#include <bits/stdc++.h>

using namespace std;

const int MAXN = 100005;
const int MAXM = 321;

int n, siz, q, a[MAXN], b[MAXN];
int lft[MAXM], rit[MAXM], bel[MAXN], tag[MAXM], cnt[MAXM];

inline int read()
{
	int x = 0, f = 1; char ch = getchar();
	while (!isdigit(ch)) { if (ch == '-') f = -1; ch = getchar(); }
	while (isdigit(ch)) { (x *= 10) += ch - '0'; ch = getchar(); }
	return x * f;
}

inline void update(int x)
{
	for (int i = lft[x]; i <= rit[x]; i++)
		a[i] = max(1, a[i]-tag[x]); tag[x] = 0;
	for (int i = lft[x]; i <= rit[x]; i++)
	{
		if (a[i] < lft[x]) b[i] = a[i];
		else b[i] = b[a[i]];
	}
}

inline void prepare()
{
	siz = sqrt(n);
	for (int i = 1; i <= (n-1)/siz+1; i++)
	{
		lft[i] = rit[i-1]+1, rit[i] = min(rit[i-1]+siz, n);
		for (int j = lft[i]; j <= rit[i]; j++)
			bel[j] = i;
	}
	for (int i = 1; i <= bel[n]; i++)
		update(i);
}

void write(int x)
{
	if (x > 9) write(x / 10);
	putchar('0' + x % 10);
}

inline void upd(int l, int r, int x)
{
	if (bel[l] == bel[r])
	{
		for (int i = l; i <= r; i++)
			a[i] = max(1, a[i]-x);
		update(bel[l]); return;
	}
	for (int i = l; i <= rit[bel[l]]; i++)
		a[i] = max(1, a[i]-x); update(bel[l]);
	for (int i = lft[bel[r]]; i <= r; i++)
		a[i] = max(1, a[i]-x); update(bel[r]);
	for (int i = bel[l]+1; i <= bel[r]-1; i++)
	{
		tag[i] = min(n, tag[i]+x); cnt[i]++;
		if (cnt[i] <= siz+2) update(i);
	}
}

inline int get_b(int x)
{ return max(1, b[x]-tag[bel[x]]); }

inline int query(int x, int y)
{
	while (get_b(x) != get_b(y) || bel[x] != bel[y])
	{
		if (bel[x] != bel[y])
		{
			if (bel[x] < bel[y]) swap(x, y);
			x = get_b(x);	
		}
		else
			x = get_b(x), y = get_b(y);
	}
	while (x != y)
	{
		if (x < y) swap(x, y);
		x = max(a[x]-tag[bel[x]], 1);
	}
	return x;
}

int main()
{
	n = read(), q = read();
	for (int i = 2; i <= n; i++)
		a[i] = read();
		
	prepare();
	
	for (int i = 1, opt, x, y, z; i <= q; i++)
	{
		opt = read();
		if (opt == 1)
			x = read(), y = read(), z = read(), upd(x, y, z);
		if (opt == 2)
			x = read(), y = read(), write(query(x, y)), putchar('\n');
	}

  return 0;
}