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. 
// Why do we fall ? So we can learn to pick ourselves up.
import java.util.*;
public class solve {
    static int mod = 1000000007;
    static int mod1 = 998244353;
    public static void  main(String[] args){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt();
        int[] ch = new int[n];
        int[] ans = new int[n];
        for(int i=1; i<=n; i++) ch[i-1] = i;
        int ss=1,f=1,r=n-1;
        if(k == 1){
            for(int i: ch){
                System.out.print(i+" ");
            }
        }else {
            int req = k-1;
            ans[0] = 1;
            while(req>0){
                if(ss%2 == 0){
                    ans[ss] = ch[f];
                    f += 1;
                }else{
                    ans[ss] = ch[r];
                    r -= 1;
                }
                ss += 1;
                req -= 1;
            }
            if(ss%2 == 1){
                for(int i=f+1; i<=r+1; i++){
                    ans[ss] = i;
                    ss += 1;
                }
            }else {
                for(int i=r+1; i>=f+1; i--){
                    ans[ss] = i;
                    ss += 1;
                }
            }
            for(int i: ans){
                System.out.print(i+" ");
            }
        }
    }
}