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.lang.reflect.Array;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

public class B {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int k = in.nextInt();
		if (k == 1) {
			for (int i = 1; i <= n; i++) {
				System.out.print(i + " ");
			}
		} else {
			int max = k;
			System.out.print(1 + " ");
			int t = 1;
			for (int i = 1; i < n; i++) {
				if (k != 0) {
					if (i % 2 == 1) {
						System.out.print(t + k+" ");
						t += k;

					} else {
						System.out.print(t - k+" ");
						t -= k;
					}
					k--;
				}else{
					System.out.print(i+1+" ");
				}
			}
		}
	}
}