#include "closing.h"
#include <bits/stdc++.h>
using namespace std;
#define m_p make_pair
#define all(x) (x).begin(),(x).end()
#define sz(x) ((int)(x).size())
#define fi first
#define se second
typedef long long ll;
mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());
mt19937 rnf(2106);
const int N = 400005;
int n;
vector<pair<int, int> > g[N];
void dfs0(int x, int p, vector<ll>& d)
{
if (x == p)
d[x] = 0;
for (int i = 0; i < g[x].size(); ++i)
{
int h = g[x][i].fi;
if (h == p)
continue;
d[h] = d[x] + g[x][i].se;
dfs0(h, x, d);
}
}
bool dfs1(int x, int p, int y, vector<int>& v)
{
v.push_back(x);
if (x == y)
return true;
for (int i = 0; i < g[x].size(); ++i)
{
int h = g[x][i].fi;
if (h == p)
continue;
if (dfs1(h, x, y, v))
return true;
}
v.pop_back();
return false;
}
bool c[N];
int u1[N], u2[N];
vector<pair<ll, int> > u;
int q[N * 4];
ll s[N * 4];
ll s1[N * 4], s2[N * 4];
int q2[N * 4];
void bil(int tl, int tr, int pos)
{
q[pos] = 0;
s[pos] = 0;
s1[pos] = s2[pos] = 0;
q2[pos] = 0;
if (tl == tr)
return;
int m = (tl + tr) / 2;
bil(tl, m, pos * 2);
bil(m + 1, tr, pos * 2 + 1);
}
void ubd(int tl, int tr, int x, int y, int pos)
{
if (tl == tr)
{
if (u[tl].se < 0)
{
s1[pos] += y * u[tl].fi / 2;
q[pos] += y;
}
else
{
s2[pos] += y * u[tl].fi / 2;
q2[pos] += y / 2;
}
s[pos] += y * u[tl].fi;
return;
}
int m = (tl + tr) / 2;
if (x <= m)
ubd(tl, m, x, y, pos * 2);
else
ubd(m + 1, tr, x, y, pos * 2 + 1);
q[pos] = q[pos * 2] + q[pos * 2 + 1];
s[pos] = s[pos * 2] + s[pos * 2 + 1];
q2[pos] = q2[pos * 2] + q2[pos * 2 + 1];
s1[pos] = s1[pos * 2] + s1[pos * 2 + 1];
s2[pos] = s2[pos * 2] + s2[pos * 2 + 1];
}
void qry1(int tl, int tr, ll& kk, int& qq, int pos)
{
if (kk >= s[pos])
{
kk -= s[pos];
qq += q[pos];
return;
}
if (tl == tr)
{
for (int i = 0; i < q[pos]; ++i)
{
if (kk >= u[tl].fi)
{
kk -= u[tl].fi;
if (u[tl].se < 0)
++qq;
}
}
return;
}
int m = (tl + tr) / 2;
qry1(tl, m, kk, qq, pos * 2);
qry1(m + 1, tr, kk, qq, pos * 2 + 1);
}
ll qry2(int tl, int tr, int qq, int pos)
{
assert(qq <= q[pos]);
if (qq == q[pos])
return s1[pos];
if (tl == tr)
return 0;
int m = (tl + tr) / 2;
if (qq <= q[pos * 2])
return qry2(tl, m, qq, pos * 2);
return s1[pos * 2] + qry2(m + 1, tr, qq - q[pos * 2], pos * 2 + 1);
}
int qry3(int tl, int tr, ll kk, int pos)
{
if (kk >= s2[pos])
return q2[pos];
if (tl == tr)
return 0;
int m = (tl + tr) / 2;
if (kk <= s2[pos])
return qry3(tl, m, kk, pos * 2);
return q2[pos * 2] + qry3(m + 1, tr, kk - s2[pos * 2], pos * 2 + 1);
}
int max_score(int N, int X, int Y, long long K,
std::vector<int> U, std::vector<int> V, std::vector<int> W)
{
n = N;
for (int i = 0; i <= n + 1; ++i)
{
c[i] = false;
g[i].clear();
}
for (int i = 0; i < n - 1; ++i)
{
int x = U[i];
int y = V[i];
