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. 
#include <bits/stdc++.h>
using namespace std;
int main() {
  int i, j, k, test, kase = 0;
  int n;
  scanf("%d %d", &n, &k);
  j = k + 1;
  bool yes = false;
  bool mark[100009];
  memset(mark, false, sizeof mark);
  int temp = 0, tot = 0;
  int lim = k / 2;
  if (k % 2 != 0) lim++;
  int x = k + 1;
  for (i = 1; i <= lim; i++) {
    if (kase) printf(" ");
    kase = 1;
    printf("%d %d", i, x);
    mark[i] = mark[x] = true;
    x--;
    yes = true;
  }
  for (i = 1; i <= n; i++) {
    if (!mark[i]) {
      if (yes) printf(" ");
      yes = true;
      printf("%d", i);
    }
  }
  printf("\n");
  return 0;
}
