Inaho is finally home! After being stuck in an \(N\)-dimensional for so long, he has started to comprehend the complexities of \(N\) dimensions and have thought of a problem. Unfortunately, he does not know of a solution as he is not yet a master of \(N\) dimensions, so he has asked you for help.

Given an \(N\)-dimensional array, and a type of operation:

Type \(1\) operation: print the normal array given the Binary Indexed Tree.

Type \(2\) operation: print the Binary Indexed Tree given the normal array.

#### Input Specification

The first line will contain two space-separated integers \(N\ (1 \le N \le 10)\), and \(T\ (1 \le T \le 2)\), the number of dimensions and the type of operation respectively.

The second line will contain \(L^N\ (L = \lfloor{\sqrt[N]{5 \times 10^6}}\rfloor{})\) space-separated integers \((-100 < a_i < 100)\), which are the values in the array. If \(T = 1\), this array is the Binary Indexed Tree, and if \(T = 2\), this array is the normal array.

\(a_i\) represents the value at position \(p_i\) where \((p_i = \displaystyle \sum_{n=1}^N (p_{i_n} \times L^{N-n}))\).

In other words, the second line will be a flattened \(N\)-dimensional grid.

#### Output Specification

The normal array, if the \(T = 1\), or the Binary Indexed Tree, if \(T = 2\).

The output should follow the same format as the second line of the input. That is, the \(i^{th}\) integer should represent the value at \(p_i\) where \((p_i = \displaystyle \sum_{n=1}^N (p_{i_n} \times L^{N-n}))\).

#### Subtasks

##### Subtask 1 [10%]

\(N = 1\)

##### Subtask 2 [20%]

\(T = 1\)

##### Subtask 3 [20%]

\(T = 2\)

##### Subtask 4 [50%]

No further constraints.

#### Sample Cases Note

For the sake of not having 10 million characters in the sample cases and for the sample cases to be useful, \(L = \lfloor{\sqrt[N]{20}}\rfloor{}\). **In the actual test cases**, however, \(L\) will follow the constraints as stated in the Input Specification (that is, \(L = \lfloor{\sqrt[N]{5 \times 10^6}}\rfloor{}\)).

#### Sample Input 1

```
1 1
1 2 1 4 1 2 1 8 1 2 1 4 1 2 1 16 1 2 1 4
```

#### Sample Output 1

`1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1`

#### Sample Input 2

```
2 2
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
```

#### Sample Output 2

`1 2 1 4 2 4 2 8 1 2 1 4 4 8 4 16`

#### Sample Input 3

```
4 1
1 9 3 2 4 7 5 8 2 9 1 8 4 9 2 10
```

#### Sample Output 3

`1 8 2 -9 3 -5 -1 9 1 -1 -3 9 -1 3 0 -6`

## Comments