A well-known sharper I*** invented a new way to swindle people. There are N thimbles on the table, and there is a small ball with the number under each of them. The balls are numbered with numbers from 1 to N from left to right. At one operation I*** changes the order of some subsequence of successive thimbles to the opposite. Your task is to find the order of numbers (from left to right) in sequence after all of his manipulations. The total number of manipulations is M.

Input

Output

Output the sequence of N numbers - the numbers of balls in the thimbles from left to right.

Sample

Input
5 2
1 3
4 5
Output
3 2 1 5 4

Input
5 2
1 4
2 5

Output
4 5 1 2 3

Note: A naive solution would result in TLE. Have fun!