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.InputStreamReader;

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/**
 *
 * @author bavudaia
 */
public class Oct24_2 {
    public static int max(int a,int b)
    {
        return a>b?a:b;
    }
    public static void main(String[] args) throws Exception
    {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String S[] = br.readLine().split(" ");
        int N = Integer.parseInt(S[0]);
        int K = Integer.parseInt(S[1]);
        int start = 1,diff = K;
        int out = 0,val = 0;
        System.out.print(start);
        for(int i=1;i<=K;i++)
        {
            val = start+diff;
            System.out.print(" "+val);
            diff = (diff>0)?diff-1:diff+1;
            diff = -diff;
            start = val;
        }
        for(int i=K+2;i<=N;i++)
        {
            System.out.print(" "+i);
        }
        System.out.println("");
    }
}
