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.HashSet;
import java.util.Scanner;
import java.util.Set;

public class C {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int k = in.nextInt();
		int last = 1;
		Set<Integer> w = new HashSet();
		System.out.print(last);
		w.add(1);
		int count = 1;
		for(int i = 1 ; i <= n ;){
			int sign = 1;
			for(int q = k ; q > 0 ; q--){
				if(i+q*sign<0||i+q*sign>n||w.contains(i+q*sign))continue;
				System.out.print(" " + (i+q*sign));
				w.add(i+q*sign);
				i += q*sign;
				sign*=-1;
				count++;
				if(count==n)return;
//				System.out.println("   " + i);
			}
		}
	}
}
