#include <bits/stdc++.h>
#define int long long
#define MULTITEST false
using namespace std;
const int INF = 5e17;
struct Road {
int a, b, cost;
int next (int u) {
return u == a ? b : a;
}
};
vector<Road> road_list;
vector<vector<int>> roads;
int N;
struct point {
int x, y;
int sum_weight;
int res_weight;
bool operator< (const point &other) {
if (x != other.x) return x > other.x;
if (y != other.y) return y > other.y;
return sum_weight > other.sum_weight;
}
};
map<int, int> ccp (vector<int> vals) {
set<int> u;
for (int i : vals) u.insert(i);
map<int, int> res;
int off = 0;
for (int i : u)
res[i] = off ++;
return res;
}
struct SegTree {
vector<int> tree;
int size, start, height;
SegTree (int _size) {
size = _size;
height = ceil(log2(size));
start = 1 << height;
tree.resize(start << 1);
}
void update (int i, int d) {
i += start;
while (i != 0) {
tree[i] += d;
i >>= 1;
}
}
int query (int l) {
int r = size;
l += start;
r += start;
int res = 0;
while (l < r) {
if ((l & 1) == 1) res += tree[l];
if ((r & 1) == 0) res += tree[r];
l = (l + 1) >> 1;
r = (r - 1) >> 1;
}
if (l == r) res += tree[l];
return res;
}
};
int sum_qp (vector<point> points, int delta) {
vector<int> px, py;
for (auto p : points) { px.push_back(p.x); py.push_back(p.y); }
map<int, int> mx = ccp(px);
map<int, int> my = ccp(py);
for (auto &p : points) {
p.x = mx[p.x];
p.y = my[p.y];
}
sort(points.begin(), points.end());
SegTree tree(my.size());
int res = 0;
for (auto p : points) {
res += p.res_weight * tree.query(p.y);
tree.update(p.y, p.sum_weight);
}
return (res - delta) >> 1;
}
vector<int> dijkstra (int start) {
priority_queue<pair<int, int>> queue;
vector<int> distances(N, INF);
distances[start] = 0;
queue.push({ 0, start });
while (queue.size() != 0) {
pair<int, int> u = queue.top();
queue.pop();
int curr = u.second;
int dist = - u.first;
if (distances[curr] != dist) continue ;
for (int r_id : roads[curr]) {
int next = road_list[r_id].next(curr);
int cost = dist + road_list[r_id].cost;
if (distances[next] <= cost) continue ;
distances[next] = cost;
queue.push({ - cost, next });
}
}
return distances;
}
void solve () {
cin >> N;
int M; cin >> M;
int s, t, l, k;
cin >> s >> t >> l >> k;
s --; t --;
roads.resize(N);
for (int i = 0; i < M; i ++) {
int a, b, c;
cin >> a >> b >> c;
a --,
b --;
road_list.push_back({ a, b, c });
roads[a].push_back(i);
roads[b].push_back(i);
}
int count = (N * (N - 1)) >> 1;
vector<int> d_s = dijkstra(s);
vector<int> d_t = dijkstra(t);
if (d_s[t] <= k) {
cout << count << "\n";
return ;
}
sort(d_t.begin(), d_t.end());
count = 0;
for (int i = 0; i < N; i ++) {
int a = -1;
int b = N;
while (b - a > 1) {
int m = (a + b) >> 1;
if (d_s[i] + l + d_t[m] <= k) a = m;
else b = m;
}
count += a + 1;
}
cout << count << "\n";
}
signed main () {
ios_base::sync_with_stdio(false); cin.tie(NULL);
int T = 1;
if (MULTITEST) cin >> T;
for (int t = 0; t < T; t ++) solve();
}
