// 別解
#include <iostream>
#include <vector>
#include <queue>
#include <algorithm>
#include <map>
using namespace std;
using P = pair<long long, int>;
struct edge{
int to;
long long cost;
};
template< typename S, S (*op)(S, S), S (*e)() >
struct segmenttree{
private:
int _n;
std::vector<S> node;
public:
segmenttree() = default;
segmenttree(int n){
_n = 1;
while(_n < n){
_n *= 2;
}
node.resize(2 * _n, e());
}
segmenttree(std::vector<S> &v){
int n = v.size();
_n = 1;
while(_n < n){
_n *= 2;
}
node.resize(2 * _n, e());
for(int i = 0; i < n; i++){
set(i, v[i]);
}
}
// [i] <- val
void set(int i, S val){
i += _n;
node[i] = val;
while(i > 1){
i >>= 1;
node[i] = op(node[2 * i], node[2 * i + 1]);
}
}
// [i] <- op([i],val)
void update(int i, S val){
i += _n;
node[i] = op(node[i], val);
while(i > 1){
i >>= 1;
node[i] = op(node[2 * i], node[2 * i + 1]);
}
}
S get(int i){
i += _n;
return node[i];
}
S prod(int l,int r){
S pdl=e(), pdr=e();
l += _n;
r += _n;
while(l < r){
if(l & 1){
pdl = op(pdl, node[l++]);
}
if(r & 1){
pdr = op(node[--r], pdr);
}
l >>= 1;
r >>= 1;
}
return op(pdl, pdr);
};
};
int op(int a, int b){
return a + b;
}
int e(){
return 0;
}
constexpr long long inf = 1e18;
int main(){
int n, m;
cin >> n >> m;
int s, t;
long long l, k;
cin >> s >> t >> l >> k;
s--;
t--;
vector<vector<edge>> g(n);
for(int i = 0; i < m; i++){
int a, b;
long long c;
cin >> a >> b >> c;
a--;
b--;
g[a].push_back({b, c});
g[b].push_back({a, c});
}
priority_queue<P, vector<P>, greater<P>> que;
vector<long long> dist_from_s(n, inf), dist_from_t(n, inf);
dist_from_s[s] = 0;
que.push({0, s});
while(!que.empty()){
auto [dist, now] = que.top();
que.pop();
if(dist_from_s[now] < dist){
continue;
}
for(auto [nxt, c]: g[now]){
if(dist_from_s[nxt] > dist + c){
dist_from_s[nxt] = dist + c;
que.push({dist + c, nxt});
}
}
}
dist_from_t[t] = 0;
que.push({0, t});
while(!que.empty()){
auto [dist, now] = que.top();
que.pop();
if(dist_from_t[now] < dist){
continue;
}
for(auto [nxt, c]: g[now]){
if(dist_from_t[nxt] > dist + c){
dist_from_t[nxt] = dist + c;
que.push({dist + c, nxt});
}
}
}
if(dist_from_s[t] <= k){
cout << (long long)(n) * (n - 1) / 2 << endl;
return 0;
}
vector<long long> val = dist_from_s;
for(int i = 0; i < n; i++){
val.emplace_back(dist_from_t[i]);
}
sort(val.begin(), val.end());
map<long long, int> index;
for(int i = 0; i < 2 * n; i++){
index[val[i]] = i;
}
segmenttree<int, op, e> seg1(2 * n), seg2(2 * n);
long long ans = 0;
for(int i = 0; i < n; i++){
long long ok = k - l - dist_from_s[i];
ans += seg2.prod(0, lower_bound(val.begin(), val.end(), ok + 1) - val.begin());
ok = k - l - dist_from_t[i];
ans += seg1.prod(0, lower_bound(val.begin(), val.end(), ok + 1) - val.begin());
seg1.update(index[dist_from_s[i]], 1);
seg2.update(index[dist_from_t[i]], 1);
}
cout << ans << endl;
}
