// 23 - 12 - 23
#include<bits/stdc++.h>
using namespace std;
#define read() ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0)
#define day() time_t now = time(0);char* x = ctime(&now);cerr<<"Right Now Is : "<<x<<"\n"
#define int long long
#define ii pair<int,int>
#define X first
#define Y second
const long long MAX = (int)2e5 + 5;
const long long INF = (int)1e18;
const long long MOD = (int)1e9 + 7;
int n,m,s,t,l,k;
vector<ii> adj[MAX];
int dist[2][MAX];
int point[2];
priority_queue<ii,vector<ii>,greater<ii>> h;
void dijstra(bool c){
h.push({0,point[c]});
dist[c][point[c]] = 0;
while(!h.empty()){
int u = h.top().Y;
int d = h.top().X;
h.pop();
if(d != dist[c][u])continue;
for(auto e : adj[u]){
int v = e.X;
int w = e.Y;
if(dist[c][v] > dist[c][u] + w){
dist[c][v] = dist[c][u] + w;
h.push({dist[c][v],v});
}
}
}
}
signed main(){
read();
cin >> n >> m >> s >> t >> l >> k;
point[0] = s;
point[1] = t;
for(int i = 1;i <= n;i++){
dist[0][i] = dist[1][i] = INF;
}
for(int i = 1,u,v,c;i <= m;i++){
cin >> u >> v >> c;
adj[u].push_back({v,c});
adj[v].push_back({u,c});
}
dijstra(0);
dijstra(1);
if(dist[1][s] <= k)return cout << (n * (n - 1) / 2),0;
sort(dist[1] + 1,dist[1] + 1 + n);
sort(dist[0] + 1,dist[0] + 1 + n);
int id = n;
int res = 0;
for(int i = 1;i <= n;i++){
while(id > 0 && dist[0][i] + l + dist[1][id] > k)id--;
if(id == 0)break;
res += id;
}
cout << res;
}
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