Problem Statement

Shuz*-kun has a toy train consisting of $N$ cars, numbered from $1$ to $N$.
Each car $i$ has a coolness value $A_i$.
With this toy, car $i$ and car $i + 1$ can be connected and separated.
Shuz*-kun is playing with this toy, and from time to time he wants to check the coolness of the connected cars.
Initially, all cars are separated.
Write a program that can process the following queries.
1. connect $x$
If car $x$ and car $x+1$ are not connected, connect them.
2. separate $x$
If car $x$ and car $x+1$ are connected, separate them.
3. remodel $x$
Car $x$ has been remodeled, and as a result the coolness of car $x$ increased by $1$.
4. attractiveness $x$
Output the total coolness of car $x$ and all cars connected to it.

Constraints

Input

$N\ Q$
$A_1\ A_2\ \dots\ A_N$
$query_1\ x_1$
$query_2\ x_2$
$\vdots$
$query_Q\ x_Q$

Output

For each attractiveness query, output the coolness on one line. Print a newline at the end.

Sample

2 7
1 3
4 1
4 2
1 1
4 1
4 2
3 1
4 1

1
3
4
4
5

10 10
1 3 10 20 3 4 12 41 2 40
1 2
1 4
1 5
4 1
4 4
3 2
1 3
2 5
4 2
4 6

1
27
37
4