#include<bits/stdc++.h>
#define pb push_back
#define fors(i, a, b) for(int i = (a); i < (b); ++i)
using namespace std;
const int maxn = 1e5 + 5;
const int B = 320;
int g[maxn], a[maxn], res[maxn], on[maxn], bel[maxn];
int in[maxn];
int n, q;
inline void go(int i, int x){
    if(g[i]==i){in[i]+=x; in[i] = min(in[i], n); return;}
    a[i] = max(a[i]-x, 1);
    if(bel[a[i]] == bel[i]) g[i] = g[a[i]];
    else g[i] = i, res[bel[i]]--;
    return;
}
int h[maxn];
void update(int l, int r, int x){
    int id1=bel[l], id2=bel[r];
    int ed = min((id2+1)*B-1, n);
    if(id1 == id2){
        while(l<=r) go(l++, x);
        fors(i,r+1,ed+1) go(i, 0);
        return;
    }
    while(l < (id1+1)*B) go(l++,x);
    fors(i,id2*B,r+1) go(i, x);
    fors(i,r+1,ed+1) go(i, 0);
    fors(i,id1+1,id2){
        if(res[i]==0) on[i]+=x, on[i] = min(on[i], n);
        else fors(j,i*B,(i+1)*B) go(j, x);
    }return;
}
inline int fa(int x){
    int t = in[x]+on[x/B];
    return max(a[x]-t, 1);
}
int lca(int x, int y){
    while(x!=y){
        if(x>y) swap(x,y);
        if(bel[x]!=bel[y]) y=fa(g[y]);
        else if(g[x]!=g[y]) x=fa(g[x]),y=fa(g[y]);
        else y=fa(y);
    }
    return x;
}
int main()
{
    scanf("%d%d", &n, &q); a[1] = 1; g[1] = 1;
    fors(i,1,n+1) bel[i] = i/B;
    fors(i,2,n+1) {
        scanf("%d", &a[i]);
        if(bel[a[i]] != bel[i]) g[i] = i;
        else g[i] = g[a[i]], res[bel[i]]++;
    }
    while(q--){
        int op,x,y; scanf("%d%d%d", &op,&x,&y);
        if(op==1){
            int w; scanf("%d", &w);
            update(x, y, w);
        }else{
            printf("%d\n", lca(x,y));
        }
    }
	return 0;
}
