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 CF275Cd2 {
	
	public static void main(String[] args) throws Exception {
		
		Scanner scan = new Scanner(System.in);
		
		int n = scan.nextInt();
		int k = scan.nextInt();
		int[] result = new int[n];
		int first = 1;
		int last = n;
		
		int i=0;
		if(k%2 == 0 && k != n-1){
			result[0] = last;
			result[1] = first;
			k--;
			first++;
			last--;
			i=2;
		}
		
		for(; i < n; i++){
			if(i%2 == 1 && k > 1){
				result[i] = last--;
				k -= 2;
			} else {
				result[i] = first++;
			}
		}
		
		boolean firstline = true;
		for(Integer elem : result){
			if(firstline){
				firstline = false;
			} else {
				System.out.print(" ");
			}
			System.out.print("" + elem);
		}
	}

}
