
int u, v, w; cin >> u >> v >> w; u--; v--;
g[u].pb({ v, w }); g[v].pb({ u, w });
}
auto dij = [&](int s) {
vi d(n, inf);
d[s] = 0;
pqg<ai2> q;
q.push({ 0, s });
vb processed(n);
while (len(q)) {
auto [e, u] = q.top(); q.pop();
if (processed[u]) continue;
processed[u] = true;
for (auto [v, w] : g[u]) if (ckmin(d[v], e + w)) {
q.push({ d[v], v });
}
}
return d;
};
vector d = { dij(s), dij(t) };
if (d[0][t] <= K) {
cout << n * (n - 1) / 2 << '\n';
return;
}
K -= L;
auto p = d[0], q = d[1];
sort(all(p));
sort(all(q));
int ans = 0;
int j = 0;
for (int i = len(p) - 1; i >= 0; i--) {
while (j < len(q) && p[i] + q[j] <= K) {
j++;
}
ans += j;
}
cout << ans << '\n';
}
signed main() {
ios::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
solve();
return 0;
}
