#include <bits/stdc++.h>
using namespace std;
long long inf = 1e18;
long long dis[2][200000];
vector<vector<vector<long long>>> gr;
priority_queue<vector<long long>> pq;
void dk(long long c,long long p,long long t)
{
for(int i = 0;i<gr[p].size();i++)
{
if(dis[t][gr[p][i][0]] > c + gr[p][i][1])
{
dis[t][gr[p][i][0]] = c + gr[p][i][1];
pq.push({(c + gr[p][i][1])*-1,gr[p][i][0],t});
}
}
}
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
long long n,m;
cin>>n>>m;
gr.resize(n);
for(int i = 0;i<n;i++)
{
dis[0][i] = inf;
dis[1][i] = inf;
}
long long s,t,xx;
long long k;
cin>>s>>t>>xx>>k;
s--;t--;
for(int i = 0;i<m;i++)
{
long long a,b,d;
cin>>a>>b>>d;
a--;b--;
gr[a].push_back({b,d});
gr[b].push_back({a,d});
}
dis[0][s] = 0;
dis[1][t] = 0;
pq.push({0,s,0});
pq.push({0,t,1});
while(!pq.empty())
{
long long a = pq.top()[0]*-1;
long long b = pq.top()[1];
long long c = pq.top()[2];
pq.pop();
if(dis[c][b] >= a)
{
dk(a,b,c);
}
}
if(dis[0][t] <= k)
{
cout<<((long long)n*(n-1))/2<<"\n";
return 0;
}
vector<long long> ct(n);
for(int i = 0;i<n;i++)
{
ct[i] = dis[1][i];
//cout<<dis[1][i]<<" "<<i<<" "<<ct[i]<<"\n";
}
sort(ct.begin(),ct.end());
reverse(ct.begin(),ct.end());
vector<long long> cs(n);
for(int i = 0;i<n;i++)
{
cs[i] =dis[0][i];
}
sort(cs.begin(),cs.end());
long long ans = 0;
long long j = 0;
for(int i = 0;i<n;i++)
{
while(j != n && ct[j]+cs[i]+xx>k)
{
j++;
}
//cout<<ct[j]<<" "<<cs[i]<<" "<<xx<<" "<<k<<" "<<j<<" "<<n <<"\n";
ans+=n-j;
}
cout<<ans<<"\n";
}
