// Judges with GCC >= 12 only needs Ofast
// #pragma GCC optimize("O3,no-stack-protector,fast-math,unroll-loops,tree-vectorize")
// MLE optimization
// #pragma GCC optimize("conserve-stack")
// Old judges
// #pragma GCC target("sse4.2,popcnt,lzcnt,abm,mmx,fma,bmi,bmi2")
// New judges. Test with assert(__builtin_cpu_supports("avx2"));
// #pragma GCC target("avx2,popcnt,lzcnt,abm,bmi,bmi2,fma,tune=native")
// Atcoder
// #pragma GCC target("avx2,popcnt,lzcnt,abm,bmi,bmi2,fma")
/*
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
typedef tree<int,null_type,less<int>,rb_tree_tag,tree_order_statistics_node_update> ordered_set;
- insert(x),erase(x)
- find_by_order(k): return iterator to the k-th smallest element
- order_of_key(x): the number of elements that are strictly smaller
*/
#include<bits/stdc++.h>
using namespace std;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
uniform_real_distribution<> pp(0.0,1.0);
#define int long long
#define ld long double
#define pii pair<int,int>
#define piii pair<pii,int>
#define mpp make_pair
#define fi first
#define se second
const int inf=1e18;
const int mod=998244353;
const int maxn=200005;
const int bl=650;
const int maxs=655;
const int maxm=200005;
const int maxq=1000005;
const int maxl=25;
const int maxa=1000000;
const int root=3;
int power(int a,int n){
int res=1;
while(n){
if(n&1) res=res*a%mod;
a=a*a%mod;n>>=1;
}
return res;
}
const int iroot=power(3,mod-2);
const int base=101;
int n,m,S,T,L,K,d[2][maxn];
vector<pii> edge[maxn];
int bit[maxn];
void update(int x){
for(int i=x;i<=n;i+=(i&(-i))) bit[i]++;
}
int query(int x){
int res=0;
for(int i=x;i>=1;i-=(i&(-i))) res+=bit[i];
return res;
}
void dijisktra(int s,int t){
for(int i=1;i<=n;i++) d[t][i]=inf;
priority_queue<pii,vector<pii>,greater<pii>> pq;
d[t][s]=0;pq.push({0,s});
while(!pq.empty()){
auto [dd,u]=pq.top();pq.pop();
if(d[t][u]!=dd) continue;
for(auto [v,w]:edge[u]){
if(d[t][v]>dd+w) pq.push({d[t][v]=dd+w,v});
}
}
}
void solve(){
cin >> n >> m >> S >> T >> L >> K;
for(int i=1;i<=m;i++){
int u,v,w;cin >> u >> v >> w;
edge[u].push_back({v,w});
edge[v].push_back({u,w});
}
dijisktra(S,0);dijisktra(T,1);
if(d[0][T]<=K){
cout << n*(n-1)/2 << '\n';
return;
}
K-=L;
int res=0;
vector<int> d1;
for(int i=1;i<=n;i++) d1.push_back(d[1][i]);
sort(d1.begin(),d1.end());
for(int i=1;i<=n;i++){
int dd=K-d[0][i];
res+=upper_bound(d1.begin(),d1.end(),dd)-d1.begin();
}
d1.erase(unique(d1.begin(),d1.end()),d1.end());
vector<piii> p;
for(int i=1;i<=n;i++){
p.push_back({{d[0][i],d[1][i]},-1});
p.push_back({{K-d[1][i],K-d[0][i]},0});
}
sort(p.begin(),p.end());
for(auto [x,id]:p){
int pos=upper_bound(d1.begin(),d1.end(),x.se)-d1.begin();
if(id==0) res-=query(pos);
else update(pos);
}
cout << res << '\n';
}
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);cout.tie(NULL);
int test=1;//cin >> test;
while(test--) solve();
}
