#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename T>
using ordered_set=tree<T,null_type,less_equal<T>,rb_tree_tag,tree_order_statistics_node_update>;\
constexpr int maxn=2e5 + 5;
constexpr long long inf=2e18;
vector<pair<int,int>> g[maxn];
void dijk(int s,vector<long long> &odl){
priority_queue<pair<long long,int>,vector<pair<long long,int>>,greater<>> pq;
pq.push({0,s});
odl[s]=0;
while (!pq.empty()){
auto [dist,v]=pq.top();
pq.pop();
if (dist!=odl[v]) continue;
for (auto [u,w]:g[v]){
if (dist+w>=odl[u]) continue;
odl[u]=dist+w;
pq.push({odl[u],u});
}
}
}
int main(){
ios_base::sync_with_stdio(0);
cin.tie(0);
int n,m;
cin>>n>>m;
long long s,t,l,k;
cin>>s>>t>>l>>k;
for (int i=0;i<m;i++){
int a,b,c;
cin>>a>>b>>c;
g[a].push_back({b,c});
g[b].push_back({a,c});
}
vector<long long> ds(n+1,inf),dt(n+1,inf);
dijk(s,ds);
dijk(t,dt);
if (ds[t]<=k){
cout<<1ll*n*(n-1)/2<<"\n";
return 0;
}
long long ans=0;
ordered_set<long long> st;
for (int i=n;i>=1;i--){
long long need=k-ds[i]-l;
ans+=st.order_of_key(need+1);
st.insert(dt[i]);
}
st.clear();
for (int i=n;i>=1;i--){
long long need=k-dt[i]-l;
ans+=st.order_of_key(need+1);
st.insert(ds[i]);
}
cout<<ans<<"\n";
return 0;
}
