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;

import java.io.IOException;

import java.util.Arrays;

import java.util.StringTokenizer;

 

public class Main {

    public static void main(String[] args) {

        MyScanner sc = new MyScanner();
int N = sc.nextInt();
int K = sc.nextInt();
int[] arr = new int[N];
int idx = 0;
for (int i = 0; i <= (K + 1) / 2; i++) {
if (idx >= N) break;
arr[idx++] = i + 1;
if (idx >= N) break;
arr[idx++] = K - i + 1;
}
for (int i = K + 1; i < N; i++) {
arr[i] = i + 1;
}

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

 

    public static class MyScanner {

        BufferedReader br;

        StringTokenizer st;

 

        public MyScanner() {

            br = new BufferedReader(new InputStreamReader(System.in));

        }

 

        int nextInt() {

            return Integer.parseInt(next());

        }

 

        long nextLong() {

            return Long.parseLong(next());

        }

 

        double nextDouble() {

            return Double.parseDouble(next());

        }

 

        String next() {

            while (st == null || !st.hasMoreElements()) {

                try {

                    st = new StringTokenizer(br.readLine());

                } catch (IOException e) {

                    e.printStackTrace();

                }

            }

            return st.nextToken();

        }

 

        String nextLine() {

            String str = "";

            try { str = br.readLine(); }

            catch (IOException e) { e.printStackTrace(); }

            return str;

        }

    }

}