#include <bits/stdc++.h>
using namespace std;
#define FOR(i,a,b) for(int i = a; i <= b; i++)
#define FOD(i,a,b) for(int i = a; i >= b; i--)
//#define int long long
#define fi first
#define se second
#define pb push_back
#define ll long long
#define ull unsigned long long
#define db double
#define lcm(a,b) a / __gcd(a, b) * b
#define ii pair<int,int>
#define iii pair<int,pair<int,int>>
#define iv pair<pair<int,int>,pair<int,int>>
#define sq(a) (a) * (a)
#define MASK(i) (1LL << i)
#define task "task"
const int inf = 1e9;
const ll INF = 1e18;
const int mod = 1e9 + 7;
const int N = 2e5 + 5;
int n, m, s, t, l;
ll k;
vector<ii> g[N];
ll d[2][N], a[N], b[N];
void Dijkstra(int sr, ll d[]) {
priority_queue<pair<ll,int>,vector<pair<ll,int>>,greater<pair<ll,int>>> pq;
pq.push({0, sr});
FOR(i, 1, n) d[i] = INF;
d[sr] = 0;
while(!pq.empty()) {
ll cost = pq.top().fi;
int u = pq.top().se;
pq.pop();
if(cost != d[u]) continue;
for(auto H : g[u]) {
int v = H.fi;
int w = H.se;
if(d[v] > d[u] + w) {
d[v] = d[u] + w;
pq.push({d[v], v});
}
}
}
}
ll ans;
vector<ll> val;
int cnt;
struct Bit {
int bit[2 * N];
void reset() {
FOR(i, 1, cnt) bit[i] = 0;
}
void up(int x, int val) {
for(; x <= cnt; x += x & -x) bit[x] += val;
}
int get(int x) {
int ret = 0;
for(; x; x -= x & -x) ret += bit[x];
return ret;
}
int getrange(int l, int r) {
return (l > 1 ? get(r) - get(l - 1) : get(r));
}
};
Bit bit;
int get_idx(int x) {
return lower_bound(val.begin(), val.end(), x) - val.begin() + 1;
}
void process(ll a[], ll b[]) {
FOR(i, 1, n) {
val.pb(a[i]);
val.pb(-b[i]);
}
sort(val.begin(), val.end());
val.erase(unique(val.begin(), val.end()), val.end());
cnt = val.size();
FOR(i, 1, n) {
ans += bit.getrange(get_idx(a[i]), cnt);
bit.up(get_idx(-b[i]), 1);
}
bit.reset();
val.clear();
}
void KhoiLe() {
Dijkstra(s, d[0]);
Dijkstra(t, d[1]);
if(d[0][t] <= k) {
cout << (1LL * n * (n - 1) / 2) << '\n';
return;
}
/// x < y
/// d1[x] + dn[y] + l <= k <=> dn[y] + l - k <= -d1[x]
/// dn[x] + d1[y] + l <= k <=> d1[y] + k - k <= -dn[x]
FOR(i, 1, n) {
a[i] = d[1][i] + l - k;
// cout << a[i] << ' ' << -d[0][i] << '\n';
b[i] = d[0][i] + l - k;
}
process(a, d[0]);
process(b, d[1]);
cout << ans << '\n';
}
signed main() {
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
int test = 1;
// cin >> test;
while(test--) {
cin >> n >> m >> s >> t >> l >> k;
FOR(i, 1, m) {
int u, v, w;
cin >> u >> v >> w;
g[u].pb({v, w});
g[v].pb({u, w});
}
KhoiLe();
}
}
