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.*;
import java.util.*;


import static java.lang.Math.*;
import static java.util.Collections.*;
import static java.util.Arrays.*;




public class CodeforcesRound275Div2ProblemC {
	
	
	static class Problem {
		
		
		Scanner reader;
		PrintWriter writer;
		
		Problem() {
			
			
			reader = new Scanner(System.in);
			writer = new PrintWriter(System.out);
			
			
		}
		
		Problem(File inputFile, File outputFile) throws IOException {
			
			
			reader = new Scanner(inputFile);
			writer = new PrintWriter(outputFile);
			
			
		}
		
		void runSolution() {
			
			
			solution();
			writer.close();
			
			
		}
		
		void solution() {	
			
			
			int n = reader.nextInt(), k = reader.nextInt();
			--k;
			int[] p = new int[n + 1];
			if (k == 0) {
				for (int i = 0; i < n; i++)
					writer.print(i + 1 + " ");
				return;
			}
			if (k % 2 == 0) {
				k /= 2;
				//writer.println(k);
				int t = 1, added = 0, cur = n;
				for (int i = n; i > 0; i--) 
					if (t == -1 && added < k) {
						added++;
						p[i] = added;
						t = -t;
					} else {
						p[i] = cur;
						cur--;
						t = -t;
					}
				for (int i = 1; i <= n; i++)
					writer.print(p[i] + " ");
			} else {
				k--;
				k /= 2;
				int t = 1, added = 0, cur = n;
				for (int i = n; i > 0; i--) 
					if (t == -1 && added < k) {
						added++;
						p[i] = added;
						t = -t;
					} else {
						p[i] = cur;
						cur--;
						t = -t;
					}
				int x = p[1];
				p[1] = p[2];
				p[2] = x;
				for (int i = 1; i <= n; i++)
					writer.print(p[i] + " ");
			}
			
			
		}


	}
	
	public static void main(String args[]) throws IOException {
		
		
		Problem C = new Problem();
		//Problem C = new Problem(new File("input.txt"), new File("output.txt"));
		C.runSolution();
		
		
	}


}