#include <iostream>
#include <vector>
#include <algorithm>
#include <stack>
#include <queue>
#include <tuple>
#include <math.h>
#include <cstring>
#include <bitset>
#include <set>
#include <map>
#define int long long
using namespace std;
using ll = long long;
using pii = pair<int,int>;
using piii = tuple<int,int,int>;
#define endl '\n'
#define f first
#define s second
#define all(x) begin(x),end(x)
int const N = 2e5+10;
vector<pii> adj[N];
int walk1[N];
int walk2[N];
signed main(){
ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
memset(walk1,-1,sizeof walk1);
memset(walk2,-1,sizeof walk2);
int n;cin >> n;
int m;cin >> m;
int st,ed;cin >> st >> ed;
int l,k;cin >> l >> k;
for(int i{};i < m;i++){
int a,b,c;cin >> a >> b >> c;
adj[a].emplace_back(b,c);
adj[b].emplace_back(a,c);
}
priority_queue<pii,vector<pii>,greater<pii>> pq;
pq.emplace(0,st);
walk1[st] = 0;
while(!pq.empty()){
auto [weight,pos] = pq.top();pq.pop();
if(weight > walk1[pos]) continue;
for(auto [k,cost]:adj[pos]){
if(walk1[k] == -1 || weight+cost < walk1[k]){
walk1[k] = weight+cost;
pq.emplace(weight+cost,k);
}
}
}
pq.emplace(0,ed);
walk2[ed] = 0;
while(!pq.empty()){
auto [weight,pos] = pq.top();pq.pop();
if(weight > walk2[pos]) continue;
for(auto [k,cost]:adj[pos]){
if(walk2[k] == -1 || weight+cost < walk2[k]){
walk2[k] = weight+cost;
pq.emplace(weight+cost,k);
}
}
}
// for(int i{1};i <= n;i++){
// cout << walk1[i] << " " << walk2[i] << endl;
// }
if(walk1[ed] != -1 && walk1[ed] <= k){
cout << (1LL*n*(n-1))/2;
return 0;
}
vector<int> vc;
for(int i{1};i <= n;i++){
if(walk2[i] == -1) continue;
vc.emplace_back(walk2[i]);
}
sort(all(vc));
// for(auto k:vc) cout << k << " ";
// cout << endl;
ll ans = 0;
for(int i{1};i <= n;i++){
if(walk1[i] == -1) continue;
auto it = upper_bound(all(vc),k-walk1[i]-l);
//cout << i << " " << walk1[i] << " " << it-vc.begin() << endl;
//if(it == vc.end()) continue;
ans += (it-vc.begin());
}
cout << ans;
}
