3123: [Sdoi2013]森林

题意：一个森林，加边，询问路径上k小值。保证任意时刻是森林

---

LCT没法搞，树上kth肯定要用树上主席树

加边？启发式合并就好了，小的树dfs重建一下

注意

1. 测试点编号不是数据组数！！！
2. 加边的时候要更新邻接链表啊，并且fa要清空
3. 并查集维护size一定初始化1

好了现在我要填报名表了

#include <iostream>

#include <cstdio>

#include <cstring>

#include <algorithm>

using namespace std;

typedef long long ll;

#define lc(x) t[x].l

#define rc(x) t[x].r

const int N=1e5+5, M=2e5+5;

inline int read(){

    char c=getchar();int x=0,f=1;

    while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}

    while(c>='0'&&c<='9'){x=x*10+c-'0';c=getchar();}

    return x*f;

}

int n, m, Q, a[N], u, v, k, mp[N]; char s[5];

namespace ufs{

	int fa[N], size[N];

	int find(int x) {return x==fa[x]?x:fa[x]=find(fa[x]);}

} using ufs::size; using ufs::find;

struct edge{int v,ne;}e[M];

int cnt, h[N];

inline void ins(int u, int v) {

	e[++cnt]=(edge){v, h[u]}; h[u]=cnt;

	e[++cnt]=(edge){u, h[v]}; h[v]=cnt;

}

int vis[N], fa[N][18], deep[N];

int lca(int x, int y) {

	if(deep[x]<deep[y]) swap(x, y);

	int bin=deep[x]-deep[y];

	for(int i=0; i<17; i++) if((1<<i)&bin) x=fa[x][i];

	if(x==y) return x;

	for(int i=16; i>=0; i--)

		if(fa[x][i] != fa[y][i]) x=fa[x][i], y=fa[y][i];

	return fa[x][0];

}

struct ChairTree{

	struct meow{int l,r,size;}t[N*85];

	int sz, root[N];

	void insert(int &x, int l, int r, int p) {

		t[++sz]=t[x]; x=sz;

		t[x].size++;

		if(l==r) return;

		int mid=(l+r)>>1;

		if(p<=mid) insert(lc(x), l, mid, p);

		else insert(rc(x), mid+1, r, p);

	}

	void build(int u) { //printf("build %d %d\n",u,fa[u][0]);

		vis[u]=1;

		for(int i=1; (1<<i)<=deep[u]; i++)

			fa[u][i] = fa[ fa[u][i-1] ][i-1];

		root[u] = root[fa[u][0]];

		insert(root[u], 1, *mp, a[u]);

		for(int i=h[u];i;i=e[i].ne)

			if(e[i].v != fa[u][0]) {

				fa[e[i].v][0]=u; deep[e[i].v]=deep[u]+1;

				build(e[i].v);

			}

	}

	int query(int u, int v, int k) {

		int f=lca(u,v), g=fa[f][0];

		int x=root[u], y=root[v], l=1, r=*mp; f=root[f]; g=root[g];

		while(l!=r) {

			int lsize = t[lc(x)].size + t[lc(y)].size - t[lc(f)].size - t[lc(g)].size;

			int mid=(l+r)>>1;

			if(k<=lsize) x=lc(x), y=lc(y), f=lc(f), g=lc(g), r=mid;

			else x=rc(x), y=rc(y), f=rc(f), g=rc(g), l=mid+1, k-=lsize;

		}

		return l;

	}

	void rebuild(int u) {

		for(int i=1; i<17; i++)

			fa[u][i] = fa[ fa[u][i-1] ][i-1];

		root[u] = root[fa[u][0]];

		insert(root[u], 1, *mp, a[u]);

		for(int i=h[u];i;i=e[i].ne)

			if(e[i].v != fa[u][0]) {

				fa[e[i].v][0]=u; deep[e[i].v]=deep[u]+1;

				rebuild(e[i].v);

			}

	}

	void Link(int u, int v) {

		int x=find(u), y=find(v);

		if(size[x]<size[y]) swap(x, y), swap(u, v);

		ufs::fa[y]=x; size[x]+=size[y];

		ins(u, v);

		fa[v][0]=u; deep[v]=deep[u]+1;

		rebuild(v);

	}

}C;

int candy;

int main() {

	freopen("in","r",stdin);

	int T=read(); T+=2333;

	n=read(); m=read(); Q=read();

	for(int i=1; i<=n; i++) a[i]=mp[i]=read(), ufs::fa[i]=i, size[i]=1;

	sort(mp+1, mp+1+n); mp[0]=unique(mp+1, mp+1+n)-mp-1;

	for(int i=1; i<=n; i++) a[i] = lower_bound(mp+1, mp+1+*mp, a[i])-mp;

	for(int i=1; i<=m; i++) {

		u=read(), v=read();

		ins(u,v);

		u=find(u); v=find(v);

		ufs::fa[v]=u; size[u]+=size[v];

	}

	for(int i=1; i<=n; i++) if(!vis[i]) C.build(i);

	int ans=0;

//candy=1;

	for(int i=1; i<=Q; i++) {

		scanf("%s",s);

		if(candy) u=read(), v=read();

		else u=read()^ans, v=read()^ans;

		if(s[0]=='Q') {

			if(candy) k=read();

			else k=read()^ans;

			ans = mp[C.query(u, v, k)];

			printf("%d\n", ans);

		}else C.Link(u, v);

	}

}