实在是调不动了，小数据根本拍不出来

#include <iostream>
#include <algorithm>
#include <vector>
#include <map>
using namespace std ;

#define int long long
namespace IO {
	const int MAXSIZE = 1 << 20;
	char buf[MAXSIZE], *p1, *p2;
	#define gc() getchar()
//#define gc()                                                               \
//	(p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, MAXSIZE, stdin), p1 == p2) \
//	 ? EOF                                                               \
//	 : *p1++)

	inline int rd() {
		int x = 0, f = 1;
		char c = gc();
		while (!isdigit(c)) {
			if (c == '-') f = -1;
			c = gc();
		}
		while (isdigit(c)) x = x * 10 + (c ^ 48), c = gc();
		return x * f;
	}

	char pbuf[1 << 20], *pp = pbuf;

	inline void push(const char &c) {
		if (pp - pbuf == 1 << 20) fwrite(pbuf, 1, 1 << 20, stdout), pp = pbuf;
		*pp++ = c;
	}

	inline void write(int x) {
		static int sta[35];
		int top = 0;
		do {
			sta[top++] = x % 10, x /= 10;
		} while (x);
		while (top) push(sta[--top] + '0');
	}
}
using namespace IO ;

//const int N = 500005 , L = 10 , K = 7 , M = 998244353 , O = 1000000007 ;
const int N = 500005 , L = 71 , K = 853 , M = 1e9 + 7 , O = 1e9 + 9 ;
int n , m , q , rt , a[N] , t[N<<2] , e[N<<2] , vl[N] , vk[N] ;
vector < int > vc[N] ;
map < int , int > mp , ap ;

int val[N] , wal[N] ;
void dfs ( int x , int w , int ww ) {
	mp [ w ] = x ;
	val [ x ] = w ;
	
	ap [ ww ] = x ;
	wal [ x ] = ww ;
	
	sort ( vc [ x ] .begin ( ) , vc [ x ] .end ( ) ) ;
	int siz = vc [ x ] .size ( ) ;
	for ( int i = 0 ; i < siz ; ++ i )
		dfs ( vc [ x ] [ i ] , ( w * L + i + 1 ) % M , ( ww * K + i + 1 ) % O ) ;
}

void build ( int k , int l , int r ) {
	if ( l == r ) {
		t [ k ] = a [ l ] ;
		e [ k ] = a [ l ] ;
		return ;
	}
	int mid = ( l + r ) >> 1 ;
	build ( k << 1 , l , mid ) ;
	build ( k << 1 | 1 , mid + 1 , r ) ;
	t [ k ] = ( t [ k << 1 ] * vl [ r - mid ] + t [ k << 1 | 1 ] ) % M ;
	e [ k ] = ( e [ k << 1 ] * vk [ r - mid ] + e [ k << 1 | 1 ] ) % O ;
}

int la , lb ;
int query ( int k , int l , int r , int x , int y , int za , int zb ) {
	if ( l == r ) {
		if ( mp .find ( ( za * L + t [ k ] ) % M ) != mp .end ( ) && ap .find ( ( zb * K + e [ k ] ) % O ) != ap .end ( ) ) {
			la = ( za * L + t [ k ] ) % M ;
			lb = ( zb * K + e [ k ] ) % O ;
			return -1 ;
		}
		return 1 ;
	}
	int mid = ( l + r ) >> 1 ;
	if ( x <= l && r <= y ) {
		if ( mp .find ( ( za * vl [ r - l + 1 ] + t [ k ] ) % M ) != mp .end ( ) && ap .find ( ( zb * vk [ r - l + 1 ] + e [ k ] ) % O ) != ap .end ( ) ) {
			la = ( za * vl [ r - l + 1 ] + t [ k ] ) % M ;
			lb = ( zb * vk [ r - l + 1 ] + e [ k ] ) % O ;
			return -1 ;
		}
		if ( mp .find ( ( za * vl [ mid - l + 1 ] + t [ k << 1 ] ) % M ) == mp .end ( ) || ap .find ( ( zb * vk [ mid - l + 1 ] + e [ k << 1 ] ) % O ) == ap .end ( ) ) {
			return query ( k << 1 , l , mid , x , y , za , zb ) ;
		}
		la = ( za * vl [ mid - l + 1 ] + t [ k << 1 ] ) % M ;
		lb = ( zb * vk [ mid - l + 1 ] + e [ k << 1 ] ) % O ;
		return query ( k << 1 | 1 , mid + 1 , r , x , y , la , lb ) ;
	}
	if ( y <= mid )
		return query ( k << 1 , l , mid , x , y , za , zb ) ;
	if ( x > mid )
		return query ( k << 1 | 1 , mid + 1 , r , x , y , za , zb ) ;
	int res = query ( k << 1 , l , mid , x , y , za , zb ) ;
	if ( res == -1 )
		return query ( k << 1 | 1 , mid + 1 , r , x , y , la , lb ) ;
	return res ;
}

void change ( int k , int l , int r , int x , int y ) {
	if ( l == r ) {
		t [ k ] = y ;
		e [ k ] = y ;
		return ;
	}
	int mid = ( l + r ) >> 1 ;
	if ( x <= mid )
		change ( k << 1 , l , mid , x , y ) ;
	else
		change ( k << 1 | 1 , mid + 1 , r , x , y ) ;
	t [ k ] = ( t [ k << 1 ] * vl [ r - mid ] + t [ k << 1 | 1 ] ) % M ;
	e [ k ] = ( e [ k << 1 ] * vk [ r - mid ] + e [ k << 1 | 1 ] ) % O ;
}

signed main ( ) {
	n = rd ( ) , m = rd ( ) , q = rd ( ) ;
	for ( int i = 1 ; i <= n ; ++ i ) {
		int x = rd ( ) ;
		if ( x == 0 ) rt = i ;
		else vc [ x ] .push_back ( i ) ;
	}
	dfs ( rt , 0 , 0 ) ;
	vl [ 0 ] = 1 ;
	vk [ 0 ] = 1 ;
	for ( int i = 1 ; i <= m ; ++ i )
		a [ i ] = rd ( ) , vl [ i ] = vl [ i - 1 ] * L % M , vk [ i ] = vk [ i - 1 ] * K % O ;
	build ( 1 , 1 , m ) ;
	for ( int i = 1 ; i <= q ; ++ i ) {
		int op = rd ( ) , x = rd ( ) , y = rd ( ) ;
		if ( op == 1 ) {
			int z = rd ( ) ;
			la = val [ x ] ;
			lb = wal [ x ] ;
			query ( 1 , 1 , m , y , z , val [ x ] , wal [ x ] ) ;
			cout << mp [ la ] << "\n" ;
		} else {
			change ( 1 , 1 , m , x , y ) ;
			a [ x ] = y ;
		}
	}
	return 0 ;
}