#include <bits/stdc++.h>
const int N = 4e5, S = 6.4e2, T = 6.4e2;
int n, q, fa[N + 5], pre[N + 5], pos[N + 5];
struct Block {
    int l, r, tag, mx;
    void build() {
        mx = 0;
        for (int i = l; i <= r; ++i) {
            fa[i] = std::max(fa[i] - tag, 1), mx = std::max(mx, fa[i]);
            if (fa[i] < l) pre[i] = fa[i];
            else pre[i] = pre[fa[i]];
        }
        tag = 0;
    }
    void update(int v) {
        if (mx < l) { tag -= v; return ; }
        for (int i = l; i <= r; ++i) fa[i] = std::max(fa[i] - v, 1);
        build();
    }
}ar[T + 5];
int query(int x) { return std::max(pre[x] - ar[pos[x]].tag, 0); }
int getfa(int x) { return x == 1 ? 0 : std::max(fa[x] - ar[pos[x]].tag, 1); }
int main() {
    std::ios::sync_with_stdio(false), std::cin.tie(0), std::cout.tie(0);
    std::cin >> n >> q;
    for (int i = 2; i <= n; ++i) std::cin >> fa[i];
    for (int i = 1; i <= n; ++i) pos[i] = (i - 1) / S + 1;
    for (int i = 1; i <= pos[n]; ++i) ar[i].l = (i - 1) * S + 1, ar[i].r = std::min(i * S, n);
    for (int i = 1; i <= pos[n]; ++i) ar[i].build();
    for (int op, x, y, v, las = 0; q--;) {
        std::cin >> op >> x >> y, x ^= las, y ^= las;
        if (op == 1) {
            std::cin >> v, v ^= las;
            int p = pos[x], q = pos[y];
            if (p == q) {
                for (int i = x; i <= y; ++i) fa[i] -= v;
                ar[p].build();
                continue;
            }
            for (int i = x; i <= ar[p].r; ++i) fa[i] -= v;
            for (int i = ar[q].l; i <= y; ++i) fa[i] -= v;
            ar[p].build(), ar[q].build();
            for (int i = p + 1; i < q; ++i) ar[i].update(v);
        }else {
            while (query(x) != query(y)) {
                if (query(x) < query(y)) std::swap(x, y);
                x = query(x);
            }
            while (x != y) {
                if (getfa(x) < getfa(y)) std::swap(x, y);
                x = getfa(x);
            }
            std::cout << (las = x) << "\n";
        }
    }
    return 0;
}