#include <bits/stdc++.h>
using namespace std;
#define int long long
#define ll long long
#define ff first
#define ss second
#define pint pair < int , int >
#define fast ios_base::sync_with_stdio(NULL); cin.tie(NULL)
typedef vector < int > vint;
const int inf = 1e9 + 9;
const int mxn = 2e5 + 2;
const int mod = 1e9 + 7;
int s , l , t , k , n , m;
int dis[2][mxn];
vector < vector < pint > > adj(mxn);
void build(int start , int id) {
priority_queue < pint > q;
q.push({0 , start});
while (!q.empty()) {
pint p = q.top();
q.pop();
int u = p.ss;
if (dis[id][u] != -1) continue;
dis[id][u] = -p.ff;
for (pint v : adj[u]) {
q.push({p.ff - v.ss , v.ff});
}
}
}
signed main() {
cin >> n >> m;
cin >> s >> t >> l >> k;
for (int i = 0; i < m; i++) {
int a , b , c;
cin >> a >> b >> c;
adj[a].push_back({b , c});
adj[b].push_back({a , c});
}
for (int j = 0; j < 2; j++) {
for (int i = 1; i <= n; i++) {
dis[j][i] = -1;
}
}
build(s , 0);
build(t , 1);
sort(dis[1] + 1 , dis[1] + 1 + n);
if (dis[0][t] <= k && dis[0][t] != -1) {
cout << n * (n - 1) / 2 << '\n';
return 0;
}
int ans = 0;
for (int i = 1; i <= n; i++) {
int L = 1 , R = n;
while (L != R) {
int M = (L + R) / 2;
// cout << M << ' ';
if (dis[1][M] + dis[0][i] + l <= k) L = M + 1;
else R = M;
}
if (dis[1][R] + dis[0][i] + l <= k) ans++;
// cout << R << '\n';
ans += R - 1;
}
cout << ans << '\n';
return 0;
}