int z = W[i];
g[x].push_back(m_p(y, z));
g[y].push_back(m_p(x, z));
}
vector<ll> dX(n);
dfs0(X, X, dX);
vector<ll> dY(n);
dfs0(Y, Y, dY);
vector<int> v;
assert(dfs1(X, X, Y, v));
assert(v[0] == X && v.back() == Y);
int ans = 0;
{
vector<ll> w;
for (int x = 0; x < n; ++x)
w.push_back(min(dX[x], dY[x]));
sort(all(w));
ll k = K;
for (int i = 0; i < n; ++i)
{
if (k >= w[i])
{
k -= w[i];
++ans;
}
}
}
u.clear();
for (int x = 0; x < n; ++x)
{
u.push_back(m_p((max(dX[x], dY[x]) - min(dX[x], dY[x])) * 2, -(x + 1)));
u.push_back(m_p(max(dX[x], dY[x]), x));
}
sort(all(u));
for (int i = 0; i < sz(u); ++i)
{
if (u[i].se >= 0)
u2[u[i].se] = i;
else
u1[-u[i].se - 1] = i;
}
ll k = K;
int pans = 0;
vector<ll> w1;
bil(0, sz(u) - 1, 1);
for (int x = 0; x < n; ++x)
ubd(0, sz(u) - 1, u2[x], 2, 1);
for (int i = 0; i < sz(v); ++i)
{
int x = v[i];
c[x] = true;
if (k >= min(dX[x], dY[x]))
{
k -= min(dX[x], dY[x]);
++pans;
w1.push_back(max(dX[x], dY[x]) - min(dX[x], dY[x]));
ubd(0, sz(u) - 1, u2[x], -2, 1);
ubd(0, sz(u) - 1, u1[x], 1, 1);
}
}
if (pans != sz(v))
return ans;
vector<pair<ll, int> > w;
for (int x = 0; x < n; ++x)
{
if (c[x])
continue;
w.push_back(m_p(min(dX[x], dY[x]), x));
}
sort(all(w));
for (int i = -1; i < sz(w); ++i)
{
if (i >= 0)
{
int x = w[i].se;
c[x] = true;
k -= min(dX[x], dY[x]);
++pans;
w1.push_back(max(dX[x], dY[x]) - min(dX[x], dY[x]));
ubd(0, sz(u) - 1, u2[x], -2, 1);
ubd(0, sz(u) - 1, u1[x], 1, 1);
if (k < 0)
break;
}
/*vector<ll> w2;
for (int x = 0; x < n; ++x)
{
if (!c[x])
{
w2.push_back(max(dX[x], dY[x]));
}
}
sort(all(w2));
sort(all(w1));
vector<ll> p1, p2;
p1.push_back(0);
for (int i = 0; i < sz(w1); ++i)
{
p1.push_back(p1.back() + w1[i]);
}
p2.push_back(0);
for (int i = 0; i < sz(w2); ++i)
{
p2.push_back(p2.back() + w2[i]);
}
/*vector<pair<ll, bool> > ww;
for (int i = 0; i < sz(w1); ++i)
{
ww.push_back(m_p(w1[i] * 2, true));
}
for (int i = 0; i < sz(w2); ++i)
{
ww.push_back(m_p(w2[i], false));
ww.push_back(m_p(w2[i], false));
}
sort(all(ww));
ll kk = k * 2;
int q = 0;
for (int i = 0; i < sz(ww); ++i)
{
if (kk >= ww[i].fi)
{
kk -= ww[i].fi;
if (ww[i].se)
++q;
}
}*/
ll kk = k * 2;
int q = 0;
qry1(0, sz(u) - 1, kk, q, 1);
/*for (int i = max(0, q - 2); i <= min(sz(p1) - 1, q + 2); ++i)
{
for (int j = 0; j < sz(p2); ++j)
{
if (k >= p1[i] + p2[j])
ans = max(ans, pans + i + 2 * j);
}
}*/
for (int i = max(0, q - 2); i <= min(::q[1], q + 2); ++i)
{
ll kk = k;
kk -= qry2(0, sz(u) - 1, i, 1);
if (kk < 0)
continue;
int yans = qry3(0, sz(u) - 1, kk, 1);
yans *= 2;
yans += i + pans;
ans = max(ans, yans);
}
}
return ans;
}
/*
1
8 3 5 100
0 1 1
1 2 1
2 3 1
3 4 1
4 5 1
5 6 1
6 7 1
2
7 0 2 10
0 1 2
0 3 3
1 2 4
2 4 2
2 5 5
5 6 3
4 0 3 20
0 1 18
1 2 1
2 3 19
6
3
*/
