Permutation p is an ordered set of integers p1, p2, ..., pn, consisting of n distinct positive integers not larger than n. We'll denote as n the length of permutation p1, p2, ..., pn.

Your task is to find such permutation p of length n, that the group of numbers |p1 - p2|, |p2 - p3|, ..., |pn - 1 - pn| has exactly k distinct elements.

Input

The single line of the input contains two space-separated positive integers n, k (1 ≤ k < n ≤ 105).

Output

Print n integers forming the permutation. If there are multiple answers, print any of them.

Examples

Input

3 2


Output

1 3 2


Input

3 1


Output

1 2 3


Input

5 2


Output

1 3 2 4 5

Note

By |x| we denote the absolute value of number x. 
   import java.util.Arrays;
   import java.util.*;
   import java.io.*;
   import java.lang.Math.*;


public class diversePermutation {
	

	public static void main(String[] args) {
  		Scanner infile = new Scanner(System.in);
         int n  = infile.nextInt(); //
         int k = infile.nextInt(); //1 - 64		
		  generatePerm(n,k); //1 <= k < n <= 1 x 10e5

	}

	public static void generatePerm(int n, int k)
	{
		int left = 1;
		int right = n;
		int count = k; 
		if(k == 1)
			for(int i = 0; i < n; i++)
				System.out.print((i + 1) + " ");
		else
		{
			for(int a = 1; a <= k; a++)
			{
				if(a % 2 == 1) 
				{
					System.out.print(left+ " ");
					left++;
				}
				else
				{
					System.out.print(right + " ");
					right--;
				}
			}	
			while(count < n)
			{
				if(k % 2 == 1)
				{
					System.out.print(left + " ");
					left++;
				}
				if(k % 2 == 0)
				{
					System.out.print(right + " ");
					right--;
				}
				count++;
			}
		}
	}
}