Yuezheng Ling gives Luo Tianyi a tree which has n hubs, established at 1. Luo Tianyi will let you know that the parent of the I-th hub is simulated intelligence (1≤ai
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Yuezheng Ling gives Luo Tianyi a tree which has n hubs, established at 1.
Luo Tianyi will let you know that the parent of the I-th hub is simulated intelligence (1≤ai<i for 2≤i≤n), and she will request that you perform q questions of 2 sorts:
She'll give you three integers l, r and x (2≤l≤r≤n, 1≤x≤105). You want to supplant man-made intelligence with max(ai−x,1) for all I with l≤i≤r.
She'll give both of you integers u, v (1≤u,v≤n). You want to find the LCA of hubs u and v (their most minimal normal progenitor).
Input
The primary line contains two integers n and q (2≤n,q≤105) — the number of hubs and the number of inquiries, individually.
The subsequent line contains n−1 integers a2,a3,… ,an (1≤ai<i), where simulated intelligence is the parent of the hub I.
Next q lines contain inquiries. For each question, the main integer of each line is t (t=1 or 2) — the kind of the inquiry.
If t=1, this addresses the inquiry of the main kind. Then, at that point, three integers will follow: l, r, x (2≤l≤r≤n, 1≤x≤105), implying that you need to supplant
In the event that t=2, this addresses the question of the subsequent sort. Then, at that point, two integers will follow: u and v (1≤u,v≤n), and you need to find the LCA of u and v.
It's dependable that there is somewhere around one question of the subsequent sort.
Output
For each question of the subsequent sort output reply on another line
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