/*
███╗ ███╗ █████╗ ██████╗ ███████╗ ██████╗ ██╗ ██╗ ███╗ ███╗ █████╗ ██████╗ ██████╗██╗ ██╗███████╗██╗ ██╗ ██╗ ██╗██╗██╗
████╗ ████║██╔══██╗██╔══██╗██╔════╝ ██╔══██╗╚██╗ ██╔╝██╗ ████╗ ████║██╔══██╗██╔══██╗██╔════╝██║ ██║██╔════╝██║ ██║ ██║ ██║██║██║
██╔████╔██║███████║██║ ██║█████╗ ██████╔╝ ╚████╔╝ ╚═╝ ██╔████╔██║███████║██████╔╝██║ ███████║█████╗ ██║ ██║ ███████║██║██║
██║╚██╔╝██║██╔══██║██║ ██║██╔══╝ ██╔══██╗ ╚██╔╝ ██╗ ██║╚██╔╝██║██╔══██║██╔══██╗██║ ██╔══██║██╔══╝ ██║ ██║ ██╔══██║██║██║
██║ ╚═╝ ██║██║ ██║██████╔╝███████╗ ██████╔╝ ██║ ╚═╝ ██║ ╚═╝ ██║██║ ██║██║ ██║╚██████╗██║ ██║███████╗███████╗███████╗█████╗██║ ██║██║██║
╚═╝ ╚═╝╚═╝ ╚═╝╚═════╝ ╚══════╝ ╚═════╝ ╚═╝ ╚═╝ ╚═╝╚═╝ ╚═╝╚═╝ ╚═╝ ╚═════╝╚═╝ ╚═╝╚══════╝╚══════╝╚══════╝╚════╝╚═╝ ╚═╝╚═╝╚═╝
*/
/*
ඞ
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠉⠉⠉⠉⠉⠻⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀ ⣠⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀ ⣿⣿⣯⠁⠀⠀⠀⠀⠀ ⠙⢿⣷⡄
⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀ ⣿⣿⣿ ⣿⣷
⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀ ⣿⣿⣿⣷⣦⣀⣀⣀⣀⣀⣀⣀⣿⣿
⢸⣿⡇ ⣿⣿⡇⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣸⣿⡇ ⣿⣿⡇⠀⠀⠀⠀ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⡿⢻⡇
⠀⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇
⠀⣿⣿⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇
⠀⣿⣿⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇
⠀⢿⣿ ⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇
⠀⠸⣿⣦⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿
⠀⠀⠛⢿⣿⣿⣿⣿⡇ ⠀⣠⣿⣿⣿⣿⣄ ⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡆ ⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀ ⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿ ⠀⠈⠻⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁
*/
#include<bits/stdc++.h>
#define ll long long
#define pii pair<int, int>
#define pll pair<ll, ll>
#define plll pair<pll, pll>
#define pdd pair<double, double>
#define pu push_back
#define po pop_back
#define fi first
#define se second
#define fifi fi.fi
#define fise fi.se
#define sefi se.fi
#define sese se.se
#define cekcek cout<<'c'<<'e'<<'k'<<endl
using namespace std;
ll N, M, S, T, l, K, a, b, c, dist[200005][2], L, R, mid, pos, ans;
vector<pll> adj[200005];
priority_queue<pll, vector<pll>, greater<pll>> q;
pll now;
vector<ll> v;
void F(ll x, ll y){
for(ll i = 1; i <= N; i++) dist[i][y] = 1e16;
dist[x][y] = 0;
q.push({0, x});
while(!q.empty()){
now = q.top();
q.pop();
if(now.fi > dist[now.se][y]) continue;
for(auto i : adj[now.se]){
if(now.fi + i.se < dist[i.fi][y]){
dist[i.fi][y] = now.fi + i.se;
q.push({dist[i.fi][y], i.fi});
}
}
}
return;
}
bool compare(ll x, ll y){
return dist[x][1] > dist[y][1];
}
int main(){
ios_base::sync_with_stdio(0); cin.tie(NULL); cout.tie(NULL);
cin >> N >> M;
cin >> S >> T >> l >> K;
for(ll j = 1; j <= M; j++){
cin >> a >> b >> c;
adj[a].pu({b, c});
adj[b].pu({a, c});
}
F(S, 0);
F(T, 1);
if(dist[T][0] <= K){
cout << N * (N - 1) / 2 << endl;
return 0;
}
for(ll i = 1; i <= N; i++) v.pu(i);
sort(v.begin(), v.end(), compare);
for(ll i = 0; i < N - 1; i++){
if(dist[i][0] > K) continue;
L = i + 1;
R = N - 1;
pos = 0;
while(L <= R){
mid = (L + R) / 2;
if(dist[i][0] + l + dist[v[mid]][1] <= K){
R = mid - 1;
pos = N - mid;
}
else L = mid + 1;
}
ans += pos;
}
cout << ans << endl;
}
