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| #include <bits/stdc++.h>
#define STC static
#define fi first
#define se second
#define FF std::function
using LL = long long;
using PII = std::pair<int, int>;
const int N = 1e5 + 100;
const LL INF = 123456789123456789;
int n, m, ctl = 0, bid[N];
std::vector<PII> G[N];
LL dis[N];
struct Line
{
int k;
LL b;
LL calc(int x){ return dis[bid[x]] * k + b; }
} li[N << 1];
namespace LC
{
using std::max;
using std::min;
int id[N << 2];
LL mn[N << 4];
#define mid (l + r >> 1)
#define lc (u << 1)
#define rc (u << 1 | 1)
bool judge(int a, int b, int x){ return li[a].calc(x) > li[b].calc(x); }
void upd(int u, int l, int r, int ql, int qr, int d)
{
STC FF<void(int, int, int)> up = [&](int u, int l, int r)
{
mn[u] = min(mn[u], min(li[id[u]].calc(l), li[id[u]].calc(r)));
mn[u] = min(mn[u], min(mn[lc], mn[rc]));
} ;
if (l >= ql && r <= qr)
{
if (judge(id[u], d, mid)) std::swap(id[u], d);
if (judge(id[u], d, l)) upd(lc, l, mid, ql, qr, d);
if (judge(id[u], d, r)) upd(rc, mid + 1, r, ql, qr, d);
return up(u, l, r);
}
if (ql <= mid) upd(lc, l, mid, ql, qr, d);
if (qr > mid) upd(rc, mid + 1, r, ql, qr, d);
up(u, l, r);
}
LL ask(int u, int l, int r, int ql, int qr)
{
if (l >= ql && r <= qr) return mn[u];
LL res = min(li[id[u]].calc(max(l, ql)), li[id[u]].calc(min(r, qr)));
if (ql <= mid) res = min(res, ask(lc, l, mid, ql, qr));
if (qr > mid) res = min(res, ask(rc, mid + 1, r, ql, qr));
return res;
}
#undef mid
#undef lc
#undef rc
}
namespace TCS
{
int fa[N], top[N], id[N], cnt, dep[N], si[N], son[N];
void prev()
{
FF<void(int, int, int, LL)> dfs1 = [&](int x, int f, int d, LL di)
{
fa[x] = f, dep[x] = d, dis[x] = di, si[x] = 1;
for (PII e : G[x]) if (e.fi != f)
{
dfs1(e.fi, x, d + 1, di + e.se);
si[x] += si[e.fi];
if (si[e.fi] > si[son[x]]) son[x] = e.fi;
}
} ;
FF<void(int, int)> dfs2 = [&](int x, int t)
{
top[x] = t, id[x] = ++cnt, bid[cnt] = x;
if (!son[x]) return ;
dfs2(son[x], t);
for (PII e : G[x]) if (e.fi != fa[x] && e.fi != son[x]) dfs2(e.fi, e.fi);
} ;
dfs1(1, 0, 1, 0), dfs2(1, 1);
}
void change(int s, int t, int a, int b)
{
STC FF<int(int, int)> lca = [&](int x, int y)
{
while (top[x] != top[y]) dep[top[x]] > dep[top[y]] ? x = fa[top[x]] : y = fa[top[y]];
return dep[x] > dep[y] ? y : x;
} ;
STC FF<void(int, int, int)> modify = [&](int x, int y, int d)
{
while (top[x] != top[y]) LC::upd(1, 1, n, id[top[x]], id[x], d), x = fa[top[x]];
LC::upd(1, 1, n, id[y], id[x], d);
} ;
int ff = lca(s, t);
li[++ctl] = {-a, dis[s] * a + b}, modify(s, ff, ctl);
li[++ctl] = {a, (dis[s] - (dis[ff] << 1)) * a + b}, modify(t, ff, ctl);
}
LL ask(int s, int t)
{
LL res = INF;
while (top[s] != top[t])
{
if (dep[top[s]] < dep[top[t]]) std::swap(s, t);
res = std::min(res, LC::ask(1, 1, n, id[top[s]], id[s])), s = fa[top[s]];
}
if (id[s] > id[t]) std::swap(s, t);
return std::min(res, LC::ask(1, 1, n, id[s], id[t]));
}
}
int main()
{
scanf("%d %d", &n, &m);
for (int i = 1, u, v, w; i < n; ++i)
{
scanf("%d %d %d", &u, &v, &w);
G[u].push_back({v, w}), G[v].push_back({u, w});
}
TCS::prev(), li[0] = {0, INF};
std::fill(LC::mn, LC::mn + (N << 4), INF);
for (int op, s, t, a, b; m--; )
{
scanf("%d %d %d", &op, &s, &t);
if (op == 1)
{
scanf("%d %d", &a, &b);
TCS::change(s, t, a, b);
}
else printf("%lld\n", TCS::ask(s, t));
}
return 0;
}
|