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;


public class Main {
    public static void main(String[] args) throws Exception{

        BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(System.in));
        String[]input = bufferedReader.readLine().split(" ");
       int n = Integer.parseInt(input[0]);
        int
                anInt = Integer.parseInt(input[1]);
       int[] arr = new int[n];
        for (int i=0; i< n; i++) {
            arr[i] = i+1;
        }
        int i1;
        if (anInt != 1) {
            i1 = 1;
            while (anInt>0) {
                if (i1%2 == 0) {
                    arr[i1] = arr[i1-1] - anInt;
                } else {
                    arr[i1] = arr[i1-1] + anInt;
                }
                anInt--;
                i1++;
            }
        }

        for (int i = 0; i < arr.length; i++) {
            System.out.println(arr[i] + " ");
        }
    }

}