luogu 3248

直接向原树加子树是不可能的
考虑重新建立这样一颗树，我们称之为 S 树
将每次需要添加的子树看做一个点，称之为 S 点
新建的树就是由这些点构成的，
那么树的大小是合理的
初始节点为整棵原树
由于添加的子树的节点的编号一定是连续的一段区间
树上的每个节点维护 l, r, rt
分别表示 左端点， 右端点， 这棵子树的根在原树上的编号
定义
宏观树：只有 S 点构成的树 -> S 树
微观树：按照题目描述所形成的树，当然这棵树是不会建立出来的
所有的询问操作都需要微观树的信息
首先考虑对于任意合法的点 B， 如何找出它在原树上的对应点 b， 显然 b 的值域为 [1, n]
S 点满足 l, r 单调
因此首先二分出 B 点在那个 S 点中，
S 点代表的子树的编号是 [S.l, S.r]
所以 B 在该子树中的编号的大小次序为第 B - S.l + 1;
查询区间 k 大 => 主席树
这样的话只需对原树建立主席树
查询以 S.rt 为根的子树中编号第 B - S.l + 1 小的编号就是 b
Link_super 函数是核心
然后考虑查询时所要维护的东西
由于查询树上点对之间的距离，所以只需知道深度就可以解决
维护这么 3 种深度
deep[] 原树的深度
Super_dep[] S 树的深度（宏观树）
Big_deep[] 微观树的深度，当然并不去维护所有存在的点的深度
Big_deep[] 相当于是维护的宏观树，只不过所有 S 点的 Big_deep[] 都是微观树上 S 的真实深度值
这里可以这样理解:
若 Link_super(u, v), u 的值域 [1, n]，
查询的 v 所在 S 树的 S 点的编号为 X；
S 的当前总数 + 1 为 Y;
这样的话 Big_deep[y] = Big_deep[x] + Dis(v, X.rt);
Dis 函数为查询原树上两点之间的距离
查询时分类讨论

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <cstring>
#include <string>

using namespace std;

#define LL long long

#define gc getchar()
inline int read() {int x = ; char c = gc; while(c < '' || c > '') c = gc;
while(c >= '' && c <= '') x = x *  + c - '', c = gc; return x;}
inline LL read_LL() {LL x = ; char c = gc; while(c < '' || c > '') c = gc;
while(c >= '' && c <= '') x = x *  + c - '', c = gc; return x;}
#undef gc

const int N = 5e5 + ;

int n, m, q;
int head[N], cnt;
LL deep[N];
int Super_node;
LL total;
struct Node {int u, v, nxt;} G[N << ];

inline void Link(int u, int v) {
    G[++ cnt].v = v, G[cnt].nxt = head[u], head[u] = cnt;
}

int Hjtjs;

struct NOde {
    int fa[N], size[N], topp[N], tree[N], lst[N], rst[N], tree_js, son[N], bef[N];
    int Lson[N << ], Rson[N << ], Size[N << ], Root[N];

    void Dfs_1(int u, int F_, int depth) {
        deep[u] = depth, fa[u] = F_, size[u] = ;
        for(int i = head[u]; ~ i; i = G[i].nxt) {
            if(G[i].v == F_) continue;
            Dfs_1(G[i].v, u, depth + );
            size[u] += size[G[i].v];
            if(size[G[i].v] > size[son[u]]) son[u] = G[i].v;
        }
    }

    void Dfs_2(int u, int tp) {
        topp[u] = tp, tree[u] = ++ tree_js, lst[u] = tree[u], bef[tree_js] = u;
        if(!son[u]) {rst[u] = tree[u]; return ;}
        Dfs_2(son[u], tp);
        for(int i = head[u]; ~ i; i = G[i].nxt) {if(G[i].v != fa[u] && G[i].v != son[u]) Dfs_2(G[i].v, G[i].v);}
        rst[u] = tree_js;
    }

    void Fill(int x, int y) {Lson[x] = Lson[y], Rson[x] = Rson[y], Size[x] = Size[y];}

    void Insert(int &rt, int l, int r, int x) {
        Fill(++ Hjtjs, rt);
        rt = Hjtjs;
        Size[rt] ++;
        if(l == r) return ;
        int mid = (l + r) >> ;
        if(x <= mid) Insert(Lson[rt], l, mid, x);
        else Insert(Rson[rt], mid + , r, x);
    }

    void Build_tree() {
        Dfs_1(, , );
        Dfs_2(, );
        for(int i = ; i <= n; i ++) {Root[i] = Root[i - ]; Insert(Root[i], , n, bef[i]);}
    }

    inline int Lca(int x, int y) {
        int tpx = topp[x], tpy = topp[y];
        while(tpx != tpy) {
            if(deep[tpx] < deep[tpy]) swap(x, y), swap(tpx, tpy);
            x = fa[tpx], tpx = topp[x];
        }
        return deep[x] < deep[y] ? x : y;
    }

    inline int Dis(int x, int y) {int lca = Lca(x, y); return deep[x] + deep[y] -  * deep[lca];}

    int Sec_A(int ljd, int rjd, int l, int r, int k) {
        if(l == r) return l;
        int mid = (l + r) >> ;
        int imp = Size[Lson[rjd]] - Size[Lson[ljd]];
        if(k <= (Size[Lson[rjd]] - Size[Lson[ljd]])) return Sec_A(Lson[ljd], Lson[rjd], l, mid, k);
        else return Sec_A(Rson[ljd], Rson[rjd], mid + , r, k - (Size[Lson[rjd]] - Size[Lson[ljd]]));
    }

