Fax McClad, Croneria's most courageous bounty hunter, often has weird dreams in his sleep. Sometimes, he dreams about his past experiences, and at other times, **he has nightmares about problem statements that have no relation to the actual problem.**

One night, Fax had a very, very bizarre dream about d:

d received an array of length () with elements numbered from , and he performed the sum operation on it.

The sum operation takes in an array and returns an array . Array has these two important properties:

- Array and array are equal in length.
- For all elements , the element satisfies
Unimpressed with the result, d fed the result back in to the sum operation repeatedly, performing the operation () times in total. At this point, d

Suddenly, Fax wakes up! Disturbed by the abstract dream, he asks you to help solve the problem so he can focus on his bounty hunting.

#### Constraints

**Subtask 1 [20%]**

Tasks satisfy the constraint .

**Subtask 2 [60%]**

Tasks satisfy the constraint .

**Subtask 3 [20%]**

No additional constraints.

#### Input Specification

The first line will contain , the number of elements in the array.

The next line will contain the elements , , each separated by a space.

The final line of input will contain , the number of times the sum operation is performed.

#### Output Specification

The array after performing sum operations on the given array.

Each element should be outputted mod and elements should be separated by a single space.

#### Sample Input

```
5
4 2 8 1 1
2
```

#### Sample Output

`4 10 24 39 55`

#### Explanation for Sample Output

After one sum operation, the array is changed to:

`4 6 14 15 16`

After the second sum operation, the array is changed to:

`4 10 24 39 55`

## Comments

So I submitted in pypy2 and got everything correct except for the last test case of the last batch is there any further optimizations i can implement?

same