Absolute Rotation

You are given an array of n integers. You need to transform this array m times according to the following rule:

• The new value of the ith element in the array is the absolute difference between the (i+1) th element and the i th element of the previous array.
• The last element of the array is updated as the absolute difference between the last and first elements of the previous array.

After applying this transformation m times, output the resulting array.

Input Format

The first line contains two integers ( n ) and ( m ) — the size of the array and the number of transformations.
The second line contains ( n ) space-separated integers representing the initial array.

Output Format

Print ( n ) space-separated integers — the array after performing the transformation ( m ) times.

Constraints

• 1 <= n*m <= 10^6
• 1 <= a[i] <= 10^9

Sample Input 0

5 3  
4 7 2 9 5  

Sample Output 0

0 1 0 1 0