#include <bits/stdc++.h>
using namespace std;
#define pb push_back
#define st first
#define nd second
typedef long long ll;
const int N = 2e5+3;
const ll INF = 2e18;
vector<pair<ll, int>> grf[N];
ll odl[2][N];
void dij(int v, int t){
odl[t][v]=0;
priority_queue<pair<ll, int>> Q;
Q.push({0, v});
while(!Q.empty()){
int cur = Q.top().nd;
ll wg = -Q.top().st;
Q.pop();
if(odl[t][cur]<wg) continue;
for(auto w:grf[cur]){
if(wg+w.nd<odl[t][w.st]){
odl[t][w.st]=wg+w.nd;
Q.push({-odl[t][w.st], w.st});
}
}
}
}
int main(){
ios_base::sync_with_stdio(0);
cin.tie(0);
ll n, m, l, k;
int s, t;
cin >> n >> m;
cin >> s >> t >> l >> k;
for(int i=0; i<m; i++){
int a, b; ll c;
cin >> a >> b >> c;
grf[a].pb({b, c});
grf[b].pb({a, c});
}
for(int i=1; i<=n; i++) odl[0][i]=odl[1][i]=INF;
dij(s, 0);
dij(t, 1);
ll out=0;
if(odl[0][t]<=k){
out=n*(n-1); out/=2;
cout << out << '\n';
return 0;
}
sort(odl[0]+1, odl[0]+1+n);
sort(odl[1]+1, odl[1]+1+n, greater<ll>());
int ptr=1;
for(int i=1; i<=n; i++){
while(ptr<=n && odl[0][i]+odl[1][ptr]>k-l) ptr++;
out+=n-ptr+1;
}
cout << out << '\n';
return 0;
}
