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.awt.image.RescaleOp;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;


public class CodeForce275C {
    
    public static void main(String[] args) throws IOException {

        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer token = new StringTokenizer(in.readLine());
        int n = Integer.parseInt(token.nextToken());
        int k = Integer.parseInt(token.nextToken());
        int count=0;
        int left=1, right=n;
        StringBuilder str = new StringBuilder();
        while(true){
            if(count<k-1) {
                str.append(left+" ");
                left++;
                count++;
            }
            else {
                break;
            }
            if(count<k-1) {
                str.append(right+" ");
                right--;
                count++;
            }
            else {
                break;
            }
        }
        if(k%2==1) {
            for(int i=left;i<=right;i++) {
                str.append(i+" ");
            }
        }
        else {
            for(int i=right;i>=left;i--) {
                str.append(i+" ");
            }
        }
        
        System.out.println(str.toString());
    }

}
