Big binary tree
TimeLimit:2000MS MemoryLimit:65536KB
64-bit integer IO format:%I64d
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Problem Description
You are given a complete binary tree with n nodes. The root node is numbered 1, and node x's father node is $\left \lfloor x/2 \right \rfloor$. At the beginning, node x has a value of exactly x. We define the value of a path as the sum of all nodes it passes(including two ends, or one if the path only has one node). Now there are two kinds of operations:
1. change u x Set node u's value as x(1≤u≤n;1≤x≤10^10)
2. query u Query the max value of all paths which passes node u.
Input
There are multiple cases.
For each case:
The first line contains two integers n,m(1≤n≤10^8,1≤m≤10^5), which represent the size of the tree and the number of operations, respectively.
Then m lines follows. Each line is an operation with syntax described above.
For each case:
The first line contains two integers n,m(1≤n≤10^8,1≤m≤10^5), which represent the size of the tree and the number of operations, respectively.
Then m lines follows. Each line is an operation with syntax described above.
Output
For each query operation, output an integer in one line, indicating the max value of all paths which passes the specific node.
SampleInput
6 13 query 1 query 2 query 3 query 4 query 5 query 6 change 6 1 query 1 query 2 query 3 query 4 query 5 query 6
SampleOutput
17 17 17 16 17 17 12 12 12 11 12 12