#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
using namespace std;
using namespace __gnu_pbds;
#pragma GCC optimize("Ofast,unroll-loops,inline-functions,no-stack-protector,03")
#pragma GCC target ("sse,sse2,sse3,ssse3,sse4,popcnt,abm,avx2,mmx,fma,avx,tune=native")
#pragma clang loop vectorize(enable)
#pragma clang loop interleave(enable)
#define int long long
#define sz(x) (int)x.size()
#define F first
#define S second
#define pb push_back
#define nl '\n'
#define o_set tree<int, null_type, less_equal<int>, rb_tree_tag, tree_order_statistics_node_update>
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
typedef pair<int, int> pii;
void file( string s = "" )
{
if( s.empty() )
return;
freopen((s + ".in").c_str(), "r", stdin);
freopen((s + ".out").c_str(), "w", stdout);
}
const int N = 2e5 + 2;
const int N1 = 1e6 + 2;
const int inf = 1e9 + 2;
const int INF = 1e18 + 2;
const int mod = 1e9 + 7;
int T = 1, n, m, s, t, l, k;
vector< pii > g[N];
void dijkstra( int u, vector< int > &d )
{
priority_queue< pii >q;
for( int &x: d )
x = INF;
d[u] = 0;
q.push({0, u});
while( !q.empty() )
{
auto [dist, v] = q.top();
q.pop();
if( -dist != d[v] )
continue;
for( auto [to, len]: g[v] )
if( d[v] + len < d[to] )
{
d[to] = d[v] + len;
q.push({-d[to], to});
}
}
}
void solve()
{
cin >>n >>m >>s >>t >>l >>k;
for( int i = 1, u, v, w; i <= m; ++i )
{
cin >>u >>v >>w;
g[u].pb({v, w});
g[v].pb({u, w});
}
vector< int > ds(n + 1), dt(n + 1);
dijkstra(s, ds);
dijkstra(t, dt);
if( ds[t] <= k )
{
cout <<n * (n - 1) / 2;
return;
}
k -= l;
int ans = 0;
o_set st;
for( int i = 1; i <= n; ++i )
if( dt[i] <= k )
st.insert(k - dt[i]);
st.insert(INF);
for( int i = 1; i <= n; ++i )
{
if( dt[i] <= k )
st.erase(st.find_by_order(st.order_of_key(k - dt[i])));
auto j = st.lower_bound(k - ds[i] + 1);
ans += st.order_of_key(*j);
if( dt[i] <= k )
st.insert(k - dt[i]);
}
cout <<ans / 2;
}
signed main()
{
file("");
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
// cin >>T;
while( T-- )
solve();
}
