Lelei La Lalena has been studying competitive programming in our world. Today, she decides to do a contest on DMOJ to prove her skill! Confident, Lelei opens the sixth problem of the October 2015 DMOPC and finds a really abstract problem with no story. So she decides to make one up and tell to add it to the problem. Anyway, here's the original problem:

Rory is playing with an array consisting of integer elements indexed from to and a positive integer . Rory will perform operations. Each operation is either type 1 or type 2.

Type 1 operation is in the form . You should add to each element in .

Type 2 operation is in the form . You should output the sum .

Lelei is confident she can solve this problem, so she tells you that she doesn't need your help, as she can solve it faster than you. Seeing this as a challenge, you obviously want to show Lelei that she could have a better time penalty, if only she asked for your help. Can you prove her wrong?

#### Input Specification

The first line of input will contain three integers , , and .

The second line of input will contain elements, the original elements of array in the order .

The next lines of input will contain an operation, either in the form for an operation of type 1 or for an operation of type 2.

#### Constraints

For all subtasks:

for all valid .

##### Subtask 1 [15%]

##### Subtask 2 [15%]

##### Subtask 3 [15%]

##### Subtask 4 [15%]

##### Subtask 5 [40%]

#### Output Specification

For each operation of type 2, output the answer on a new line.

#### Sample Input

```
2 5 3
1 2 3 4 5
2 1 4
1 2 5 7
2 1 5
```

#### Sample Output

```
0
1
```

#### Explanation

For the first operation, , and .

For the second operation, the array is now .

For the third operation, and .

## Comments

How come the author doesn't mention M as prime ?

Because maybe thats something you can observe yourself?

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No comment, reread the problem statement.

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A link that will take you to the exact same web page?

A comment that will take you to the same comment? Mind = blown!