#include<bits/stdc++.h>
using namespace std;
#define ll long long
const bool Multitest = 0;
const int N = 2e5 + 10;
int a[N];
vector<pair<int, int>> adj[N];
int n, m, l; ll k;
int s, t; ll d[5][N];
struct Data
{
int u; ll w;
Data(int _u, ll _w) : u(_u), w(_w) {}
};
struct cmp
{
bool operator() (Data a, Data b)
{
return a.w > b.w;
}
};
void dijsktra(int s, int id)
{
priority_queue<Data, vector<Data>, cmp> q;
for(int i = 1 ; i <= n ; i++) d[id][i] = 1e18;
q.push(Data(s, 0));
d[id][s] = 0;
while(!q.empty())
{
Data x = q.top(); q.pop();
if(d[id][x.u] != x.w) continue;
for(auto [v, w] : adj[x.u])
{
if(d[id][v] > x.w + w)
{
d[id][v] = x.w + w;
q.push(Data(v, d[id][v]));
}
}
}
}
void Work()
{
cin >> n >> m;
cin >> s >> t >> l >> k;
for(int i = 1 ; i <= m ; i++)
{
int u, v, w; cin >> u >> v >> w;
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
dijsktra(s, 1);
dijsktra(t, 2);
if(d[1][t] <= k)
{
cout << 1ll * (n - 1) * n / 2 << '\n';
return;
}
sort(d[1] + 1, d[1] + 1 + n);
sort(d[2] + 1, d[2] + 1 + n);
ll ans = 0;
for(int i = 1 ; i <= n ; i++)
{
int li = 1, ri = n, pos = 0;
while(li <= ri)
{
int mid = (li + ri) >> 1;
if(d[1][i] + d[2][mid] + l <= k)
{
li = mid + 1, pos = mid;
}
else ri = mid - 1;
}
ans += pos;
}
cout << ans;
}
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
int q = 1;
if(Multitest) cin >> q;
while(q--) Work();
}
