#include <bits/stdc++.h>
using namespace std;
typedef unsigned long long ull;
typedef long long ll;
typedef long double db;
#define int ll
#define all(x) (x).begin(), (x).end()
#define md ((tl + tr) >> 1)
#define TL v + v, tl, md
#define TR v + v + 1, md + 1, tr
#define Tl t[v].l, tl, md
#define Tr t[v].r, md + 1, tr
constexpr int maxn = 1'000'007;
constexpr ll inf = 1e18 + 7;
constexpr ll M = 998244353;
int binpow(int a, int n) {
if (n == 0)
return 1;
if (n & 1)
return a * binpow(a, n - 1) % M;
int x = binpow(a, n >> 1);
return x * x % M;
}
const int dx[4] = {-1, 0, 1, 0};
const int dy[4] = {0, 1, 0, -1};
const db eps = 0.000000000000001;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int random(int l, int r) {
return uniform_int_distribution<int>(l, r)(rng);
}
int n, m, s, t, l, k, ds[maxn], dt[maxn];
vector<pair<int, int>> g[maxn];
void solve() {
cin >> n >> m >> s >> t >> l >> k;
for (int i = 1; i <= m; i++) {
int a, b, c;
cin >> a >> b >> c;
g[a].emplace_back(b, c);
g[b].emplace_back(a, c);
}
for (int i = 1; i <= n; i++) {
ds[i] = dt[i] = inf;
}
set<pair<int, int>> q;
ds[s] = 0;
q.insert({0, s});
while (!q.empty()) {
int v = q.begin()->second;
q.erase(q.begin());
for (auto [to, len] : g[v]) {
if (ds[v] + len < ds[to]) {
q.erase({ds[to], to});
ds[to] = ds[v] + len;
q.insert({ds[to], to});
}
}
}
q.clear();
dt[t] = 0;
q.insert({0, t});
while (!q.empty()) {
int v = q.begin()->second;
q.erase(q.begin());
for (auto [to, len] : g[v]) {
if (dt[v] + len < dt[to]) {
q.erase({dt[to], to});
dt[to] = dt[v] + len;
q.insert({dt[to], to});
}
}
}
if (ds[t] <= k) {
cout << n * (n - 1) / 2;
return;
}
vector<int> vs, vt;
for (int i = 1; i <= n; i++) {
vs.push_back(ds[i]);
vt.push_back(dt[i]);
}
sort(all(vs)), sort(all(vt));
int ans = 0;
int j = n - 1;
for (int i = 0; i < n; i++) {
while (j >= 0 && vs[i] + vt[j] + l > k) {
j--;
}
ans += j + 1;
}
cout << ans;
}
signed main() {
// freopen("qi.in", "r", stdin);
// freopen("qi.out", "w", stdout);
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cout.tie(nullptr);
int test = 1;
// cin >> test;
while (test--) {
solve();
// cout << '\n';
}
return 0;
}
