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.*;
import java.io.*;
import java.math.*;

public class C {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n,k;
		n = in.nextInt();
		k = in.nextInt();
		System.out.print("1 ");
		int L = 1;
		int[] kk = new int[k];
		int[] kkk = new int[k];
		for (int i = 0; i < k; i++){
			kk[i] = i;
			kkk[i] = k-i;
		}
		for (int i:kk){
    		int xx = kkk[i];
    		if (i%2==0){
        		System.out.print(L+xx);
        		System.out.print(" ");
        		L += xx;
        	}else{
        		System.out.print(L-xx);
        		System.out.print(" ");
        		L -= xx;
        	}
        }
		for (int i = k+2; i <= n; i++){
			System.out.print(i);
			System.out.print(" ");
		}
	}
}