// author : anhtun_hi , nqg
#include <bits/stdc++.h>
#define ll long long
#define ii pair<ll, ll>
#define fi first
#define se second
#define all(x) x.begin(), x.end()
#define reset(h, v) memset(h, v, sizeof h)
#define Forv(i, a) for(auto& i : a)
#define For(i, a, b) for(int i = a; i <= b; ++i)
#define Ford(i, a, b) for(int i = a; i >= b; --i)
#define c_bit(i) __builtin_popcountll(i)
#define Bit(mask, i) ((mask >> i) & 1LL)
#define onbit(mask, i) ((mask) bitor (1LL << i))
#define offbit(mask, i) ((mask) &~ (1LL << i))
using namespace std;
namespace std {
template <typename T, int D>
struct _vector : public vector <_vector <T, D - 1>> {
static_assert(D >= 1, "Dimension must be positive!");
template <typename... Args>
_vector(int n = 0, Args... args) : vector <_vector <T, D - 1>> (n, _vector <T, D - 1> (args...)) {}
};
template <typename T> struct _vector <T, 1> : public vector <T> {
_vector(int n = 0, const T& val = T()) : vector <T> (n, val) {}
};
template <class A, class B> bool minimize(A &a, B b){return a > b ? a = b, true : false;}
template <class A, class B> bool maximize(A &a, B b){return a < b ? a = b, true : false;}
}
const int dx[] = {0, 0, +1, -1}, dy[] = {-1, +1, 0, 0}, LOG = 20, base = 311, inf = 1e9 + 5;
const int MAXN = 1e6 + 5;
const ll mod = 1e9 + 7;
const ll oo = 1e18;
//#define int long long
int n, m, s, t; ll L, k;
vector<ii> g[MAXN];
ll d[2][MAXN];
void Solve() {
cin >> n >> m >> s >> t >> L >> k;
For(i, 1, m){
int u, v; ll w;
cin >> u >> v >> w;
g[u].push_back({v, w});
g[v].push_back({u, w});
}
priority_queue<array<ll, 3>, vector<array<ll, 3>>> pq;
reset(d, 0x3f);
pq.push({0, s, 0}); d[0][s] = 0;
pq.push({0, t, 1}); d[1][t] = 0;
while(pq.size()){
auto [du, u, op] = pq.top(); pq.pop();
if(du != d[op][u]) continue;
for(auto [v, w] : g[u]){
if(d[op][v] > d[op][u] + w){
d[op][v] = d[op][u] + w;
pq.push({d[op][v], v, op});
}
}
}
if(d[0][t] <= k) cout << 1LL * n * (n - 1) / 2 << '\n';
else {
ll ans = 0;
For(i, 0, 1) sort(d[i] + 1, d[i] + n + 1);
For(i, 1, n) {
int l = 0, r = n + 1;
while(r - l > 1){
int mid = l + r >> 1;
if(d[0][i] + d[1][mid] <= k - L) l = mid;
else r = mid;
}
ans += l;
}
cout << ans << '\n';
}
}
int32_t main() {
cin.tie(0) -> sync_with_stdio(0);
if(fopen("JOI24_ho_t2.inp", "r")) {
freopen("JOI24_ho_t2.inp", "r", stdin);
freopen("JOI24_ho_t2.out", "w", stdout);
}
int t = 1;
// cin >> t;
for (int test = 1; test <= t; test++) {
Solve();
}
return 0;
}
