#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/detail/standard_policies.hpp>
#define ll long long
#define ld long double
#define endl "\n"
#define yeap cout<<"YES"<<endl
#define nope cout<<"NO"<<endl
#define all(v) v.begin(), v.end()
using namespace std;
using namespace __gnu_pbds;
template<class T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<class T> using ordered_multiset = tree<T, null_type, less_equal<T>, rb_tree_tag, tree_order_statistics_node_update>;
const ll infp = 1e18;
const ll infn = 1e18 * (-1);
const ll N = 2e6 + 10;
const ll M = 5e3 + 10;
const ll MOD = 998244353;
ll hceil(ll a, ll b){
return (a+b-1)/b;
}
vector<pair<ll, ll>> graph[N];
vector<ll> dist(N, infp), vis(N, 0LL);
void dijkstra(ll source){
set<pair<ll, ll>> s;
s.insert({0, source});
dist[source] = 0;
while(s.size()>0){
auto node = *s.begin();
ll v = node.second;
ll v_dist = node.first;
s.erase(s.begin());
if(vis[v]==0){
for(auto child : graph[v]){
ll v2 = child.first;
ll wt = child.second;
if((dist[v]+wt)<(dist[v2])){
dist[v2] = dist[v]+wt;
s.insert({dist[v2], v2});
}
}
vis[v] = 1;
}
}
}
void solve(ll testcase){
ll n, m, s, t, l, k;
cin>>n>>m>>s>>t>>l>>k;
for(int i=1; i<=m; i++){
ll a, b, c;
cin>>a>>b>>c;
graph[a].push_back({b, c});
graph[b].push_back({a, c});
}
ordered_multiset<ll> sts, stt;
dijkstra(s);
for(int i=1; i<=n; i++){
sts.insert(dist[i]);
}
for(int i=1; i<=n; i++){
vis[i] = 0, dist[i] = infp;
}
dijkstra(t);
for(int i=1; i<=n; i++){
stt.insert(dist[i]);
}
if(dist[s]<=k){
cout << (n * (n-1)) / 2 << endl;
} else if(l > k){
cout << 0 << endl;
} else {
ll ans = 0;
for(int i=1; i<=n; i++){
ll temp = k - l - dist[i];
ans += sts.order_of_key(temp + 1);
}
cout << ans << endl;
}
}
int main(){
#if __has_include("LOCAL.hh")
#include "LOCAL.hh"
#endif
#ifdef LOCAL
freopen("input.txt", "r", stdin);
freopen("output3.txt", "w", stdout);
using namespace std::chrono;
cout << fixed << setprecision(9);
auto begin = steady_clock::now();
#else
std::ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
#endif
int T = 1;
//cin>>T;
for(int i=1; i<=T; i++){
solve(i);
}
#ifdef LOCAL
auto end = steady_clock::now();
cout << "\nTime : "
<< (ld)duration_cast<nanoseconds>
(end - begin).count()/1000000000
<< "s" << endl;
#endif
return 0;
}
