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.io.*;
import java.util.*;

public class CF483C {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(br.readLine());
		int n = Integer.parseInt(st.nextToken());
		int k = Integer.parseInt(st.nextToken());
		int[] aa = new int[n];
		if (k % 2 == 0) {
			for (int i = 1; i <= k / 2; i++) {
				aa[i + i - 1] = i;
				aa[i + i] = -i;
			}
			for (int i = k + 1, j = -k / 2 - 1; i < n; i++, j--)
				aa[i] = j;
		} else {
			for (int i = 1; i <= k / 2; i++) {
				aa[i + i - 1] = i;
				aa[i + i] = -i;
			}
			for (int i = k, j = k / 2 + 1; i < n; i++, j++)
				aa[i] = j;
		}
		int min = 0;
		for (int i = 1; i < n; i++)
			if (min > aa[i])
				min = aa[i];
		for (int i = 0; i < n; i++)
			aa[i] -= min - 1;
		StringBuilder sb = new StringBuilder();
		for (int i = 0; i < n; i++)
			sb.append(aa[i] + " ");
		System.out.println(sb);
	}
}
