//#pragma optimize("Ofast")
//#pragma optimize("unroll-loops")
//#pragma traget("avx,avx2")
#include <iostream>
#include <cmath>
#include <algorithm>
#include <stdio.h>
#include <cstdint>
#include <cstring>
#include <string>
#include <cstdlib>
#include <vector>
#include <bitset>
#include <map>
#include <queue>
#include <ctime>
#include <stack>
#include <set>
#include <list>
#include <random>
#include <deque>
#include <functional>
#include <iomanip>
#include <sstream>
#include <fstream>
#include <complex>
#include <numeric>
#include <cassert>
#include <array>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <thread>
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
#define el '\n'
#define ff first
#define ss second
#define pb push_back
#define pf push_front
#define popb pop_back
#define popf pop_front
#define point pair <ll, ll>
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
using namespace std;
#include <random>
mt19937 rnd(time(0));
const ll INF = 2e18 + 10;
const ll inf = 1e9 + 10;
const ll N = 2e5 + 10;
const ll mod = 1e9 + 7;
const ll LOG = 20;
vector <point> gr[N];
void solve() {
ll n, m;
cin >> n >> m;
ll s, t, l, k;
cin >> s >> t >> l >> k;
for (ll i = 0; i < m; i++) {
ll u, v, c;
cin >> u >> v >> c;
gr[u].pb({v, c});
gr[v].pb({u, c});
}
auto bfs = [&](ll start) -> vector <ll> {
vector <ll> dist(n + 1, INF);
dist[start] = 0;
dist[0] = -INF;
set <point> st;
st.insert({dist[start], start});
while (!st.empty()) {
ll v = st.begin()->ss;
st.erase(st.begin());
for (point to : gr[v]) {
if (dist[to.ff] > dist[v] + to.ss) {
st.erase({dist[to.ff], to.ff});
dist[to.ff] = dist[v] + to.ss;
st.insert({dist[to.ff], to.ff});
}
}
}
return dist;
};
vector <ll> dist[2];
dist[0] = bfs(s);
dist[1] = bfs(t);
if (dist[0][t] <= k)
return void(cout << n * (n - 1) / 2 << el);
ll ans = 0;
sort(all(dist[0]));
sort(all(dist[1]));
for (ll i = 1; i <= n; i++) {
ll lb, rb;
lb = 0, rb = n + 1;
while (lb + 1 < rb) {
ll mid = (lb + rb) >> 1;
if (dist[0][i] + l + dist[1][mid] <= k)
lb = mid;
else
rb = mid;
}
ans += lb;
lb = 0, rb = n + 1;
while (lb + 1 < rb) {
ll mid = (lb + rb) >> 1;
if (dist[0][mid] + l + dist[1][i] <= k)
lb = mid;
else
rb = mid;
}
ans += lb;
}
cout << ans / 2 << el;
return;
}
signed main() {
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
//freopen("deleg.in", "r", stdin);
//freopen("deleg.out", "w", stdout);
int tests = 1;
//cin >> tests;
while (tests--)
solve();
return 0;
}
/*
*/
