#include <bits/stdc++.h>
using namespace std;
#include<ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
#define int long long
typedef tree<
int,
null_type,
less_equal<int>,
rb_tree_tag,
tree_order_statistics_node_update>
ordered_set;
vector<pair<int,int>> adj[2000005];
int n,m;
int s,t,l,k;
signed main() {
ios::sync_with_stdio(0);
cin.tie(NULL);
cin>>n>>m;
cin>>s>>t>>l>>k;
for(int i=0; i<m; i++){
int u,v,w;
cin>>u>>v>>w;
adj[u].push_back({w,v});
adj[v].push_back({w,u});
}
vector<int> d1(200005,1e16);
vector<int> d2(200005,1e16);
priority_queue<pair<int,int>, vector<pair<int,int>>, greater<pair<int,int>>> q;
d1[s]=0;
q.push({0,s});
while(!q.empty()){
int w=q.top().first, node=q.top().second;
q.pop();
if(w!=d1[node]) continue;
for(pair<int,int> &j: adj[node]){
int nw=j.first+w, next=j.second;
if(d1[next]>nw){
d1[next]=nw;
q.push({nw,next});
}
}
}
while(!q.empty()) q.pop();
d2[t]=0;
q.push({0,t});
while(!q.empty()){
int w=q.top().first, node=q.top().second;
q.pop();
if(w!=d2[node]) continue;
for(pair<int,int> &j: adj[node]){
int nw=j.first+w, next=j.second;
if(d2[next]>nw){
d2[next]=nw;
q.push({nw,next});
}
}
}
ordered_set s,t;
for(int i=1; i<=n; i++){
s.insert(d1[i]);
}
for(int i=1; i<=n; i++){
t.insert(d2[i]);
}
int ans=0;
for(int i=1; i<=n; i++){
ans+=t.order_of_key(k-l-d1[i]+1);
ans+=s.order_of_key(k-l-d2[i]+1);
}
cout<<ans<<endl;
}
