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.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;


public class A {

	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer tok = new StringTokenizer(br.readLine());
		int N, K;
		N = Integer.parseInt( tok.nextToken() );
		K = Integer.parseInt( tok.nextToken() );
		System.out.println( print(solve(N, K)) );
	}

	static String print(int[] res) {
		StringBuilder sb = new StringBuilder();
		sb.append(res[0]);
		for (int i = 1; i < res.length; i++) {
			sb.append(' ').append(res[i]);
		}
		return sb.toString();
	}

	static int[] solve(int n, int k) {
		int[] res = new int[n];
		int f = 1;
		int last = n;
		int idx = 0;
		boolean fromEnd = true;
		while (k > 0) {
			if (fromEnd) {
				res[idx++] = last--;				
			} else {
				res[idx++] = f++;				
			}
			fromEnd = !fromEnd;
			if (idx == 0) continue;
			--k;
		}
		if (fromEnd) {
			for (int i = idx; i < n; i++) {
				res[i] = f++;
			}
		} else {
			for (int i = idx; i < n; i++) {
				res[i] = last--;
			}
		}
		return res;
    }
	
}
