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;
const int N = 1e5 + 5;
int a[N], l = 1, r, n, p = 0, cur = 1;
void preencher(int d) {
  if (d == 0) return;
  a[p] = cur;
  a[p + 1] = n - cur + 1;
  l++;
  r--;
  p += 2;
  cur++;
  d--;
  while (d) {
    a[p] = cur;
    l++;
    p++;
    d--;
    if (d == 0) return;
    a[p] = n - cur + 1;
    r--;
    p++;
    d--;
    cur++;
  }
}
int main() {
  int k;
  scanf("%d %d", &n, &k);
  r = n;
  preencher(k - 1);
  for (int i = p; i < (int)n; i++) {
    if (((k - 1) & 1) == 1)
      a[i] = r--;
    else
      a[i] = l++;
  }
  for (int i = 0; i < (int)n; i++) {
    printf("%d ", a[i]);
  }
  return 0;
}
