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 C {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int k = in.nextInt();

		int[] ar = new int[n];
		for (int i = 0; i < ar.length; i++) {
			ar[i] = i + 1;
		}
		int st = 0;
		int end = n - 1;
		int cnt = 0;
		// while (true) {
		// if (cnt % 2 == 0)
		// System.out.print(" " + ar[end--] + " ");
		// else
		// System.out.print(" " + ar[st++] + " ");
		//
		// k--;
		// if(k==0){
		// for (int i = st; i <= end; i++) {
		// System.out.print(ar[i]);
		// }
		// break;
		// }
		// cnt++;
		// }
		if (k == 1) {
			for (int i = 0; i < ar.length; i++) {
				System.out.print(ar[i] + " ");
			}
		} else {
			int start = 0;
			int m = n - 1;
			boolean ss = false;
			boolean ee = false;
			for (int i = 0; i < k; i++) {
				ss = false;
				ee = false;
				if (i % 2 == 0) {
					System.out.print(ar[start++]);
					ss = true;
				} else {
					System.out.print(ar[m--]);
					ee = true;
				}
				System.out.print(" ");

			}
			if (ss)
				for (int i = start; i <= m; i++) {
					System.out.print(ar[i]);
					if (i != m)
						System.out.print(" ");
				}
			else
				for (int i = m; i >= start; i--) {
					System.out.print(ar[i]);
					if (i != start)
						System.out.print(" ");
				}
		}
	}
}
