#include <bits/stdc++.h>
using namespace std;
#define int long long
const int MAX = 200007;
const int INF = LLONG_MAX;
vector <pair<int,int>> adjlist[MAX]; // {weight,node}
//return distance, node
vector <pair<int,int>> dijkstra(int source, int x) { // find nodes with distance less than or equal to x from source
int dist[MAX];
fill(dist,dist+MAX-1,INF);
priority_queue <pair<int,int>,vector<pair<int,int>>,greater<pair<int,int>>>pq;
pq.push({0,source});
vector<pair<int,int>> candidates;
while (!pq.empty()) {
int d = pq.top().first;
int n = pq.top().second;
if (d>x) break;
pq.pop();
if (dist[n] != INF) continue;
dist[n] = d;
candidates.push_back({d,n});
for (int i=0;i<adjlist[n].size();i++) {
int v = adjlist[n][i].first; // neighbour
int u = adjlist[n][i].second; // neighbour weight
if (dist[v] == INF) {
pq.push({dist[n] + u,v});
}
}
}
return candidates;
}
struct CompareByFirst {
bool operator()(const pair<int,int> &a, const pair<int,int> &b) const {
return a.first < b.first;
}
};
int32_t main() {
ios::sync_with_stdio(0);
cin.tie(0);
int N,M,S,T,L,K;
cin >> N >> M >> S >> T >> L >> K;
int a,b,c;
for (int i=0;i<M;i++) {
cin >> a >> b >> c;
adjlist[a].push_back({b,c});
adjlist[b].push_back({a,c});
}
//run dijkstra twice
vector <pair<int,int>> from_source;
from_source = dijkstra(S,K);
for (auto &pair: from_source) {
if (pair.second == T) {
cout << (N) * (N-1) / 2;
return 0;
}
}
/*
for (auto &z: from_source) {
cout << z.first << " " << z.second << endl;
}
cout << "-----" << endl;
*/
vector <pair<int,int>> to_source = dijkstra(T,K-L);
/*
for (auto &z: to_source) {
cout << z.first << " " << z.second << endl;
}
cout << "-----" << endl;
*/
int count = 0;
for (auto &candidate: to_source) {
//cout << candidate.first << endl;
auto it = upper_bound(from_source.begin(),from_source.end(),make_pair(K - L - candidate.first, INF));
if (it == from_source.end()) {
count += from_source.size();
continue;
}
int t = distance(from_source.begin(), it);
//cout << t << endl;
count += t;
}
cout << count;
}
