#include <bits/stdc++.h>
#define int long long
#define ll long long
#define pb push_back
#define fi first
#define se second
#define lf (id<<1)
#define rg ((id<<1)|1)
#define md ((l+r)>>1)
#define ld long double
using namespace std;
typedef pair<int,int> pii;
typedef pair<char,char> pcc;
typedef pair<int,pii> ipii;
typedef pair<pii,pii> ipiii;
const int MAXN = 3e5+50;
const int SQRT = 610;
const int MAXA = 50;
const int MOD = 998244353;
const int LOG = 21;
const int INF = 1e18;
const ld EPS = 1e-12;
int n, m, s, t, l, k;
vector <pii> adj[MAXN];
priority_queue <pii, vector<pii>, greater<pii>> pq;
int dis[MAXN], dis2[MAXN];
void dji2(){
for(int i=1; i<=n; i++) dis2[i] = INF;
dis2[t] = 0; pq.push({0, t});
while(!pq.empty()){
int nw = pq.top().se, dist = pq.top().fi; pq.pop();
if(dist > dis2[nw]) continue;
for(auto [nx, ed] : adj[nw]){
if(dis2[nx] > dist+ed){
dis2[nx] = dist+ed; pq.push({dis2[nx], nx});
}
}
}
}
void dji(){
for(int i=1; i<=n; i++) dis[i] = INF;
dis[s] = 0; pq.push({0, s});
while(!pq.empty()){
int nw = pq.top().se, dist = pq.top().fi; pq.pop();
if(dist > dis[nw]) continue;
for(auto [nx, ed] : adj[nw]){
if(dis[nx] > dist+ed){
dis[nx] = dist+ed; pq.push({dis[nx], nx});
}
}
}
}
struct seg {
int st[4*MAXN];
int que(int id, int l, int r, int x, int y){
if(x<=l && r<=y) return st[id];
if(r<x || y<l) return 0;
return que(lf,l,md,x,y) + que(rg,md+1,r,x,y);
}
int upd(int id, int l, int r, int x, int p){
if(l==r && l==x) return st[id] += p;
if(r<x || x<l) return st[id];
return st[id] = upd(lf,l,md,x,p) + upd(rg,md+1,r,x,p);
}
} A;
vector <pii> que[MAXN];
signed main(){
// ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
cin>>n>>m;
cin>>s>>t>>k>>l;
for(int i=1; i<=m; i++){
int x, y, z; cin>>x>>y>>z;
adj[x].pb({y,z}); adj[y].pb({x,z});
}
dji(); dji2();
// for(int i=1; i<=n; i++){
// cout << i << ' ' <<dis[i]<<' '<<dis2[i]<< "pp\n";
// }
if(dis[t] <= l){
cout << n*(n-1)/2 << '\n'; exit(0);
}
int ans = 0;
vector <pii> vec; vec.pb({-INF, -INF});
for(int i=1; i<=n; i++) vec.pb({dis[i], dis2[i]});
sort(vec.begin(), vec.end());
vector <int> up; up.pb(-INF);
for(int i=1; i<=n; i++){
int val = vec[i].se; // dis+dis2 <= l-k
int idx = upper_bound(up.begin(), up.end(), l-k-val) - up.begin() - 1;
ans += idx;
if(idx != i-1){
que[idx].pb({-1, l-k-vec[i].fi});
que[i-1].pb({1, l-k-vec[i].fi});
}
up.pb(vec[i].fi);
}
vector <int> cc; cc.pb(-INF);
for(int i=1; i<=n; i++)
cc.pb(vec[i].se);
sort(cc.begin(), cc.end());
cc.resize(unique(cc.begin(), cc.end()) - cc.begin());
for(int i=1; i<=n; i++){
int id = upper_bound(cc.begin(), cc.end(), vec[i].se)-cc.begin()-1;
A.upd(1,1,n,id,1);
for(auto [x, y] : que[i]){
int id = upper_bound(cc.begin(), cc.end(), y)-cc.begin()-1;
int val = A.que(1,1,n,1,id);
if(x==-1) ans -= val;
else ans += val;
}
}
cout << ans << '\n';
}
