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. 
// package Div2;

import java.util.ArrayList;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.List;
import java.util.Random;
import java.util.Scanner;
import java.util.Stack;

public class Sketch {
	public static void main(String[] args){
		Scanner input = new Scanner(System.in);
		int n = input.nextInt(); int k = input.nextInt();
		input.close();
		int[] result = new int[n];
		for(int i=0; i<n-k-1; i++){
			result[i] = i+1;
		}
		int cnt = n-k;
		for(int i=n-k-1; i<n; i+=2, cnt++){
			result[i] = cnt;
		}
		cnt = n;
		for(int i=n-k; i<n; i+=2, cnt--){
			result[i] = cnt;
		}
		for(int i=0; i<n; i++){
			System.out.print(result[i] + " ");
		}
	}
}