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\n", Query(root));
    }
    return 0;
}