#include <iostream>
#include <iomanip>
#include <vector>
#include <cmath>
#include <algorithm>
#include <set>
#include <queue>
#include <map>
#include <unordered_map>
#include <stack>
#include <bitset>
#include <string>
#include <cstring>
#include <iterator>
#include <random>
#define ll long long
#define ld long double
#define inf (ll)(2*1e18)
#define sort(a) sort(a.begin(), a.end())
#define reverse(a) reverse(a.begin(), a.end())
#define pb push_back
#define endl "\n"
using namespace std;
void Dijkstra(ll start, vector<vector<pair<ll, ll>>>& a, vector<ll>& dis){
set<pair<ll, ll>> s;
s.insert({0, start});
dis[start] = 0;
while(!s.empty()){
auto [val, x] = *s.begin();
s.erase(s.begin());
for(auto [y, w]: a[x]){
if(dis[y] > val + w){
s.erase({dis[y], y});
dis[y] = val + w;
s.insert({dis[y], y});
}
}
}
}
void solve(){
ll n, m, k, l, i, start, finish, x, y, w, res=0;
cin>>n>>m>>start>>finish>>l>>k;
--start;
--finish;
vector<vector<pair<ll, ll>>> a(n);
vector<ll> dis1(n, inf);
vector<ll> dis2(n, inf);
for(i=0;i<m;++i){
cin>>x>>y>>w;
--x;
--y;
a[x].pb({y, w});
a[y].pb({x, w});
}
Dijkstra(start, a, dis1);
Dijkstra(finish, a, dis2);
if(dis1[finish] <= k){
cout<<n*(n-1)/2<<endl;
return;
}
sort(dis1);
sort(dis2);
k -= l;
for(i=0;i<n;++i){
res += upper_bound(dis2.begin(), dis2.end(), k - dis1[i]) - dis2.begin();
}
cout<<res<<endl;
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cout.tie(nullptr);
srand(time(nullptr));
ll t=1;
// cin>>t;
for(;t>0;--t){
solve();
}
return 0;
}
