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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

public class DiversePermutation {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer stk = new StringTokenizer(br.readLine());
		int n,k;
		n = Integer.parseInt(stk.nextToken());  
		k = Integer.parseInt(stk.nextToken());
		System.out.println(print(findPermutation(n,k)));
		
	}
	public static int[] findPermutation(int n,int k)
	{
		int[] ary = new int[n];
		for(int i=1;i<=n;i++){
			ary[i-1] = i;
		}
		int[] aryResult = new int[n];
		int count = n-1;
		//前段
		for(int j=1,i=0;j<=k;j+=2,i++){
			aryResult[j-1] = ary[i];
			aryResult[j] = ary[count--];
		}
		//后段
		if(k%2==0){
			for(int index=k;index<n;index++){
				aryResult[index] = ary[count--];
			}
		}else{
			for(int index=k;index<n;index++){
				aryResult[index] = aryResult[index-1]+1;
			}
		}
		return aryResult;
	}
	public static String print(int[] ary){
		StringBuffer sb = new StringBuffer("");
		for(int i=0;i<ary.length;i++){
			sb.append(ary[i]);
			sb.append(" ");
		}
		return sb.toString();
	}

}