#include<bits/stdc++.h>
#include<bits/extc++.h>
using namespace std;
using namespace __gnu_pbds;
#define S second
#define F first
#define ll long long
//#pragma GCC optimize("Ofast, unroll-loop")
//#pragma GCC target("avx,avx2")
#pragma GCC optimize("O3")
const int inf=0x3f3f3f3f;
const ll inff=0x3f3f3f3f3f3f3f3f;
const int X=1000000007;
typedef tree<ll,null_type,less_equal<ll>,rb_tree_tag,tree_order_statistics_node_update> oset;
vector<pair<int,int>> adj[200005];
ll len[200005], alen[200005];
signed main(){
ios::sync_with_stdio(false), cin.tie(nullptr);
memset(len,0x3f,sizeof len);
memset(alen,0x3f,sizeof alen);
int n, m; cin >> n >> m;
ll s, t, L, K; cin >> s >> t >> L >> K;
for(int i=1 ; i<=m ; i++){
int u, v, c; cin >> u >> v >> c;
adj[u].push_back({v,c});
adj[v].push_back({u,c});
}
std::priority_queue<pair<ll,int>,vector<pair<ll,int>>,greater<pair<ll,int>>> pq;
len[s]=0;
pq.push({0,s});
while(!pq.empty()){
auto[l,u]=pq.top();
pq.pop();
if(len[u]<l) continue;
for(auto[v,c]:adj[u]) if(l+c<len[v]){
len[v]=l+c;
pq.push({len[v],v});
}
}
if(len[t]<=K){
cout << 1LL*n*(n-1)/2 << '\n';
return 0;
}
alen[t]=0;
pq.push({0,t});
while(!pq.empty()){
auto[l,u]=pq.top();
pq.pop();
if(alen[u]<l) continue;
for(auto[v,c]:adj[u]) if(l+c<alen[v]){
alen[v]=l+c;
pq.push({alen[v],v});
}
}
//for(int i=1 ; i<=n ; i++) cout << len[i] << (i==n ? '\n' : ' ');
//for(int i=1 ; i<=n ; i++) cout << alen[i] << (i==n ? '\n' : ' ');
oset st;
ll ans=0;
for(int i=1 ; i<=n ; i++) st.insert(alen[i]);
for(int i=1 ; i<=n ; i++) ans+=st.order_of_key(K-L-len[i]+1);
cout << ans << '\n';
return 0;
}
