Pizzeria Queries

There are n buildings on a street, numbered 1,2,\dots,n. Each building has a pizzeria and an apartment. The pizza price in building k is p_k. If you order a pizza from building a to building b, its price (with delivery) is p_a+|a-b|. Your task is to process two types of queries:

The pizza price p_k in building k becomes x.

You are in building k and want to order a pizza. What is the minimum price?

Input

The first input line has two integers n and q: the number of buildings and queries. The second line has n integers p_1,p_2,\dots,p_n: the initial pizza price in each building. Finally, there are q lines that describe the queries. Each line is either "1 k x" or "2 k".

Output

Print the answer for each query of type 2.

Constraints

$1 \le n,q \le 2 \cdot 10^5$

$1 \le p_i, x \le 10^9$

$1 \le k \le n$

Example

Input

6 3
8 6 4 5 7 5
2 2
1 5 1
2 2

Output

5
4