#include <bits/stdc++.h>
using namespace std;

char buf[1 << 20], *p1 = buf, *p2 = buf, ouf[1 << 23], *p3 = ouf;
inline char input() {
    if (p1 == p2) p2 = buf + fread(p1 = buf, 1, 1 << 20, stdin);
    return *(p1++);
}
inline void read(int &x) {
    static char ch = input();
    x = 0;
    while (!isdigit(ch)) ch = input();
    while (isdigit(ch)) x = (x << 3) + (x << 1) + (ch ^ 48), ch = input();
}

const int N = 4e5 + 15;
int n, q, B, a[N], pre[N];
int pos[N];

int m, l[N], r[N], flag[N], cnt[N];

inline int del(int x, int d) { return max(x - d, 1); }
inline void init() {
    for (int i = 1; i * B <= n; i++) ++m, l[m] = r[m - 1] + 1, r[m] = i * B;
    if (m * B < n) ++m, l[m] = r[m - 1] + 1, r[m] = n;
    
    for (int i = 1; i <= m; i++)
        for (int j = l[i]; j <= r[i]; j++) pos[j] = i;
}
inline void build(int u) { for (int i = l[u]; i <= r[u]; i++) pre[i] = (a[i] < l[u]) ? a[i] : pre[a[i]]; }
inline void pushdown(int u) {
    if (flag[u])
        for (int i = l[u]; i <= r[u]; i++) a[i] = del(a[i], flag[u]);
    flag[u] = 0; build(u);
}

inline void change(int x, int y, int d) {
    if (pos[x] == pos[y]) {
        for (int i = x; i <= y; i++) a[i] = del(a[i], d);
        build(pos[x]);
        return;
    }
    for (int i = x; i <= r[pos[x]]; i++) a[i] = del(a[i], d);
    for (int i = l[pos[y]]; i <= y; i++) a[i] = del(a[i], d);
    build(pos[x]), build(pos[y]);

    for (int u = pos[x] + 1; u <= pos[y] - 1; u++) {
        flag[u] = min(flag[u] + d, n), cnt[u] = min(cnt[u] + d, n);
        if (cnt[u] <= B) pushdown(u);  //更新次数较少，暴力重构
    }
}

inline int lca(int x, int y) {
    while (pos[x] != pos[y]) {
        if (pos[x] < pos[y]) swap(x, y);
        if (cnt[pos[x]] <= B) x = del(pre[x], flag[pos[x]]);
        else x = del(a[x], flag[pos[x]]);
    }
    while (x != y) {
        if (x < y) swap(x, y);
        x = del(a[x], flag[pos[x]]);
    }
    return x;
}

int main() {
    read(n), read(q), B = 500;
    init();
    for (int i = 2; i <= n; i++) read(a[i]);
    for (int i = 1; i <= m; i++) build(i);
    int lst = 0;
    while (q--) {
        int opt; read(opt);
        if (opt == 1) {
            int l, r, x; read(l), read(r), read(x);
            l ^= lst, r ^= lst, x ^= lst;
            change(l, r, x);
        } else {
            int u, v; read(u), read(v);
            u ^= lst, v ^= lst;
            lst = lca(u, v);
            printf("%d\n", lst);
        }
    }
    return 0;
}