B"Yuezheng Ling gives Luo Tianyi a tree which has n nodes, rooted at 1 . Luo Tianyi will tell you that the parent of the i -th node is a_i ( 1 <= q a_i<i for 2 <= i <= n ), and she will ask you to perform q queries of 2 types: The first line contains two integers n and q ( 2 <= q n,q <= q 10^5 ) -- the number of nodes and the number of queries, respectively. The second line contains n-1 integers a_2, a_3, ... , a_n ( 1 <= a_i < i ), where a_i is the parent of the node i . Next q lines contain queries. For each query, the first integer of each line is t ( t = 1 or 2 ) -- the type of the query. If t = 1 , this represents the query of the first type. Then, three integers will follow: l , r , x ( 2 <= l <= r <= n , 1 <= x <= 10^5 ), meaning that you have to replace a_i with max(a_i-x,1) for all i with l <= q i <= q r . If t = 2 , this represents the query of the second type. Then, two integers will follow: u and v ( 1 <= u, v <= n ), and you have to find the LCA of u and v . It's guaranteed that there is at least one query of the second type. For each query of the second type output answer on a new line. The tree in example is shown below. After the query of the first type, the tree changes and is looking as shown below. "...