Sequence Generation and Iterative Modification

You are given two integers n and m. Your task is to first generate a sequence of n integers where:

• The first element is 1.
• Each subsequent element is twice the previous one, i.e. \( a_i = 2 \times a_{i-1} \) for \( i \ge 2 \).

Then, perform exactly m iterations. In each iteration, for every odd-positioned element (positions 1, 3, 5, ... in 1-based indexing), if there exists a next element, add the value of the next element to it.

For example:

• For \( n=5 \) and \( m=0 \), the sequence is: 1 2 4 8 16.
• For \( n=5 \) and \( m=1 \), the updated sequence is: 3 2 12 8 16 (first element becomes \(1+2=3\) and third element becomes \(4+8=12\)).
• For \( n=5 \) and \( m=2 \), the sequence becomes: 5 2 20 8 16.

Output the final sequence as space-separated integers.

inputFormat

The input consists of a single line containing two integers n and m, separated by a space.

\( 1 \leq n \leq 10^3 \) and \( m \geq 0 \).

outputFormat

Output the final sequence after performing the iterative modifications. The sequence should be printed as space-separated integers on one line.

## sample

5 0

1 2 4 8 16