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() {
  long b[100010];
  long n, m, i, l, r, kol, id, d;
  cin >> n >> m;
  for (i = 0; i < n; i++) b[i] = 0;
  l = 1;
  r = n;
  kol = 0;
  while (2 > 1) {
    b[kol] = l;
    b[kol + 1] = r;
    kol = kol + 2;
    l++;
    r--;
    if (l > r) break;
  }
  for (i = 0; i < m; i++) cout << b[i] << " ";
  id = n - m;
  d = 0;
  sort(b + m, b + n);
  if (fabs(b[m - 1] - b[n - 1]) == 1) d = 1;
  if (fabs(b[m - 1] - b[m]) == 1) d = 2;
  if (d == 2)
    for (i = m; i <= n - 1; i++) cout << b[i] << " ";
  if (d == 1)
    for (i = n - 1; i >= m; i--) cout << b[i] << " ";
  return 0;
}
