#include <cstdio>
#include <stdio.h>
#include <stdbool.h>
#include <iostream>
#include <map>
#include <vector>
#include <climits>
#include <stack>
#include <string>
#include <queue>
#include <algorithm>
#include <set>
#include <unordered_set>
#include <unordered_map>
#include <cmath>
#include <cctype>
#include <bitset>
#include <iomanip>
#include <cstring>
#include <numeric>
#include <cassert>
using namespace std;
#define int long long
#define pii pair<int, int>
#define mp make_pair
#define pb push_back
#define fi first
#define se second
int n;
vector<vector<pii> > graph;
vector<int> dijk(int s){
vector<int> dj(n+1, LLONG_MAX/2);
vector<bool> visited(n+1, 0);
priority_queue<pii, vector<pii>, greater<pii> > pq;
pq.push(mp(0, s));
dj[s]=0;
while (pq.size()){
int node=pq.top().se;
pq.pop();
if (visited[node])continue;
visited[node]=1;
for (auto num:graph[node])if (!visited[num.fi]&&num.se+dj[node]<dj[num.fi]){
dj[num.fi]=num.se+dj[node];
pq.push(mp(dj[num.fi], num.fi));
}
}
return dj;
}
int32_t main(){
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
int m, s, t, l, k, a, b, c, ans=0;
cin>>n>>m>>s>>t>>l>>k;
graph.resize(n+1);
while (m--){
cin>>a>>b>>c;
graph[a].pb(mp(b, c));
graph[b].pb(mp(a, c));
}
vector<int> ds=dijk(s), dt=dijk(t);
if (ds[t]<=k){
cout<<n*(n-1)/2;
return 0;
}
vector<pii> vect;
for (int i=1; i<=n; ++i)vect.pb(mp(dt[i], i));
sort(vect.begin(), vect.end());
for (int i=1; i<=n; ++i)ans+=upper_bound(vect.begin(), vect.end(), mp(k-l-ds[i], LLONG_MAX/2))-vect.begin()-(dt[i]<=k-l-ds[i]);
cout<<ans;
}
