Big binary tree

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¡Üu¡Ün;1¡Üx¡Ü10^10) 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¡Ün¡Ü10^8,1¡Üm¡Ü10^5), 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.

Sample Input

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

Sample Output

17

17

17

16

17

17

12

12

12

11

12

12

Source

2017 Multi-University Training Contest - Team 9