#include<bits/stdc++.h>
#include<chrono>
#include<random>
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef double db;
ll gcd(ll a , ll b) {return b ? gcd(b , a % b) : a ;} // greatest common divisor (PGCD)
ll lcm(ll a , ll b) {return (a * b) / gcd(a , b);} // least common multiple (PPCM)
int dx[8] = {1, 0, 0, -1, 1, 1, -1, -1};
int dy[8] = {0, 1, -1, 0, 1, -1, -1, 1};
#define endl "\n"
#define ss second
#define ff first
#define all(x) (x).begin() , (x).end()
#define pb push_back
#define vi vector<int>
#define vii vector<pair<int,int>>
#define vl vector<ll>
#define vll vector<pair<ll,ll>>
#define pii pair<int,int>
#define pll pair<ll,ll>
#define pdd pair<double,double>
#define vdd vector<pdd>
#define speed ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define pbds tree<pii, null_type, less<pii>,rb_tree_tag, tree_order_statistics_node_update>
using namespace __gnu_pbds;
using namespace std;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
////////////////////Only Clear Code//////////////////////////
void usaco_problem(){
freopen("milkvisits.in", "r", stdin);
freopen("milkvisits.out", "w", stdout);
}
void init(){
#ifndef ONLINE_JUDGE
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
#endif // ONLINE_JUDGE
}
const int mx = 2e5+5;
const int LOG = 22;
const int inf = 1e9;
const ll mod = 1e9+7;
const int sq = 300;
ll n, m;
ll s, t, l, k;
ll distances_s[mx], distances_t[mx];
vll graph[mx];
bool vis[mx];
int32_t main(){
speed;
cin >> n >> m;
cin >> s >> t >> l >> k;
while(m--){
ll a, b, c;cin >> a >> b >> c;
graph[a].pb({b, c});
graph[b].pb({a, c});
}
for(int i = 1; i <= n;i++){
distances_s[i] = distances_t[i] = 1e18;
}
priority_queue<pll, vll, greater<pll>> pq;
distances_s[s] = 0;
pq.push({0, s});
while(!pq.empty()){
int node = pq.top().ss;
ll dis = pq.top().ff;
pq.pop();
if(vis[node])continue;
vis[node] = 1;
for(pll adj : graph[node]){
ll nw = dis + adj.ss;
if(nw < distances_s[adj.ff]){
distances_s[adj.ff] = nw;
pq.push({nw, adj.ff});
}
}
}
memset(vis, 0, sizeof vis);
distances_t[t] = 0;
pq.push({0, t});
while(!pq.empty()){
int node = pq.top().ss;
ll dis = pq.top().ff;
pq.pop();
if(vis[node])continue;
vis[node] = 1;
for(pll adj : graph[node]){
ll nw = dis + adj.ss;
if(nw < distances_t[adj.ff]){
distances_t[adj.ff] = nw;
pq.push({nw, adj.ff});
}
}
}
/*for(int i = 1; i <= n;i++){
cout << i << " " << distances_s[i] << " " << distances_t[i] << endl;
}*/
for(int i = 1; i <= n;i++){
ll tot = distances_s[i] + distances_t[i];
if(tot <= k){
cout << (n*(n-1))/2 << endl;
return 0;
}
}
ll ans = 0;
k-=l;
memset(vis, 0, sizeof vis);
vll a, b;
for(int i = 1; i <= n;i++){
a.pb({distances_s[i], i});
b.pb({distances_t[i], i});
}
sort(all(a), greater<pll>());
sort(all(b));
ll j = 0;
while(j < b.size() && ((a[0].ff + b[j].ff) <= k)){
vis[b[j].ss] = 1;
j++;
}
ans += j - vis[a[0].ss];
for(int i = 1; i < a.size();i++){
while(j < b.size() && ((a[i].ff + b[j].ff) <= k)){
vis[b[j].ss] = 1;
j++;
}
ans += j - vis[a[i].ss];
}
cout << ans << endl;
}
/*
NEVER GIVE UP!
DOING SMTHNG IS BETTER THAN DOING NTHNG!!!
Your Guide when stuck:
- Continue keyword only after reading the whole input
- Don't use memset with testcases
- Check for corner cases(n=1, n=0)
- Check where you declare n(Be careful of declaring it globally and in main)
*/
