#include <bits/stdc++.h>
#define tt cin.tie(0), cout.tie(0), ios_base::sync_with_stdio(0)
#define fo freopen((NAME+".INP").c_str(), "r", stdin), freopen((NAME+".OUT").c_str(), "w", stdout)
#define ll long long
#define ull unsigned long long
#define i128 __int128
#define db long double
#define sz(a) ((int)(a).size())
#define pb emplace_back
#define pf emplace_front
#define pob pop_back
#define pof pop_front
#define lb lower_bound
#define ub upper_bound
#define fi first
#define se second
#define ins emplace
#define mp make_pair
using namespace std;
const int MOD = 1e9+7, MAXN = 2e5+5;
const string NAME = "";
int n,m,s,t,l,bit[MAXN<<1];
ll k,distS[MAXN],distT[MAXN],rs=0;
vector<pair<int,int>> adj[MAXN];
vector<ll> v;
void dijkstra(int start, ll dist[]){
priority_queue<pair<ll,int>, vector<pair<ll,int>>, greater<pair<ll,int>>> pq;
dist[start]=0, pq.ins(0,start);
while(!pq.empty()){
pair<ll,int> top = pq.top();
pq.pop();
if(top.fi>dist[top.se]) continue;
for(pair<int,int>& p : adj[top.se])
if(dist[p.fi]>top.fi+p.se) dist[p.fi]=top.fi+p.se, pq.ins(dist[p.fi],p.fi);
}
}
void update(int pos, int val){
while(pos<=n<<1) bit[pos]+=val, pos+=pos&-pos;
}
int getsum(int pos){
int rs=0;
while(pos>0) rs+=bit[pos], pos-=pos&-pos;
return rs;
}
int main()
{
tt;
if(fopen((NAME + ".INP").c_str(), "r")) fo;
cin >> n >> m;
cin >> s >> t >> l >> k;
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);
}
memset(distS,0x3f,sizeof(distS));
memset(distT,0x3f,sizeof(distT));
dijkstra(s,distS);
dijkstra(t,distT);
if(distS[t]<=k) return cout << 1ll*n*(n-1)/2, 0;
for(int i = 1; i<=n; ++i)
v.pb(l+distS[i]), v.pb(k-distT[i]);
sort(v.begin(),v.end());
v.resize(unique(v.begin(),v.end())-v.begin());
update(lb(v.begin(),v.end(),l+distS[1])-v.begin(),1);
for(int i = 2; i<=n; ++i)
rs+=getsum(lb(v.begin(),v.end(),k-distT[i])-v.begin()), update(lb(v.begin(),v.end(),l+distS[i])-v.begin(),1);
memset(bit,0,sizeof(bit));
update(lb(v.begin(),v.end(),l+distS[n])-v.begin(),1);
for(int i = n-1; i>0; --i)
rs+=getsum(lb(v.begin(),v.end(),k-distT[i])-v.begin()), update(lb(v.begin(),v.end(),l+distS[i])-v.begin(),1);
cout << rs;
}
