#include <iostream>
#include <iomanip>
#include <vector>
#include <cmath>
#include <algorithm>
#include <set>
#include <queue>
#include <map>
#include <stack>
#include <bitset>
#include <string>
#include <cstring>
#include <iterator>
#include <random>
using namespace std;
typedef long long ll;
typedef pair<ll, ll> pll;
typedef long double ld;
const ll dim = 1e6+7;
//const ll mod = 1e9 + 7;
const ll inf = 1e18 + 77;
#define endl "\n"
#define fi first
#define pb push_back
#define se second
#define vll vector<ll>
ll n, m;
ll l, t;
vector<pll> a[dim];
ll dst1[dim];
ll dst2[dim];
ll vis[dim];
int main() {
cin>>n>>m;
ll s, f;
cin>>s>>f>>l>>t;
for(int i=1; i<=m; i++){
ll u, v, w;
cin>>u>>v>>w;
a[u].pb({v, w});
a[v].pb({u, w});
}
for(int i=1; i<=n; i++){
dst1[i]=inf;
dst2[i]=inf;
}
priority_queue<pll, vector<pll>, greater<pll>> q;
q.push({0, s});
dst1[s]=0;
while(q.size()>0){
ll v=q.top().se;
q.pop();
if(vis[v])continue;
vis[v]=1;
for(auto x: a[v]){
if(dst1[x.fi]>dst1[v]+x.se){
dst1[x.fi]=dst1[v]+x.se;
q.push({dst1[x.fi], x.fi});
}
}
}
q.push({0, f});
dst2[f]=0;
for(int i=1; i<=n; i++)vis[i]=0;
while(q.size()>0){
ll v=q.top().se;
q.pop();
if(vis[v])continue;
vis[v]=1;
for(auto x: a[v]){
if(dst2[x.fi]>dst2[v]+x.se){
dst2[x.fi]=dst2[v]+x.se;
q.push({dst2[x.fi], x.fi});
}
}
}
if(dst1[f]<=t){
cout<<(n)*(n-1)/2<<endl;
return 0;
}
//cout<<dst1[4]<<endl;
sort(dst2+1, dst2+1+n);
ll cnt=0;
for(int i=1; i<=n; i++){
auto id=upper_bound(dst2+1, dst2+1+n, t-l-dst1[i]);
ll d=distance(dst2+1, id);
cnt+=d;
}
cout<<cnt<<endl;
return 0;
}
