#include<bits/stdc++.h>
using namespace std;
using i64 = long long;
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int n,m;
cin >> n >> m;
int s,t,l;
i64 k;
cin >> s >> t >> l >> k;
s --;
t --;
vector<vector<pair<int,int>>> adj(n);
for(int i = 0;i < m;i++){
int u,v,w;
cin >> u >> v >> w;
u --;
v --;
adj[u].push_back({v,w});
adj[v].push_back({u,w});
}
const i64 inf = 1e18;
function<vector<i64>(int)> f = [&](int src){
vector<i64> dist(n,inf);
priority_queue<pair<i64,int>,vector<pair<i64,int>>,greater<pair<i64,int>>> pq;
pq.push({0,src});
dist[src] = 0;
while(!pq.empty()){
int u = pq.top().second;
i64 w = pq.top().first;
pq.pop();
if(dist[u] < w) continue;
for(auto p : adj[u]){
int v = p.first;
if(p.second + w < dist[v]){
dist[v] = p.second + w;
pq.push({dist[v],v});
}
}
}
return dist;
};
vector<i64> d_s = f(s);
vector<i64> d_t = f(t);
vector<i64> d_ss = d_s;
vector<i64> d_ts = d_t;
sort(d_ss.begin(),d_ss.end());
sort(d_ts.begin(),d_ts.end());
i64 ans = 0;
for(int i = 0;i < n;i++){
// if this node is involved in the extra
i64 ds = d_s[i];
i64 dt = d_t[i];
// if s -> i -> v -> t
{
i64 d = ds + l;
// we want that d + x <= k
// x <= k - d
int up = upper_bound(d_ts.begin(),d_ts.end(),k - d) - d_ts.begin();
ans += up;
}
{
i64 d = dt + l;
// we want that d + x <= k
// x <= k - d
int up = upper_bound(d_ss.begin(),d_ss.end(),k - d) - d_ss.begin();
ans += up;
}
}
cout << ans / 2 << '\n';
return 0;
}
