/*#pragma GCC optimize("O3")
#pragma GCC optimization("Ofast,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")*/
#include <bits/stdc++.h>
/*#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>*/
#define ll long long
#define ll1 long long
#define ull unsigned long long
#define dou long double
#define str string
#define vll vector<ll>
#define vi vector<int>
#define pll pair<ll, ll>
#define vpll vector<pll>
#define vbool vector<bool>
#define vstr vector<str>
#define vvll vector<vll>
#define pb push_back
#define pf push_front
#define endl "\n"
#define fr first
#define se second
// #define sortcmp(a) sort(a.begin(), a.end(), cmp)
#define sort(a) sort(a.begin(), a.end())
#define reverse(a) reverse(a.begin(), a.end())
#define speed ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0)
#define INF 1000000000000000007
#define ordered_set tree<ll, null_type, less_equal<ll>, rb_tree_tag, tree_order_statistics_node_update>
using namespace std;
//using namespace __gnu_pbds;
mt19937 rng(time(0));
ll randll(ll l, ll r) {
return uniform_int_distribution<ll>(l, r)(rng);
}
vector<vpll> g;
void dijkstra(ll n, vll& d, vector<vpll>& g1) {
set<pll> s;
for (int i = 1; i <= n; i ++) {
s.insert({d[i], i});
}
while (s.size()) {
pll p = *s.begin();
s.erase(s.begin());
for (auto i : g1[p.se]) {
if (p.fr+i.se < d[i.fr]) {
s.erase({d[i.fr], i.fr});
d[i.fr] = p.fr+i.se;
s.insert({d[i.fr], i.fr});
}
}
}
}
int main(){
speed;
srand(time(0));
ll n, m;
cin >> n >> m;
ll a, b, l, k;
cin >> a >> b >> l >> k;
g.resize(n+7);
for (int i =0 ; i < m; i ++) {
ll a, b, c;
cin >> a >> b >> c;
g[a].pb({b, c});
g[b].pb({a, c});
}
vll d(n+7, INF);
d[a] = 0;
dijkstra(n, d, g);
if (d[b] <= k) {
cout << n*(n-1)/2 << endl;
return 0;
}
vll d_ = d;
sort(d);
vll d1(n+7, INF);
d1[b] = 0;
dijkstra(n, d1, g);
ll res = 0;
for (int i = 1; i <= n; i ++) {
ll l1 = -1, r1 = n;
while (r1-l1 > 1) {
ll x = (l1+r1)/2;
if (d[x]+l+d1[i] > k) r1 = x;
else l1 = x;
}
res += l1+1;
if (d1[i]+l+d_[i] <= k) res --;
}
cout << res << endl;
}
