#include <bits/stdc++.h>
using namespace std;
#define F0R(i, n) for (ll i = 0; i < n;i++)
#define FOR(i,j, n) for (ll i = j; i < n;i++)
using ll = long long;
template<typename T>
using V = vector<T>;
using vi = V<ll>;
using pi = pair<ll,ll>;
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
template <class T>
using Tree =
tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
constexpr ll INF = 1e18;
ll solve(const vi &d1,const vi &d2, ll n, ll k) {
V<pair<pi, ll>> updates; // Y, X, type
FOR(i, 1, n + 1) {
updates.emplace_back(make_pair(d1[i], d2[i]), 1ll);
updates.emplace_back(make_pair(k - d2[i] + 1, k - d1[i] + 1),0);
}
std::sort(updates.begin(), updates.end());
std::reverse(updates.begin(), updates.end());
Tree<pi> items;
ll R = 0;
ll ans = 0;
for (auto [p, t] : updates) {
if (t == 1) {
items.insert({p.second,R++ });
}
if (t == 0) {
ans += items.size() - items.order_of_key({p.second, -INF}) - 1; // Self
}
}
ans /= 2;
return n * (n - 1) / 2 - (ans);
}
vi dikstra(ll x, V<V<pi>> &g) {
vi results(g.size(), INF);
priority_queue<pi, V<pi>, greater<>> pq;
pq.emplace(0, x);
while (!pq.empty()) {
auto [d, node] = pq.top(); pq.pop();
if (results[node] != INF) continue;
results[node] = d;
for (auto [y, c] : g[node]) {
if (results[y] != INF) continue;
pq.emplace(c + d, y);
}
}
return results;
}
int main() {
ios_base::sync_with_stdio(false); cin.tie(nullptr);
ll n, m; cin >> n >> m;
ll a, b, t, k; cin >> a >> b >> t >> k;
ll k2 = k;
k -= t;
V<V<pi>> g(n + 1);
F0R(i, m) {
ll x, y, z; cin >> x >> y >> z;
g[x].emplace_back(y,z);
g[y].emplace_back(x,z);
}
vi d1 = dikstra(a, g);
vi d2 = dikstra(b, g);
if (d1[b] <= k2) {
cout << (n * (n - 1)) / 2;
return 0;
}
cout << solve(d1, d2, n, k);
return 0;
}
