#include <iostream>
#include <vector>
#include <queue>
#include <algorithm>
using namespace std;
using P = pair<long long, int>;
struct edge{
int to;
long long cost;
};
constexpr long long inf = 1e18;
int main(){
int n, m;
cin >> n >> m;
int s, t;
long long l, k;
cin >> s >> t >> l >> k;
s--;
t--;
vector<vector<edge>> g(n);
for(int i = 0; i < m; i++){
int a, b;
long long c;
cin >> a >> b >> c;
a--;
b--;
g[a].push_back({b, c});
g[b].push_back({a, c});
}
priority_queue<P, vector<P>, greater<P>> que;
vector<long long> dist_from_s(n, inf), dist_from_t(n, inf);
dist_from_s[s] = 0;
que.push({0, s});
while(!que.empty()){
auto [dist, now] = que.top();
que.pop();
if(dist_from_s[now] < dist){
continue;
}
for(auto [nxt, c]: g[now]){
if(dist_from_s[nxt] > dist + c){
dist_from_s[nxt] = dist + c;
que.push({dist + c, nxt});
}
}
}
dist_from_t[t] = 0;
que.push({0, t});
while(!que.empty()){
auto [dist, now] = que.top();
que.pop();
if(dist_from_t[now] < dist){
continue;
}
for(auto [nxt, c]: g[now]){
if(dist_from_t[nxt] > dist + c){
dist_from_t[nxt] = dist + c;
que.push({dist + c, nxt});
}
}
}
if(dist_from_s[t] <= k){
cout << (long long)(n) * (n - 1) / 2 << endl;
return 0;
}
long long ans = 0;
sort(dist_from_t.begin(), dist_from_t.end());
for(int u = 0; u < n; u++){
long long ok = k - l - dist_from_s[u];
ans += lower_bound(dist_from_t.begin(), dist_from_t.end(), ok + 1) - dist_from_t.begin();
}
cout << ans << endl;
}
