#include <bits/stdc++.h>
using namespace std;
//#define USACO
#define fi first
#define se second
#define TIME (1.0 * clock() / CLOCKS_PER_SEC)
#define ALL(v) (v).begin(), (v).end()
#define BIT(i) (1LL << (i))
#define MASK(x, i) (((x) >> (i)) & 1)
#define REP(i, v) for( __typeof((v).begin()) i = (v).begin(); i != (v).end(); ++ i)
#define FOR(i, a, b) for(int i = (a), _b = (b); i <= _b; ++ i)
#define FORD(i, b, a) for(int i = (b), _a = (a); i >= _a; -- i)
const string NAME = "BAITAP";
const string name = "";
const long long INF = 1e18;
const int inf = 0x3f3f3f3f;
const int MOD = 1e9 + 7;
const int mod = 998244353;
const int mxN = 2e5 + 5;
int N, M, S, T;
long long K, L;
vector<pair<int, long long>> adj[mxN];
vector<long long> dist_from_t(mxN, INF);
vector<long long> dist_from_s(mxN, INF);
void init(void){
cin >> N >> M;
cin >> S >> T >> L >> K;
FOR(i, 1, M){
int u, v;
long long w;
cin >> u >> v >> w;
adj[u].push_back(make_pair(v, w));
adj[v].push_back(make_pair(u, w));
}
}
void dijkstra(const int &st, const int &ty){
if(ty == 1){
dist_from_s[st] = 0;
priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<pair<long long, int>>> pq;
pq.push(make_pair(dist_from_s[st], st));
while(pq.empty() == false){
pair<long long, int> cur = pq.top();
pq.pop();
if(dist_from_s[cur.se] != cur.fi) continue;
for(pair<int, long long> v : adj[cur.se]){
if(dist_from_s[v.fi] > dist_from_s[cur.se] + v.se){
pq.push(make_pair(dist_from_s[v.fi] = dist_from_s[cur.se] + v.se, v.fi));
}
}
}
}
else{
dist_from_t[st] = 0;
priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<pair<long long, int>>> pq;
pq.push(make_pair(dist_from_t[st], st));
while(pq.empty() == false){
pair<long long, int> cur = pq.top();
pq.pop();
if(dist_from_t[cur.se] != cur.fi) continue;
for(pair<int, long long> v : adj[cur.se]){
if(dist_from_t[v.fi] > dist_from_t[cur.se] + v.se){
pq.push(make_pair(dist_from_t[v.fi] = dist_from_t[cur.se] + v.se, v.fi));
}
}
}
}
}
void process(void){
dijkstra(S, 1);
dijkstra(T, 2);
if(dist_from_s[T] <= K){
cout << 1LL * N * (N - 1) / 2;
return;
}
long long ans = 0;
sort(dist_from_t.begin() + 1, dist_from_t.begin() + 1 + N);
FOR(i, 1, N){
long long ok = K - L - dist_from_s[i];
ans += lower_bound(dist_from_t.begin() + 1, dist_from_t.begin() + 1 + N, ok + 1) - (dist_from_t.begin() + 1);
}
cout << ans;
// FOR(i, 1, N){
// cerr << dist_from_s[i] << ' ' << dist_from_t[i] << '\n';
// }
}
signed main(void){
ios::sync_with_stdio(false);
cin.tie(nullptr);
#ifdef LOCAL
freopen((NAME + ".INP").c_str(), "r", stdin);
freopen((NAME + ".OUT").c_str(), "w", stdout);
#elif defined(USACO)
freopen((name + ".in").c_str(), "r", stdin);
freopen((name + ".out").c_str(), "w", stdout);
#endif
init();
process();
cerr << "\nTime elapsed: " << TIME << "s.\n";
}
