#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define MOD 998244353
const int N = 200005;
vector<pair<ll, ll>> g[N];
void solve()
{
ll n, m, s, t, l, k, u, v, c, ans = 0;
cin >> n >> m;
cin >> s >> t >> l >> k;
vector<ll> dists(n + 1), distt(n + 1);
for (int i = 0; i < m; i++)
{
cin >> u >> v >> c;
g[u].push_back({v, c});
g[v].push_back({u, c});
}
priority_queue<pair<ll, ll>, vector<pair<ll, ll>>, greater<pair<ll, ll>>> pq;
for (int i = 0; i <= n; i++)
{
dists[i] = 1e18;
distt[i] = 1e18;
}
dists[s] = 0;
pq.push({s, 0});
while (!pq.empty())
{
auto [u, w] = pq.top();
pq.pop();
for (auto [i, j] : g[u])
{
if (dists[u] + j < dists[i])
{
dists[i] = dists[u] + j;
pq.push({i, dists[i]});
}
}
}
distt[t] = 0;
pq.push({t, 0});
while (!pq.empty())
{
auto [u, w] = pq.top();
pq.pop();
for (auto [i, j] : g[u])
{
if (distt[u] + j < distt[i])
{
distt[i] = distt[u] + j;
pq.push({i, distt[i]});
}
}
}
sort(distt.begin(), distt.end());
for (int i = 1; i <= n; i++)
{
ll ch = upper_bound(distt.begin(), distt.end(), k - dists[i] - l) - distt.begin();
ans += ch;
}
cout << ans << '\n';
}
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
int tests = 1;
// cin >> tests;
for (int i = 1; i <= tests; i++)
solve();
}
