#include<bits/stdc++.h>
using namespace std;
const long long INF = (long long)4e18;
struct Fenwick{
int n;
vector<long long> bit;
Fenwick(int n = 0){
this->n = n;
bit.assign(n + 1, 0);
}
void add(int idx, long long val){
idx++;
while(idx <= n){
bit[idx] += val;
idx += idx & -idx;
}
}
long long sum(int idx){
if(idx < 0) return 0;
long long res = 0;
idx++;
while(idx > 0){
res += bit[idx];
idx -= idx & -idx;
}
return res;
}
};
vector<long long> dijkstra(int src, vector<vector<pair<int, long long> > > &adj){
int n = adj.size();
vector<long long> dist(n, INF);
priority_queue<pair<long long, int>, vector<pair<long long, int> >, greater<pair<long long, int> > > pq;
dist[src] = 0;
pq.push({0, src});
while(!pq.empty()){
auto [d, u] = pq.top();
pq.pop();
if(d != dist[u]) continue;
for(auto [v, w] : adj[u]){
if(dist[u] + w < dist[v]){
dist[v] = dist[u] + w;
pq.push({dist[v], v});
}
}
}
return dist;
}
int main(){
int N, M;
cin >> N >> M;
int S, T;
long long L, K;
cin >> S >> T >> L >> K;
S--;
T--;
vector<vector<pair<int, long long> > > adj(N);
for(int i = 0; i < M; i++){
int A, B;
long long C;
cin >> A >> B >> C;
A--;
B--;
adj[A].push_back({B, C});
adj[B].push_back({A, C});
}
vector<long long> dS = dijkstra(S, adj);
vector<long long> dT = dijkstra(T, adj);
long long totalPairs = 1LL * N * (N - 1) / 2;
if(dS[T] <= K){
cout << totalPairs << '\n';
return 0;
}
long long B = K - L;
if(B < 0){
cout << 0 << '\n';
return 0;
}
vector<long long> sortedDT = dT;
sort(sortedDT.begin(), sortedDT.end());
long long directed = 0;
for(int i = 0; i < N; i++){
long long need = B - dS[i];
long long cnt = upper_bound(sortedDT.begin(), sortedDT.end(), need) - sortedDT.begin();
if(dS[i] + dT[i] <= B){
cnt--;
}
directed += cnt;
}
vector<long long> vals = dT;
sort(vals.begin(), vals.end());
vals.erase(unique(vals.begin(), vals.end()), vals.end());
vector<int> points(N);
iota(points.begin(), points.end(), 0);
sort(points.begin(), points.end(), [&](int x, int y){
return dS[x] < dS[y];
});
vector<int> queries(N);
iota(queries.begin(), queries.end(), 0);
sort(queries.begin(), queries.end(), [&](int x, int y){
return B - dT[x] < B - dT[y];
});
Fenwick fw(vals.size());
int ptr = 0;
long long bothDirected = 0;
for(int i : queries){
long long maxDS = B - dT[i];
while(ptr < N && dS[points[ptr]] <= maxDS){
int node = points[ptr];
int pos = lower_bound(vals.begin(), vals.end(), dT[node]) - vals.begin();
fw.add(pos, 1);
ptr++;
}
long long maxDT = B - dS[i];
int pos = upper_bound(vals.begin(), vals.end(), maxDT) - vals.begin() - 1;
long long cnt = fw.sum(pos);
if(dS[i] + dT[i] <= B){
cnt--;
}
bothDirected += cnt;
}
long long answer = directed - bothDirected / 2;
cout << answer << '\n';
return 0;
}
