**Time limit:**1.00 s**Memory limit:**512 MB

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