## Inaho VII

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Points: 25 (partial)
Time limit: 5.0s
Memory limit: 256M

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Problem types

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 $$(p_i = \displaystyle \sum_{n=1}^N (p_{i_n} \times L^{N-n}))$$.

$$N = 1$$

$$T = 1$$

$$T = 2$$

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