#include <bits/stdc++.h>
using namespace std;
void setup()
{
// #ifndef ONLINE_JUDGE
// freopen("test.inp", "r", stdin);
// freopen("test.out", "w", stdout);
// #endif
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
}
int n, m, a, b, c, s, t, l;
long long res, k;
long long dist_from_s[200000], dist_from_t[200000];
vector<pair<int, int>> g[200000];
priority_queue<pair<long long, int>> pq;
inline void Dijkstra(int node, long long (&dist)[200000])
{
long long cost;
fill_n(dist, 2e5, 1e18);
dist[node] = 0;
pq.push({0, node});
while (!pq.empty())
{
node = pq.top().second;
cost = -pq.top().first;
pq.pop();
if (dist[node] != cost)
{
continue;
}
for (auto &i : g[node])
{
if (dist[i.first] > cost + i.second)
{
dist[i.first] = cost + i.second;
pq.push({-dist[i.first], i.first});
}
}
}
}
int main()
{
setup();
cin >> n >> m >> s >> t >> l >> k;
while (m--)
{
cin >> a >> b >> c;
g[a - 1].push_back({b - 1, c});
g[b - 1].push_back({a - 1, c});
}
Dijkstra(s - 1, dist_from_s);
Dijkstra(t - 1, dist_from_t);
if (dist_from_s[t - 1] <= k)
{
cout << (long long)n * (n - 1) / 2;
return 0;
}
sort(dist_from_s, dist_from_s + n);
sort(dist_from_t, dist_from_t + n);
for (int i = 0; i < n; ++i)
{
res += upper_bound(dist_from_t, dist_from_t + n, k - l - dist_from_s[i]) - dist_from_t;
}
cout << res;
return 0;
}
