#include <bits/stdc++.h>
using namespace std;
#ifdef LOCAL
#include "debug.h"
#else
#define dbg(...) 47
#endif
#define int long long
constexpr int N = 2e5;
constexpr int inf = 1e18;
vector<array<int, 2>> g[N];
vector<int> get(int t, int n) {
vector<int> dp(n, inf);
priority_queue<array<int, 2>, vector<array<int, 2>>, greater<array<int, 2>>> q;
dp[t] = 0;
q.push({0, t});
while (!q.empty()) {
auto [k, u] = q.top();
q.pop();
if (dp[u] < k) continue;
for (auto [v, w] : g[u]) {
if (k + w < dp[v]) {
dp[v] = k + w;
q.push({dp[v], v});
}
}
}
return dp;
}
signed main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int n, m, s, t, l, k;
cin >> n >> m >> s >> t >> l >> k;
for (int i = 0; i < m; i++) {
int x, y, w;
cin >> x >> y >> w;
x--; y--;
g[x].push_back({y, w});
g[y].push_back({x, w});
}
s--; t--;
vector<int> d1 = get(s, n);
vector<int> d2 = get(t, n);
sort(d2.begin(), d2.end());
int ans = 0;
for (int i = 0; i < n; i++) {
int x = k - d1[i] - l;
ans += upper_bound(d2.begin(), d2.end(), x) - d2.begin();
}
cout << ans << '\n';
return 0;
}
