// Cookie197
// i am absolute trash
//#pragma GCC optimize("O4,unroll-loops,no-stack-protector")
//#pragma GCC optimize("Ofast")
//#pragma GCC target("avx,avx2,fma")
#include<iostream>
#include<algorithm>
#include<vector>
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<string>
#include<iomanip>
#include<math.h>
#include<unordered_map>
#include <cassert>
#include<random>
using namespace std;
#define i_am_trashQ_Q ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define ll long long
#define pii pair<ll,ll>
#define mp make_pair
#define mod 998244353
//#define mod 1000000007
#define endl "\n"
#define inf (ll)1e18
#define out(x) cout << #x << " = " << x <<endl
#define out2(a,b) cout<< #a << "[" << b << "]" << " = " << a[b] << endl;
#define outp(x) cout << #x << " first = " << x.first << " second = " << x.second << endl
ll n,m,s,t;
ll L,K,ds[200005],dt[200005];
vector<pii> adj[200005];
vector<pii> P,Q;
set<ll> all;
map<ll,ll> tosmall;
int tobig[600005];
bool sort_ds(pii a,pii b){
return a.first < b.first;
}
bool sort_dt(pii a,pii b){
return a.second < b.second;
}
ll bit[600005];
void update(int id,int x){
for (int i=id;i<=600002;i+=(i&-i)){
bit[i] += x;
}
}
int sum(int k){
if (k <= 0) return 0;
int ans = 0;
for (int i=k;i>0;i-=(i&-i)){
ans += bit[i];
}
return ans;
}
signed main(){
i_am_trashQ_Q;
cin>>n>>m;
cin>>s>>t>>L>>K;
for (int i=1;i<=m;i++){
ll a,b,c; cin>>a>>b>>c;
adj[a].push_back(mp(b,c));
adj[b].push_back(mp(a,c));
}
for (int i=1;i<=n;i++) ds[i] = dt[i] = 1e18;
priority_queue<pii,vector<pii>,greater<pii> > pq;
pq.push(mp(0,s));
while(!pq.empty()){
int now=pq.top().second;
ll dis=pq.top().first;
pq.pop();
if(ds[now] != 1e18)continue;
ds[now] = dis;
for (pii p:adj[now]){
if (ds[p.first] != 1e18) continue;
pq.push(mp(dis+p.second,p.first));
}
}
pq.push(mp(0,t));
while(!pq.empty()){
int now=pq.top().second;
ll dis=pq.top().first;
pq.pop();
if(dt[now] != 1e18)continue;
dt[now] = dis;
for (pii p:adj[now]){
if (dt[p.first] != 1e18) continue;
pq.push(mp(dis+p.second,p.first));
}
}
if (ds[t] <= K) {cout<<n*(n-1)/2<<endl; return 0;}
//n = 7; K = 24; L = 0;
//ds[1] = 5; ds[2] = 7; ds[3] = 10; ds[4] = 13; ds[5] = 14; ds[6] = 16; ds[7] = 19;
//dt[1] = 10; dt[2] = 8; dt[3] = 16; dt[4] = 9; dt[5] = 8; dt[6] = 15; dt[7] = 9;
for (int i=1;i<=n;i++) P.push_back(mp(ds[i], dt[i])), Q.push_back(mp(ds[i], dt[i])), all.insert(ds[i]), all.insert(dt[i]), all.insert(K-L+1-dt[i]);
sort(P.begin(), P.end(), sort_ds); sort(Q.begin(), Q.end(), sort_dt);
//for (int i=0;i<n;i++) cout<<Q[i].first<<" "<<Q[i].second<<endl;
int cnt = 0;
for (ll u:all) cnt++, tosmall[u] = cnt, tobig[cnt] = u;
//for (int i=1;i<=cnt;i++) out2(tobig, i);
ll bad_pairs = 0;
int r = n;
for (int i=0;i<n;i++){
while(r >= 1){
if (P[i].first + Q[r-1].second >= K-L+1){
r--;
update(tosmall[Q[r].first], 1);
//out(Q[r].first);
}else break;
}
ll x = 0;
if (P[i].second >= K-L+1) x = sum(600002);
else x = sum(600002) - sum(tosmall[K-L+1-P[i].second] - 1);
//out(x);
bad_pairs += x;
}
for (int i=1;i<=n;i++) if (ds[i] + dt[i] >= K-L+1) bad_pairs--;
cout<<n*(n-1)/2 - bad_pairs/2<<endl;
}
