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 sett(int n, int pos) { return n = n | (1 << pos); }
int reset(int n, int pos) { return n = n & ~(1 << pos); }
bool check(int n, int pos) { return (bool)(n & (1 << pos)); }
int a[100000 + 2];
int main() {
  ios_base ::sync_with_stdio(false);
  cin.tie(0);
  int k, cs = 0, tc, n;
  cin >> n >> k;
  for (int i = 1, j = 1; i <= n; i += 2) a[i] = j++;
  for (int i = 2, j = n; i <= n; i += 2) a[i] = j--;
  if (k & 1) {
    int i, lim = n - k;
    for (i = 1; i <= k; i++) cout << a[i] << " ";
    for (i = a[i - 1] + 1; lim; lim--, i++) cout << i << " ";
  } else {
    int i, lim = n - k;
    for (i = 1; i <= k; i++) cout << a[i] << " ";
    for (i = a[i - 1] - 1; lim; i--, lim--) cout << i << " ";
  }
  return 0;
}
