#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ordered_set tree<int, null_type,less<int>, rb_tree_tag,tree_order_statistics_node_update>
using namespace __gnu_pbds;
using namespace std;
#define pb push_back
#define st first
#define nd second
typedef long long ll;
typedef long double ld;
const ll I = 1000LL * 1000LL * 1000LL * 1000LL * 1000LL * 1000LL;
const ll M = 1000LL * 1000LL * 1000LL + 7LL;
const int N = 1<<18;
bool vis[N];
ll dis[2][N];
pair<ll, int> ds[N], dt[N];
vector<pair<int, ll>> ed[N];
void Dijkstra(int r, int s, int n)
{
    int v;
    priority_queue<pair<ll, int>> q;
    for(int i = 1; i <= n; ++i)
    {dis[r][i] = I; vis[i] = false;}
    dis[r][s] = 0LL;
    q.push(make_pair(0, s));
    while((int)q.size() > 0)
    {
        v = q.top().nd; q.pop();
        if(vis[v]) continue;
        vis[v] = true;
        for(int i = 0; i < (int)ed[v].size(); ++i)
        {
            ll o = dis[r][v] + ed[v][i].nd;
            if(o < dis[r][ed[v][i].st])
            {
                dis[r][ed[v][i].st] = o;
                q.push(make_pair(-o, ed[v][i].st));
            }
        }
    }
}
void Solve()
{
    int n, m, a, b, s, t, l, c; 
    ll k;
    ll ans = 0LL;
    cin >> n >> m;
    cin >> s >> t >> l >> k;
    for(int i = 1; i <= m; ++i)
    {
        cin >> a >> b >> c;
        ed[a].pb(make_pair(b, c));
        ed[b].pb(make_pair(a, c));
    }
    Dijkstra(0, s, n);
    Dijkstra(1, t, n);
    if(dis[0][t] <= k)
    {
        cout << ((ll)n * (ll)(n - 1)) / 2LL << "\n";
        return;
    }
    for(int i = 1; i <= n; ++i)
    {
        ds[i] = make_pair(dis[0][i], i);
        dt[i] = make_pair(dis[1][i], i);
    }
    sort(ds + 1, ds + 1 + n);
    sort(dt + 1, dt + 1 + n);
    int j = n;
    for(int i = 1; i <= n; ++i)
    {
        while(j > 0 && ds[i].st + dt[j].st + (ll)l > k)
            --j;
        ans += (ll)j;
    }
    
    cout << ans << "\n";
}
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    //int t; cin >> t;
    //while(t--)
        Solve();
    return 0;
}
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