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 CF482 {
	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		int n = s.nextInt();
		int k = s.nextInt();
		
		int[] A = new int[n];
		int i = 0;
		int u = n;
		int l = 1;
		boolean top = true;
		while (i < k-1) {
			if (top) {
				A[i++] = u--;
			} else {
				A[i++] = l++;
			}
			top = !top;
		}
		while (i < n) {
			if (top) { 
				A[i++] = u--;
			} else {
				A[i++] = l++;
			}
		}		
		
		for (int a : A) {
			System.out.print(a + " ");
		}
		s.close();
	}
}
