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 Div1_275_A {
	public static void main(String[] args) throws IOException{
		InputStreamReader isr = new InputStreamReader(new BufferedInputStream(System.in));
		BufferedReader br = new BufferedReader(isr);
		int n,k;
		StringTokenizer st = new StringTokenizer(br.readLine());
		n = Integer.parseInt(st.nextToken());
		k = Integer.parseInt(st.nextToken());
		StringBuilder sb = new StringBuilder("1");
		int j = 1, currNum = 1;
		boolean [] nums = new boolean[n+1];
		nums[1] = true;
		for(int d=k;d >= 1;d--) {
			sb.append(" ");
			currNum = currNum + j*d;
			sb.append(currNum);
			nums[currNum] = true;
			j *= -1;
		}
		for(int i = 1;i <= n;i++)
			if(!nums[i])
				sb.append(" "+i);
		System.out.println(sb);
	}
}
