#include<bits/stdc++.h>
using namespace std;
#define task "a"
#define ll long long
#define fi first
#define se second
#define ii pair<ll, ll>
const int mxN = 1e5 + 7;
const ll inf = 1e18;
int n, m, s, t;
ll mn[mxN][2], ex, lim;
ii val[mxN];
map<ll, int> mp;
vector<ii> w[mxN];
vector<ll> tree[mxN * 4];
void Dij(int tt, int j)
{
for (int i = 1; i <= n; i++)
mn[i][tt] = inf;
priority_queue<ii, vector<ii>, greater<ii>> pq;
pq.push({0, j});
mn[j][tt] = 0;
while (pq.size())
{
ii j = pq.top();
pq.pop();
if (j.fi != mn[j.se][tt])
continue;
for (ii i : w[j.se])
{
if (mn[i.fi][tt] > j.fi + i.se)
{
mn[i.fi][tt] = j.fi + i.se;
pq.push({j.fi + i.se, i.fi});
}
}
}
}
void Build(int j = 1, int l = 1, int r = n)
{
if (l == r)
{
tree[j].push_back(val[l].se);
return;
}
int mid = (l + r) / 2;
Build(j * 2, l, mid);
Build(j * 2 + 1, mid + 1, r);
merge(tree[j * 2].begin(), tree[j * 2].end(), tree[j * 2 + 1].begin(), tree[j * 2 + 1].end(), back_inserter(tree[j]));
}
ll Get(ll vt, ll dif, int j = 1, int l = 1, int r = n)
{
if (vt < val[l].fi)
return 0;
if (val[r].fi <= vt)
{
int u = lower_bound(tree[j].begin(), tree[j].end(), dif) - tree[j].begin();
int v = upper_bound(tree[j].begin(), tree[j].end(), dif) - tree[j].begin();
mp[dif] += v - u;
return r - l + 1 - v;
}
int mid = (l + r) / 2;
return Get(vt, dif, j * 2, l, mid) + Get(vt, dif, j * 2 + 1, mid + 1, r);
}
int main()
{
ios_base::sync_with_stdio(false);
cin.tie();
cout.tie();
//freopen(task".INP", "r", stdin);
//freopen(task".OUT", "w", stdout);
cin >> n >> m;
cin >> s >> t >> ex >> lim;
for (int i = 1; i <= m; i++)
{
int u, v, cost;
cin >> u >> v >> cost;
w[u].push_back({v, cost});
w[v].push_back({u, cost});
}
Dij(0, s);
Dij(1, t);
for (int i = 1; i <= n; i++)
val[i] = {mn[i][1], mn[i][0] - mn[i][1]};
sort(val + 1, val + n + 1);
Build();
// for (int i = 1; i <= n; i++)
// cout << val[i].fi << " " << val[i].se << " : ";
// cout << '\n';
if (mn[t][0] <= lim)
{
cout << n * (n - 1) / 2;
return 0;
}
ll ans = 0;
for (int i = 1; i <= n; i++)
{
mn[i][1] = mn[i][0] - mn[i][1];
ans += Get(lim - (mn[i][0] + ex), mn[i][1]);
}
for (int i = 1; i <= n; i++)
{
ans += mp[mn[i][1]] / 2;
mp[mn[i][1]] = 0;
}
cout << ans;
}
