Median II

You are given an array ~a~ of ~n~ elements. Furthermore, there are ~q~ queries. Each query is of the form QUERY l r or UPDATE i v. The former is the query from the previous problem, and the letter means to update index i to value v.

Sample Input

5 3
1 2 3 4 5
QUERY 1 4
UPDATE 2 10
QUERY 1 4

Sample Output

3
4

Constraints

~1 \le n,q \le 1e5~ ~1 \le a[i] \le 1e4~