} Tree;

struct Node_ {
    #define E exit(0)

    struct Node_3 {LL l, r; int rt;} Super_graph[N];

    struct Pair {
        // yvan shu zhong de bian hao, fei shu shang
        int Bef_number;
        // chao ji shu de dian de gen , shi yvan shu shang de dian de bian hao
        int Super_rt;
        // chao ji shu de dian de bian hao
        int Super_number;
    };

    int Super_dep[N];
    LL Big_deep[N];
    int f[N][];
    int fa[N];

    Pair Get_information(LL x) {
        int l = , r = Super_node, ans;
        while(l <= r) {
            int mid = (l + r) >> ;
            if(x <= Super_graph[mid].r) ans = mid, r = mid - ;
            else l = mid + ;
        }
        int nottree = Super_graph[ans].rt;
        int imp = Tree.Sec_A(Tree.Root[Tree.lst[nottree] - ], Tree.Root[Tree.rst[nottree]], , n, x - Super_graph[ans].l + );
        return (Pair) {imp, nottree, ans};
    }

    void Link_Super(LL u, LL v) {
        Super_node ++;
        Pair Nodev = Get_information(v);
        Super_graph[Super_node].l = total + , Super_graph[Super_node].r = total + Tree.size[u], Super_graph[Super_node].rt = u;
        total += Tree.size[u];
        Super_dep[Super_node] = Super_dep[Nodev.Super_number] + ;
        int a = Nodev.Super_rt, b = Nodev.Bef_number;
        Big_deep[Super_node] = Big_deep[Nodev.Super_number] + Tree.Dis(b, a) + ;
        f[Super_node][] = Nodev.Super_number;
        fa[Super_node] = Nodev.Bef_number;
        for(int i = ; i <= ; i ++) f[Super_node][i] = f[f[Super_node][i - ]][i - ];
    }

    int Lca(int x, int y) {
        if(Super_dep[x] < Super_dep[y]) swap(x, y);
        int del = Super_dep[x] - Super_dep[y];
        for(int i = ; i <= ; i ++) if(( << i) & del) x = f[x][i];
        if(x == y) return x;
        for(int i = ; i >= ; i --) if(f[x][i] != f[y][i]) x = f[x][i], y = f[y][i];
        return f[x][];
    }

    LL Ask(LL x, LL y) {
        Pair Nodex = Get_information(x), Nodey = Get_information(y);
        if(Super_dep[Nodex.Super_number] <= Super_dep[Nodey.Super_number]) swap(Nodex, Nodey);
        if(Nodex.Super_number == Nodey.Super_number) return Tree.Dis(Nodex.Bef_number, Nodey.Bef_number);
        else {
            int lca = Lca(Nodex.Super_number, Nodey.Super_number);
            LL ret;
            if(lca == Nodey.Super_number) {
                int g = Nodex.Super_number;
                for(int i = ; i >= ; i --) if(f[g][i] && Super_dep[f[g][i]] > Super_dep[lca]) g = f[g][i];
                ret = Big_deep[Nodex.Super_number] - Big_deep[g] +  + Tree.Dis(Nodex.Super_rt, Nodex.Bef_number);
                ret += Tree.Dis(fa[g], Nodey.Bef_number);
            } else {
                int a = Nodex.Super_number, b = Nodey.Super_number;
                for(int i = ; i >= ; i --) {if(f[a][i] && Super_dep[f[a][i]] > Super_dep[lca]) a = f[a][i];}
                for(int i = ; i >= ; i --) {if(f[b][i] && Super_dep[f[b][i]] > Super_dep[lca]) b = f[b][i];}
                ret = Big_deep[Nodex.Super_number] - Big_deep[a] +  + Big_deep[Nodey.Super_number] - Big_deep[b] +  + Tree.Dis(fa[a], fa[b]);
                ret += Tree.Dis(Nodex.Super_rt, Nodex.Bef_number) + Tree.Dis(Nodey.Super_rt, Nodey.Bef_number);
            }
            return ret;
        }
    }
    #undef E
} S_graph;

int main() {
    n = read(), m = read(), q = read();
    for(int i = ; i <= n; i ++) head[i] = -;
    for(int i = ; i < n; i ++) {int u = read(), v = read(); Link(u, v), Link(v, u);}
    Tree.Build_tree();
    total = n, Super_node = ;
    S_graph.Super_dep[] = ;
    S_graph.f[][] = ;
    S_graph.Super_graph[].l = , S_graph.Super_graph[].r = n, S_graph.Super_graph[].rt = ;
    for(int i = ; i <= m; i ++) {
        LL x = read_LL(), y = read_LL();
        S_graph.Link_Super(x, y);
    }
    for(int i = ; i <= q; i ++) {
        LL x = read_LL(), y = read_LL();
        cout << S_graph.Ask(x, y) << "\n";
    }

    return ;
}