#include <bitset>
#include <cmath>
#include <functional>
#include <algorithm>
#include <numeric>
#include <deque>
#include <fstream>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <unordered_map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <vector>
#include <cstring>
#include <climits>
#define pb push_back
#define MOD 1000000007
#define NMAX 200001
#define nl '\n'
#define INF 1e18
#define pii1 pair<int, pair<int,int>> (1,(1,2));
#define pii pair<int,int>
#define tpl tuple<int,int,int,int,int>
#define int long long
using namespace std;
ifstream fin("data.in");
ofstream fout("data.out");
/*
====================DEMONSTRATION======================
=========================END===========================
*/
int n,m,s,t,l,k;
vector<int>v;
vector<vector<pii>>G(NMAX);
vector<int>dist_s,dist_t;
priority_queue<pii,vector<pii>,greater<pii>>pq;
void dijkstra(int node,vector<int>&dist)
{
for(int i=0;i<n;++i)
dist[i]=INF;
dist[node]=0;
pq.push({0,node});
while(!pq.empty())
{
auto [dis,first]=pq.top();
pq.pop();
if(dist[first]<dis)
continue;
for(auto [u,w]:G[first])
{
if(dist[u]>dist[first]+w)
{
dist[u]=dist[first]+w;
pq.push({dist[u],u});
}
}
}
}
signed main() {
cin>>n>>m;
cin>>s>>t>>l>>k;
s--;
t--;
dist_s.resize(n,INF);
dist_t.resize(n,INF);
for(int i=1;i<=m;++i)
{
int x,y,c;
cin>>x>>y>>c;
x--;
y--;
G[x].pb({y,c});
G[y].pb({x,c});
}
dijkstra(s,dist_s);
dijkstra(t,dist_t);
if(dist_s[t]<=k)
{
cout<<(n*(n-1)/2);
return 0;
}
sort(dist_t.begin(),dist_t.end());
int ans=0;
for(int i=0;i<n;++i)
{
int dis=k-l-dist_s[i];
int pos= lower_bound(dist_t.begin(),dist_t.end(),dis+1)-dist_t.begin();
ans+=pos;
}
cout<<ans;
return 0;
}
