#include<bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<long long, long long>;
#define pb push_back
#define ins insert
#define fi first
#define se second
#define btpc __builtin_popcount
#define btclz __builtin_clz
#define sz(x) (int)(x.size());
#define all(x) x.begin(), x.end()
#define debug(...) " [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] "
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int d4x[4] = {1, 0, -1, 0}; int d4y[4] = {0, 1, 0, -1};
int d8x[8] = {0, 1, 1, 1, 0, -1, -1, -1};
int d8y[8] = {1, 1, 0, -1, -1, -1, 0, 1};
template<class X, class Y>
bool minimize(X &x, const Y &y) {
if (x > y)
{
x = y;
return true;
}
return false;
}
template<class X, class Y>
bool maximize(X &x, const Y &y) {
if (x < y)
{
x = y;
return true;
}
return false;
}
const int MOD = 1e9 + 7; //998244353
/* Author : Le Ngoc Bao Anh, A5K37 Le Quy Don High School for Gifted Student, Da Nang */
/* University of Wollongong */
const long long INF = 1e9;
const int N = 2e5 + 10;
vector<pll> adj[N];
#define int ll
void BaoJiaoPisu() {
int n, m; cin >> n >> m;
ll S, T, L, K; cin >> S >> T >> L >> K;
for(int i = 1; i <= m; i++) {
int u, v, w; cin >> u >> v >> w;
adj[u].pb({v, w});
adj[v].pb({u, w});
}
auto F = [&](int S) -> vector<ll> {
vector<ll> dist(n + 1, INF * INF);
dist[S] = 0;
struct PQ {
int u; ll w;
bool operator < (const PQ & temp) const {
return w > temp.w;
}
};
priority_queue<PQ> q;
q.push({S, 0});
while(q.size()) {
PQ T = q.top(); q.pop();
int u = T.u;
if(T.w != dist[u]) continue;
for(auto nxt : adj[u]) {
int v = nxt.fi;
ll w = nxt.se;
if(minimize(dist[v], dist[u] + w)) q.push({v, dist[v]});
}
}
return dist;
};
vector<ll> distS = F(S);
vector<ll> distT = F(T);
if(distS[T] <= K) {
cout << 1ll * n * (n - 1) / 2;
return;
}
ll ans = 0;
sort(all(distT));
for(int i = 1; i <= n; i++) {
int pos = -1;
int l = 0, r = n - 1;
while(l <= r) {
int mid = (l + r) >> 1;
if(distS[i] + distT[mid] + L <= K) {
pos = mid;
l = mid + 1;
} else {
r = mid - 1;
}
}
ans += pos + 1;
}
cout << ans;
}
signed main()
{
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#ifndef ONLINE_JUDGE
#else
//online
#endif
int tc = 1, ddd = 0;
// cin >> tc;
while(tc--) {
//ddd++;
//cout << "Case #" << ddd << ": ";
BaoJiaoPisu();
}
}
