#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef vector<vi> vii;
typedef pair<int,int> pi;
typedef vector<pi> pii;
typedef tuple<int,int,int> tii;
#define REP(i,a,b) for(int i=a;i<b;i++)
#define F first
#define S second
#define PB push_back
#define MP make_pair
#define LSOne(s) ((s)&(-s))
ll INF=1e18+10;
int inf=1e9+10;
ll M=1e9+7;
vector<vector<pair<int,ll>>> a;
void djikistra(vector<ll> &c,int s){
priority_queue<pi,vector<pi>,greater<pi>> pq;
c[s]=0;
pq.push({0,s});
while(!pq.empty()){
ll x=pq.top().F;
int y=pq.top().S;
pq.pop();
if(c[y]<x)continue;
for(auto u:a[y]){
if(c[u.F]<=c[y]+u.S)continue;
c[u.F]=c[y]+u.S;
pq.push({c[u.F],u.F});
}
}
}
int main() {
//ios::sync_with_stdio(0);
//cin.tie(0);
//freopen("test_input.txt", "r", stdin);
//freopen("test_output.txt", "w", stdout);
int n,m;cin>>n>>m;
int s,t;ll l,k;cin>>s>>t>>l>>k;
s--;t--;
a.resize(n);
vector<ll> b(n,INF),c(n,INF);
REP(i,0,m){
int x,y,z;cin>>x>>y>>z;
x--;y--;
a[x].PB({y,z});
a[y].PB({x,z});
}
djikistra(b,s);
djikistra(c,t);
if(b[t]<=k){
cout<<((ll)n*(n-1))/2;
return 0;
}
sort(c.begin(),c.end());
ll ans=0;
REP(i,0,n)ans+=upper_bound(c.begin(),c.end(),k-l-b[i])-c.begin();
cout<<ans;
}
