#include <bits/stdc++.h>
using namespace std;
#define int long long
int dist1[200010];
int dist2[200010];
vector<pair<int, int> > adjList[200010];
priority_queue<pair<int, int>, vector<pair<int, int> >, greater<pair<int, int> > > pq;
int S, T, L, K;
int N, M;
int inp1, inp2, inp3;
int32_t main(){
ios::sync_with_stdio(0);
cin.tie(0);
cin >> N >> M >> S >> T >> L >> K;
for(int a=1; a<=N; a++) dist1[a] = dist2[a] = LLONG_MAX/2;
for(int a=1; a<=M; a++) {
cin >> inp1 >> inp2 >> inp3;
adjList[inp1].push_back({inp3, inp2});
adjList[inp2].push_back({inp3, inp1});
}
dist1[S] = 0;
dist2[T] = 0;
pq.push({0, S});
while(!pq.empty()){
int d, node;
tie(d, node) = pq.top();
pq.pop();
if(d > dist1[node]) continue;
for(auto it: adjList[node]){
if(dist1[it.second]>dist1[node] + it.first){
dist1[it.second] = dist1[node] + it.first;
pq.push({dist1[it.second], it.second});
}
}
}
pq.push({0, T});
while(!pq.empty()){
int d, node;
tie(d, node) = pq.top();
pq.pop();
if(d > dist2[node]) continue;
for(auto it: adjList[node]){
if(dist2[it.second]>dist2[node] + it.first){
dist2[it.second] = dist2[node] + it.first;
pq.push({dist2[it.second], it.second});
}
}
}
if(dist1[T] <= K){
cout << N*(N-1)/2;
return 0;
}
vector<int> v;
for(int a=1; a<=N; a++){
v.push_back(-dist1[a]);
}
sort(v.begin(), v.end());
int ans = 0;
for(int a=1; a<=N; a++){
int todo = K - L - dist2[a]; //upperbound
auto it = lower_bound(v.begin(), v.end(), -todo);
if(it == v.end()) continue;
ans += (v.end() - it);
}
cout << ans;
}
