#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ll long long
#define ld long double
#define ull unsigned long long
#define ff first
#define ss second
#define pii pair<int,int>
#define pll pair<long long, long long>
#define vi vector<int>
#define vl vector<long long>
#define pb push_back
#define rep(i, b) for(int i = 0; i < (b); ++i)
#define rep2(i,a,b) for(int i = a; i <= (b); ++i)
#define rep3(i,a,b,c) for(int i = a; i <= (b); i+=c)
#define count_bits(x) __builtin_popcountll((x))
#define all(x) (x).begin(),(x).end()
#define siz(x) (int)(x).size()
#define forall(it,x) for(auto& it:(x))
using namespace __gnu_pbds;
using namespace std;
typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;
//mt19937 mt;void random_start(){mt.seed(chrono::time_point_cast<chrono::milliseconds>(chrono::high_resolution_clock::now()).time_since_epoch().count());}
//ll los(ll a, ll b) {return a + (mt() % (b-a+1));}
const int INF = 1e9+50;
const ll INF_L = 1e18+40;
const ll MOD = 1e9+7;
ll dist[200'001][2];
vector<pll> graph[200'001];
int n,m,s,t;
ll L,K;
void dij(int start, int type)
{
rep2(i,1,n) dist[i][type] = 1e18;
priority_queue<pll,vector<pll>,greater<pll>> pq;
pq.push({0,start});
while(!pq.empty())
{
pll t = pq.top();
pq.pop();
if(dist[t.ss][type] != 1e18) continue;
dist[t.ss][type] = t.ff;
forall(it,graph[t.ss])
{
pq.push({t.ff+it.ss,it.ff});
}
}
}
int main()
{
ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
//random_start();
cin >> n >> m >> s >> t >> L >> K;
rep(i,m)
{
int a,b,c;
cin >> a >> b >> c;
graph[a].pb({b,c});
graph[b].pb({a,c});
}
dij(s,0);
dij(t,1);
ll ans = 0;
vector<ll> dists;
rep2(i,1,n) dists.pb({dist[i][1]});
sort(all(dists));
rep2(i,1,n)
{
if(dist[i][0] + dist[i][1] + L <= K) ans--;
int l = 0;
int r = n-1;
int ans_ = -1;
while(l <= r)
{
int mid = (l+r)/2;
if(dist[i][0] + L + dists[mid] <= K)
{
ans_ = mid;
l = mid+1;
}
else
{
r = mid-1;
}
}
ans += ans_+1;
}
cout << ans << "\n";
}
