#include <bits/stdc++.h>
#define int long long
#define fi first
#define se second
#define pii pair <int , int>
#define arr3 array <int , 3>
using namespace std;
const int INF = 1e17;
const int maxn = 2e5 + 7;
int n , m , S , T , K , L;
vector <pii> g[maxn];
vector <int> dijkstra(int st)
{
vector <int> d(n , INF);
priority_queue <pii , vector <pii> , greater <pii>> Q;
Q.push({0 , st});
d[st] = 0;
while(!Q.empty())
{
int c = Q.top().fi;
int u = Q.top().se;
Q.pop();
if(c != d[u]) continue;
for(pii tmp: g[u])
{
int v = tmp.fi;
int w = tmp.se;
if(d[v] > d[u] + w)
{
d[v] = d[u] + w;
Q.push({d[v] , v});
}
}
}
return d;
}
void solve()
{
cin >> n >> m;
cin >> S >> T >> L >> K;
S--;
T--;
for(int i = 1; i <= m; i++)
{
int u , v , w; cin >> u >> v >> w;
u--;
v--;
g[u].push_back({v , w});
g[v].push_back({u , w});
}
vector <int> a = dijkstra(S);
vector <int> b = dijkstra(T);
if(a[T] <= K)
{
cout << n*(n-1)/2 << '\n';
return;
}
sort(b.begin() , b.end());
sort(a.begin() , a.end());
int ans = 0;
for(int i = 0; i < n; i++)
{
int j = upper_bound(b.begin() , b.end() , K - L - a[i]) - b.begin();
ans += j;
}
cout << ans << '\n';
}
signed main()
{
ios_base::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
solve();
return 0;
}
