#include <bits/stdc++.h>
#pragma GCC optimize("O3")
// #define int long long
#define ll long long
#define se second
#define fi first
#define pb push_back
#define lf (id<<1)
#define rg ((id<<1)|1)
#define md ((l+r)>>1)
using namespace std;
typedef pair<ll,int> pii;
typedef pair<pii,pii> ipii;
const int MAXN = 5e5+100;
const int MAXA = 2e5+10;
const int SQRT = 450;
const ll INF = 1e18;
const int MOD = 998244353;
const int LOG = 30;
int sum(int a, int b){
int te = a+MOD+b;
for(; te >= MOD; ) te -= MOD;
return te;
}
void chsum(int &a, int b){ a = sum(a,b); }
int mul(int a, int b){ return a*b%MOD; }
void chmul(int &a, int b){ a = mul(a,b); }
void chmn(auto &a, auto b){ a = min(a, b); }
void chmx(auto &a, auto b){ a = max(a, b); }
int expo(int a, int b){
if(b==0) return 1;
int te = expo(a, b/2); te = mul(te,te); // temporary -> te
return (b%2 ? mul(te, a) : te);
}
ll n, m, s,t,l,k;
ll dis[MAXN], dis2[MAXN];
vector<pii> adj[MAXN];
priority_queue <pii, vector<pii>, greater<pii>> pq;
void dji(int sta){
for(int i=1; i<=n; i++) dis[i] = INF;
dis[sta] = 0;
pq.push({0, sta});
while(!pq.empty()){
auto [x, nw] = pq.top(); pq.pop();
if(dis[nw] > x) continue;
for(auto [nx, wei] : adj[nw]){
if(dis[nx] > x+wei){
dis[nx] = x+wei;
pq.push({dis[nx], nx});
}
}
}
}
signed main(){
ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
cin>>n>>m;
cin>>s>>t>>l>>k;
for(int i=1; i<=m; i++){
int x, y, w; cin>>x>>y>>w;
adj[x].pb({y, w}); adj[y].pb({x, w});
}
dji(t);
for(int i=1; i<=n; i++) dis2[i] = dis[i];
dji(s);
if(dis[t] <= k){
cout << 1ll*n*(n-1)/2 << '\n'; exit(0);
}
k -= l;
ll ans = 0;
for(int i=1; i<=n; i++)
if(dis[i]+dis2[i] <= k) ans--;
sort(dis2+1, dis2+n+1);
sort(dis+1, dis+n+1);
int las = n;
for(int i=1; i<=n; i++){
// itung yg memenuhi ini
while(las>=1 && dis[i]+dis2[las] > k) las--;
ans += las;
// if(te<=k-dis[i]) ans++;
}
cout << ans << '\n';
}
