// Alir3za.Zar3 -> Shiraz , Iran
#include <bits/stdc++.h>
using namespace std;
#define int long long
#define pii pair<int,int>
const int mxN = 2e5+7 , Inf = 2e18;
int n,m , S,T,L,K , ln[2][mxN];
bool mrk[mxN];
vector<pair<int,int>> e[mxN];
void iN ()
{
cin >> n >> m;
cin >> S >> T >> L >> K;
for (int i=1; i<=m; i++)
{
int u,v,w; cin >> u >> v >> w;
e[u].push_back( { v , w } );
e[v].push_back( { u , w } );
}
for (int i=1; i<=n; i++)
ln[0][i] = ln[1][i] = Inf;
}
void Dijkstra (int st , int typ)
{
memset(mrk , 0 , sizeof(mrk));
priority_queue<pii , vector<pii> , greater<pii>> pq;
pq.push( { 0 , st } ); ln[typ][st] = 0;
while (!pq.empty())
{
auto [o , v] = pq.top();
pq.pop();
if (mrk[v]) continue;
mrk[v] = true;
for (auto [to , w] : e[v])
{
if (ln[typ][to] > o + w)
{
ln[typ][to] = o + w;
pq.push( { o + w , to } );
}
}
}
}
void ouT ()
{
if (ln[0][T] <= K)
{
cout << n*(n-1)/2 << '\n';
return;
}
int out = 0;
vector<int> q;
for (int i=1; i<=n; i++)
q.push_back( ln[1][i] );
sort(q.begin(),q.end());
for (int i=1; i<=n; i++)
out += upper_bound(q.begin(),q.end(),K-L-ln[0][i])-q.begin();
cout << out << '\n';
}
signed main()
{
ios::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
iN ();
Dijkstra (S,0);
Dijkstra (T,1);
ouT ();
}
