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.Scanner;

public class Diverse_Permutation {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		StringBuilder sb = new StringBuilder();
		int n = sc.nextInt();
		int k = sc.nextInt();
		
		int i = 1;
		int j = n;
		int count = k - 1;
		int turn = 0;
		while(count >= 0)
		{
			if(turn == 0) {
			sb.append(i + " ");
			turn = 1;
			i++;
			}
			else
			{
				turn = 0;
				sb.append(j + " ");
				j--;
			}
			count--;
		}
		if(turn == 1)
		for (int l = i; l <= j; l++) {
			sb.append(l + " ");
		}
		else
			for (int l = i; l <= j; l++) {
				sb.append((n-l + 1) + " ");
			}
		System.out.println(sb);
	}
}
