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 Main {

	private int k, n;

	public Main(int tn, int tk) {
		n = tn;
		k = tk;
	}

	public void printMain() {
		boolean flag = true;
		int count = k - 1;
		int i = 1;
		while (count > 0) {
			if (count != k - 1) {
				--count;
				if (count <= 0) {
					flag = false;
					break;
				}
				System.out.print(" ");
			}

			System.out.print(i);
			System.out.print(" " + (n - i + 1));
			++i;
			--count;
		}
		int j = n - i + 1;
		if (count != k - 1 && i <= j)
			System.out.print(" ");
		if (flag) {
			while (i <= j) {
				System.out.print(j);
				--j;
				if (i <= j)
					System.out.print(" ");
			}
		} else {
			while (i <= j) {
				System.out.print(i);
				++i;
				if (i <= j)
					System.out.print(" ");
			}
		}
		System.out.println();
	}

	public static void main(String[] args) {
		Scanner input = new Scanner(System.in);
		while (input.hasNext()) {
			int tn = input.nextInt();
			int tk = input.nextInt();
			Main AC = new Main(tn, tk);
			AC.printMain();
		}
		input.close();
	}
}
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