#include <bits/stdc++.h>
typedef long long ll;
#define FOR(i,x,y) for(ll i=x; i<y; i++)
#define FORNEG(i,x,y) for(ll i=x; i>y; i--)
using namespace std;
const ll maxn = 200005;
const ll INF = 10000000000000000;
vector<array<ll, 2>> edges[maxn];
ll dists[maxn];
ll distt[maxn];
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
FOR(i,0,maxn) dists[i] = INF, distt[i] = INF;
ll n,m;
cin >> n >> m;
ll s, t, l, k;
cin >> s >> t >> l >> k;
FOR(i,0,m){
ll a,b,c;
cin >> a >> b >> c;
edges[a].push_back({b,c});
edges[b].push_back({a,c});
}
priority_queue<vector<ll>> pq;
dists[s] = 0;
pq.push({0, s});
while (pq.size()){
vector<ll> node = pq.top(); pq.pop();
node[0] = -node[0];
if (dists[node[1]] != node[0]) continue;
for (auto&i : edges[node[1]]){
if (dists[i[0]] > dists[node[1]] + i[1]){
dists[i[0]] = dists[node[1]] + i[1];
pq.push({-dists[i[0]] , i[0]});
}
}
}
distt[t] = 0;
pq.push({0, t});
while (pq.size()){
vector<ll> node = pq.top(); pq.pop();
node[0] = -node[0];
if (distt[node[1]] != node[0]) continue;
for (auto&i : edges[node[1]]){
if (distt[i[0]] > distt[node[1]] + i[1]){
distt[i[0]] = distt[node[1]] + i[1];
pq.push({-distt[i[0]] , i[0]});
}
}
}
if (dists[t] <= k) cout << n * (n-1) / 2;
else{
ll ans = 0;
vector<ll> S, T;
FOR(i,1,n+1) S.push_back(dists[i]), T.push_back(distt[i]);
sort(S.begin(), S.end());
sort(T.begin(), T.end());
FOR(i,0,n){
ll req = k - (S[i]+l);
ll sus = upper_bound(T.begin(), T.end(), req) - T.begin();
ans += sus;
}
cout << ans << endl;
}
}
