#include<bits/stdc++.h>
using namespace std;
using ll = long long;
#define F first
#define S second
#define all(x) (x).begin(), (x).end()
template<typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p)
{
return os << "(" << p.F << "," << p.S << ")";
}
template<typename T>
void print(const T &v, int lim = 1e9)
{
for(auto x : v)
if(lim-- > 0) cout << x << " ";
cout << "\n";
}
#define int long long
int N, M, S, T, L, K;
using node = pair<ll, ll>;
vector<node> adj[200005];
struct Node {
ll val; // Value of the segment (e.g., sum)
Node *left; // Left child
Node *right; // Right child aa
Node() : val(0), left(nullptr), right(nullptr) {}
};
class DynamicSegmentTree {
private:
Node* root;
ll l_bound, r_bound;
void update(Node*& node, ll l, ll r, ll idx, ll value) {
if (!node) node = new Node();
if (l == r) {
node->val += value;
return;
}
ll mid = l + (r - l) / 2;
if (idx <= mid) {
update(node->left, l, mid, idx, value);
} else {
update(node->right, mid + 1, r, idx, value);
}
node->val = getValue(node->left) + getValue(node->right);
}
ll query(Node* node, ll l, ll r, ll ql, ll qr) {
if (!node || ql > r || qr < l) return 0;
if (ql <= l && r <= qr) {
return node->val;
}
ll mid = l + (r - l) / 2;
return query(node->left, l, mid, ql, qr) + query(node->right, mid + 1, r, ql, qr);
}
ll getValue(Node* node) {
return node ? node->val : 0;
}
public:
DynamicSegmentTree(ll l_bound, ll r_bound) : l_bound(l_bound), r_bound(r_bound), root(nullptr) {}
void update(ll idx, ll value) {
update(root, l_bound, r_bound, idx, value);
}
ll query(ll ql, ll qr) {
return query(root, l_bound, r_bound, ql, qr);
}
};
signed main()
{
ios::sync_with_stdio(0); cin.tie(NULL); cout.tie(NULL);
cin >> N >> M >> S >> T >> L >> K;
for(int i = 0; i < M; i++)
{
int u, v, w;
cin >> u >> v >> w;
adj[u].emplace_back(v, w);
adj[v].emplace_back(u, w);
}
auto dij = [&](int start)
{
priority_queue<node, vector<node> , greater<node>> q;
vector<ll> d(N + 5, 1e17);
d[start] = 0;
q.emplace(0, start);
while(!q.empty())
{
auto [c, v] = q.top(); q.pop();
if(c != d[v]) continue;
for(auto [u, w] : adj[v])
{
if(c + w < d[u])
{
d[u] = c + w;
q.emplace(c + w, u);
}
}
}
return d;
};
auto ds = dij(S);
auto dt = dij(T);
// print(ds);
// print(dt);
ll cnt = 0;
vector<int> vert;
for(int i = 1; i <= N; i++)
vert.push_back(i);
sort(vert.begin(), vert.end(), [&](int v, int u)
{
return ds[v] - dt[v] < ds[u] - dt[u];
});
DynamicSegmentTree st(0, 1e18);
for(int v : vert)
{
// cout <<"node "<< v << " " << dt[v] << " " << ds[v] << endl;
cnt += st.query(0, K - L - dt[v]);
st.update(ds[v], 1);
}
cout << cnt << "\n";
}
