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.Arrays;
import java.util.Scanner;

public class Test {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc = new Scanner(System.in);

		int n = sc.nextInt();
		int k = sc.nextInt();
		int a[] = new int[n+1];

		for (int i = 0, j = 1; i < n - 1; i += 2, j++) {
			a[i] = j;
			a[i + 1] = n - j + 1;
		}
		
		
		
		if(n % 2 != 0)
			a[n - 1] = n/2 + 1;
		
//		for(int i = 0;i < n;i++) {
//			if(i > 0)
//				System.out.print(" ");
//			System.out.print(a[i]);
//		}
//		System.out.println();
		a[n] = n/2 + 1;
		int l = Math.min(a[k], a[k+1]);
		int m = Math.max(a[k], a[k+1]);
//		System.out.println(a[k - 1]);
		if(a[k-1] - 1 != m)
			for(int i = l, id = k;i <= m;i++, id++) {
				a[id] = i;
			}
		else
			for(int i = m, id = k;i >= l;i--, id++) {
				a[id] = i;
			}
		
		for(int i = 0;i < n;i++) {
			if(i > 0)
				System.out.print(" ");
			System.out.print(a[i]);
		}

	}
}