Sol
作为一个刚刚学动态点分治的新手，表示这道题很难啃动。。。
既然是动态点分治，那么先建出点分树，之后暴跳父亲就是log的
这道题就是要求带权重心，可以证明，随意在点分树上从一个点出发，每次选最小答案的子重心，最后一定能找到答案。。感觉就相当于在树上二分。。。
修改就爆跳父亲
# include <bits/stdc++.h>
# define RG register
# define IL inline
# define Fill(a, b) memset(a, b, sizeof(a))
using namespace std;
typedef long long ll;
const int _(2e5 + 10);
IL ll Read(){
RG ll x = 0, z = 1; RG char c = getchar();
for(; c < '0' || c > '9'; c = getchar()) z = c == '-' ? -1 : 1;
for(; c >= '0' && c <= '9'; c = getchar()) x = (x << 1) + (x << 3) + (c ^ 48);
return x * z;
}
int n, fst[_], nxt[_], w[_], to[_], cnt, Q;
IL void Add(RG int u, RG int v, RG int ww){ nxt[cnt] = fst[u]; to[cnt] = v; w[cnt] = ww; fst[u] = cnt++; }
namespace ChainDiv{
int fa[_], size[_], top[_], deep[_], son[_], dfn[_], Index;
IL void Dfs1(RG int u){
size[u] = 1;
for(RG int e = fst[u]; e != -1; e = nxt[e]){
if(size[to[e]]) continue;
deep[to[e]] = deep[u] + w[e]; fa[to[e]] = u;
Dfs1(to[e]);
size[u] += size[to[e]];
if(size[to[e]] > size[son[u]]) son[u] = to[e];
}
}
IL void Dfs2(RG int u, RG int Top){
top[u] = Top; dfn[u] = ++Index;
if(son[u]) Dfs2(son[u], Top);
for(RG int e = fst[u]; e != -1; e = nxt[e]) if(!dfn[to[e]]) Dfs2(to[e], to[e]);
}
IL ll Dis(RG int u, RG int v){
RG ll dis = deep[u] + deep[v];
while(top[u] ^ top[v]){ if(deep[top[u]] < deep[top[v]]) swap(u, v); u = fa[top[u]]; }
if(deep[u] > deep[v]) swap(u, v);
return dis - 2 * deep[u];
}
}
int size[_], mx[_], frt[_], vis[_], rt, sz, root, ft[_];
struct Edge{ int nt, to, rt; } edge[_];
ll sum[_], pres[_], alls[_];
IL void _Add(RG int u, RG int v, RG int rrt){ edge[cnt] = (Edge){ft[u], v, rrt}; ft[u] = cnt++; }
IL void Getroot(RG int u, RG int ff){
size[u] = 1; mx[u] = 0;
for(RG int e = fst[u]; e != -1; e = nxt[e]){
if(vis[to[e]] || to[e] == ff) continue;
Getroot(to[e], u);
size[u] += size[to[e]];
mx[u] = max(mx[u], size[to[e]]);
}
mx[u] = max(mx[u], sz - size[u]);
if(mx[u] < mx[rt]) rt = u;
}
IL void Create(RG int u, RG int ff){
frt[u] = ff; vis[u] = 1;
for(RG int e = fst[u]; e != -1; e = nxt[e]){
if(vis[to[e]]) continue;
rt = 0; sz = size[to[e]];
Getroot(to[e], u);
_Add(u, to[e], rt);
Create(rt, u);
}
}
IL void Modify(RG int u, RG ll d){
sum[u] += d;
for(RG int v = u; frt[v]; v = frt[v]){
RG ll dis = ChainDiv::Dis(u, frt[v]);
sum[frt[v]] += d; pres[v] += d * dis;
alls[frt[v]] += d * dis;
}
}
IL ll Calc(RG int u){
RG ll ret = alls[u];
for(RG int v = u; frt[v]; v = frt[v]){
RG ll dis = ChainDiv::Dis(u, frt[v]);
ret += dis * (sum[frt[v]] - sum[v]);
ret += alls[frt[v]] - pres[v];
}
return ret;
}
IL ll Query(RG int u){
RG ll tmp = Calc(u);
for(RG int e = ft[u]; e != -1; e = edge[e].nt)
if(Calc(edge[e].to) < tmp) return Query(edge[e].rt);
return tmp;
}
int main(RG int argc, RG char* argv[]){
sz = n = Read(); Q = Read(); Fill(fst, -1); Fill(ft, -1);
for(RG int i = 1, a, b, c; i < n; ++i) a = Read(), b = Read(), c = Read(), Add(a, b, c), Add(b, a, c);
ChainDiv::Dfs1(1); ChainDiv::Dfs2(1, 1);
mx[0] = n + 1; cnt = 0;
Getroot(1, 0); root = rt; Create(rt, 0);
while(Q--){
RG int u = Read(), d = Read();
Modify(u, d);
printf("%lld
", Query(root));
}
return 0;
}